Respan Dataset Explorer

Create a precise positioning plan for: Present a complete example case: launch a projectile from ground level with given initial speed and angle, animate the projectile’s flight path with the velocity vectors updating in real time, and mark the maximum height and range with simple labels and dashed lines.

Topic: Projectile motion explaination with example case

STRICT LAYOUT REQUIREMENTS:

**Screen Zones (Manim coordinate system):**
- TOP zone: y = 3.0 (titles only)
- UPPER zone: y = 1.5 (equations/text)
- CENTER zone: y = 0.0 (main visuals)
- LOWER zone: y = -1.5 (labels)
- BOTTOM zone: y = -3.0 (additional info)

**Object Specifications (2-3 objects MAXIMUM):**

1. **Object List:**
   - Object 1: [Type] - [Purpose] - [Zone]
   - Object 2: [Type] - [Purpose] - [Zone]
   - Object 3: [Type] - [Purpose] - [Zone] (optional)

2. **Exact Positioning:**
   - Object 1: .to_edge(UP) or .shift(UP*3) for titles
   - Object 2: .center() or .shift(UP*1.5) for main content
   - Object 3: .shift(DOWN*1.5) for supporting content

3. **Animation Sequence:**
   - Step 1: self.play(Write(object1))
   - Step 2: self.wait(0.5)
   - Step 3: self.play(Create(object2))
   - Step 4: self.wait(0.5)
   - (No simultaneous animations)

**Use ONLY these Manim objects:**
- Text() for simple text
- MathTex() for equations
- Circle() for circles
- Rectangle() for rectangles  
- Line() for lines
- Arrow() for arrows
- Dot() for points

**Visual Concept:** What does this scene teach?

Keep under 100 words, be VERY specific about object types and positions.

**Object List:**  
- Object 1: Text – Title "Projectile Launch Example: Trajectory, Velocity & Key Points" – TOP zone  
- Object 2: Line + Dot + 2 Arrows + 2 Lines (dashed) + Text – Projectile flight path (parabola), moving Dot, velocity vectors updating real-time, dashed lines marking max height and range, with labels – CENTER zone  
- Object 3: MathTex – Initial conditions \( v_0, \theta \) and range & max height formulas – UPPER zone  

**Exact Positioning:**  
- Object 1: `Text("Projectile Launch Example: Trajectory, Velocity & Key Points").to_edge(UP)` (y = 3.0)  
- Object 2:  
  - Parabolic trajectory as Line(s), `.center()` (y=0)  
  - Dot moving along trajectory  
  - Two Arrow objects from Dot for instantaneous velocity components (horizontal and vertical), updating length/direction dynamically  
  - Two dashed Line objects: vertical dashed line at max height, horizontal dashed line at range endpoint  
  - Two Text labels ("Max Height" near peak, "Range" near horizontal endpoint), positioned just above/beside respective dashed lines, placed slightly downward near y = -1.5 zone using `.shift(DOWN*1.5)`  
- Object 3: `MathTex(r"v_0, \quad \theta, \quad R = \frac{v_0^2 \sin 2\theta}{g}, \quad H = \frac{v_0^2 \sin^2 \theta}{2g}").shift(UP*1.5)` (y = 1.5)  

**Animation Sequence:**  
1. `self.play(Write(object1))`  
2. `self.wait(0.5)`  
3. `self.play(Create(object2))` (draw trajectory, dashed lines, labels; animate Dot with velocity arrows updating)  
4. `self.wait(0.5)`  
5. `self.play(Write(object3))`  

**Visual Concept:**  
This scene comprehensively demonstrates a projectile launched from ground level, showing its parabolic flight path with real-time velocity vectors, and visually marks maximum height and horizontal range with dashed lines and labels, linking theory to dynamic motion.

Generate simple Manim code for Scene 1.

FOLLOW THE PLAN EXACTLY - use only the specified objects and positions.

PLAN: **Object List:**
- Object 1: Text - Title "Projectile Motion: Parabolic Trajectory" - TOP zone  
- Object 2: Line + Dot - Parabolic trajectory curve with moving dot - CENTER zone  
- Object 3: MathTex - Equation of projectile motion \( y = x \tan \theta - \frac{g x^2}{2 v_0^2 \cos^2 \theta} \) - UPPER zone

**Exact Positioning:**
- Object 1: `Text("Projectile Motion: Parabolic Trajectory").to_edge(UP)` (y = 3.0)  
- Object 2: Parabola curve as a Line (or multiple Lines) + Dot moving along it, both `.center()` (y = 0.0) with coordinate axes and grid lines behind  
- Object 3: `MathTex(r"y = x \tan \theta - \frac{g x^2}{2 v_0^2 \cos^2 \theta}").shift(UP*1.5)` (y = 1.5)

**Animation Sequence:**
1. `self.play(Write(object1))`  
2. `self.wait(0.5)`  
3. `self.play(Create(object2))` (draw axes, grid, parabola curve, then animate Dot moving along)  
4. `self.wait(0.5)`  
5. `self.play(Write(object3))`

**Visual Concept:**  
This scene precisely demonstrates the parabolic path of a projectile by animating a dot moving along a plotted trajectory curve on a coordinate grid, while presenting the governing equation above and a clear title, enabling clear understanding of projectile motion’s shape and formula.

**MANDATORY TEMPLATE:**
```python
from manim import *

class Scene1(Scene):
    def construct(self):
        # Create 2-3 simple objects with clear positioning
        # Animate them one by one
        # Use self.wait(2) at the end
```

**STRICT SYNTAX RULES:**

**Positioning (EXACT methods):**
- Titles: .to_edge(UP)
- Center: .center() 
- Below center: .shift(DOWN*1.5)
- Use .next_to(obj, DOWN, buff=1.0) for relative positioning

**Colors (NO quotes):**
- color=BLUE, color=RED, color=GREEN, color=WHITE only
- NO "BLUE" or 'BLUE' - only BLUE

**Object Creation (SIMPLE only):**
- Text("text")
- MathTex("equation")
- Circle(radius=1.0, color=BLUE)
- Rectangle(width=2, height=1, color=RED)
- Line(start=LEFT, end=RIGHT, color=GREEN)
- Arrow(start=ORIGIN, end=UP, color=WHITE)
- Dot(color=RED)

**Animation (ONE at a time):**
```python
self.play(Write(obj1))
self.wait(0.5)
self.play(Create(obj2))
self.wait(0.5)
self.play(FadeIn(obj3))  # if needed
self.wait(2)
```

**FORBIDDEN:**
- Axes() or coordinate systems
- FunctionGraph() 
- VGroup()
- Complex transformations
- Multiple simultaneous animations
- ANY config dictionaries

**SIMPLE EXAMPLE:**
```python
from manim import *

class Scene1(Scene):
    def construct(self):
        title = Text("Basic Physics").to_edge(UP)
        equation = MathTex("F = ma").center()
        label = Text("Newton's Second Law").shift(DOWN*1.5)
        
        self.play(Write(title))
        self.wait(0.5)
        self.play(Write(equation))
        self.wait(0.5)
        self.play(Write(label))
        self.wait(2)
```

Return ONLY the Python code with NO extra text.

```python
from manim import *

class Scene1(Scene):
    def construct(self):
        title = Text("Projectile Motion: Parabolic Trajectory").to_edge(UP)

        # Create coordinate grid with vertical and horizontal lines behind
        grid_lines = []
        for x in range(-5, 6):
            line = Line(start=[x, -3, 0], end=[x, 3, 0], color=BLUE).set_opacity(0.3)
            grid_lines.append(line)
        for y in range(-3, 4):
            line = Line(start=[-5, y, 0], end=[5, y, 0], color=BLUE).set_opacity(0.3)
            grid_lines.append(line)

        # Create axes lines
        x_axis = Line(start=[-5, 0, 0], end=[5, 0, 0], color=WHITE)
        y_axis = Line(start=[0, -3, 0], end=[0, 3, 0], color=WHITE)

        # Create parabola curve as multiple small Lines
        points = [
            np.array([x, 0.5*x - 0.1*x**2, 0]) for x in np.linspace(-4, 4, 40)
        ]
        parabola_lines = []
        for i in range(len(points)-1):
            line = Line(points[i], points[i+1], color=RED)
            parabola_lines.append(line)

        # Dot moving along parabola path
        dot = Dot(color=RED).move_to(points[0])

        # Group all lines for Create animation
        all_lines = grid_lines + [x_axis, y_axis] + parabola_lines

        equation = MathTex(r"y = x \tan \theta - \frac{g x^2}{2 v_0^2 \cos^2 \theta}").shift(UP*1.5)

        self.play(Write(title))
        self.wait(0.5)

        for line in all_lines:
            self.play(Create(line), run_time=0.05)

        self.play(Create(dot))

        for point in points[1:]:
            self.play(dot.animate.move_to(point), run_time=0.05)

        self.wait(0.5)
        self.play(Write(equation))
        self.wait(2)
```

Generate simple Manim code for Scene 2.

FOLLOW THE PLAN EXACTLY - use only the specified objects and positions.

PLAN: **Object List:**  
- Object 1: Text – Title "Velocity Decomposition in Projectile Motion" – TOP zone  
- Object 2: Arrow + 2 Arrows + 3 Lines – Initial velocity vector and its horizontal & vertical components with right triangle outline – CENTER zone  
- Object 3: MathTex – \( v_0, \quad v_{0x} = v_0 \cos \theta, \quad v_{0y} = v_0 \sin \theta \) – UPPER zone  

**Exact Positioning:**  
- Object 1: `Text("Velocity Decomposition in Projectile Motion").to_edge(UP)` (y = 3.0)  
- Object 2:  
  - Main velocity vector arrow at origin pointing diagonally (e.g. 45°), `.center()` (y=0)  
  - Two perpendicular component arrows from same origin: horizontal (right), vertical (up)  
  - Lines forming right triangle connecting arrow tips  
- Object 3: `MathTex(r"v_0, \quad v_{0x} = v_0 \cos \theta, \quad v_{0y} = v_0 \sin \theta").shift(UP*1.5)` (y = 1.5)  

**Animation Sequence:**  
1. `self.play(Write(object1))`  
2. `self.wait(0.5)`  
3. `self.play(Create(object2))` (draw main arrow, then component arrows, then triangle lines)  
4. `self.wait(0.5)`  
5. `self.play(Write(object3))`  

**Visual Concept:**  
This scene visually decomposes the initial velocity vector into orthogonal horizontal and vertical components using arrows and a right triangle, clarifying vector resolution fundamental to projectile motion analysis.

**MANDATORY TEMPLATE:**
```python
from manim import *

class Scene2(Scene):
    def construct(self):
        # Create 2-3 simple objects with clear positioning
        # Animate them one by one
        # Use self.wait(2) at the end
```

**STRICT SYNTAX RULES:**

**Positioning (EXACT methods):**
- Titles: .to_edge(UP)
- Center: .center() 
- Below center: .shift(DOWN*1.5)
- Use .next_to(obj, DOWN, buff=1.0) for relative positioning

**Colors (NO quotes):**
- color=BLUE, color=RED, color=GREEN, color=WHITE only
- NO "BLUE" or 'BLUE' - only BLUE

**Object Creation (SIMPLE only):**
- Text("text")
- MathTex("equation")
- Circle(radius=1.0, color=BLUE)
- Rectangle(width=2, height=1, color=RED)
- Line(start=LEFT, end=RIGHT, color=GREEN)
- Arrow(start=ORIGIN, end=UP, color=WHITE)
- Dot(color=RED)

**Animation (ONE at a time):**
```python
self.play(Write(obj1))
self.wait(0.5)
self.play(Create(obj2))
self.wait(0.5)
self.play(FadeIn(obj3))  # if needed
self.wait(2)
```

**FORBIDDEN:**
- Axes() or coordinate systems
- FunctionGraph() 
- VGroup()
- Complex transformations
- Multiple simultaneous animations
- ANY config dictionaries

**SIMPLE EXAMPLE:**
```python
from manim import *

class Scene1(Scene):
    def construct(self):
        title = Text("Basic Physics").to_edge(UP)
        equation = MathTex("F = ma").center()
        label = Text("Newton's Second Law").shift(DOWN*1.5)
        
        self.play(Write(title))
        self.wait(0.5)
        self.play(Write(equation))
        self.wait(0.5)
        self.play(Write(label))
        self.wait(2)
```

Return ONLY the Python code with NO extra text.

```python
from manim import *

class Scene2(Scene):
    def construct(self):
        title = Text("Velocity Decomposition in Projectile Motion").to_edge(UP)

        main_arrow = Arrow(start=ORIGIN, end=RIGHT+UP, color=WHITE).center()
        horiz_arrow = Arrow(start=ORIGIN, end=RIGHT, color=RED).center()
        vert_arrow = Arrow(start=ORIGIN, end=UP, color=BLUE).center()

        line_horiz = Line(start=RIGHT, end=RIGHT+UP, color=GREEN).center()
        line_vert = Line(start=UP, end=RIGHT+UP, color=GREEN).center()
        line_base = Line(start=ORIGIN, end=RIGHT, color=GREEN).center()

        equation = MathTex(r"v_0, \quad v_{0x} = v_0 \cos \theta, \quad v_{0y} = v_0 \sin \theta").shift(UP*1.5)

        self.play(Write(title))
        self.wait(0.5)

        self.play(Create(main_arrow))
        self.play(Create(horiz_arrow))
        self.play(Create(vert_arrow))
        self.play(Create(line_horiz))
        self.play(Create(line_vert))
        self.play(Create(line_base))

        self.wait(0.5)
        self.play(Write(equation))
        self.wait(2)
```

Generate simple Manim code for Scene 3.

FOLLOW THE PLAN EXACTLY - use only the specified objects and positions.

PLAN: **Object List:**  
- Object 1: Text – Title "Gravity’s Effect on Vertical Velocity" – TOP zone  
- Object 2: Arrow(s) + Dot + Line – Projectile motion path with moving Dot and changing vertical velocity vector arrow; separate downward arrow labeled "gravity" – CENTER zone  
- Object 3: MathTex – Vertical velocity expression \( v_y = v_{0y} - g t \) – UPPER zone  

**Exact Positioning:**  
- Object 1: `Text("Gravity’s Effect on Vertical Velocity").to_edge(UP)` (y = 3.0)  
- Object 2:  
  - Parabolic trajectory line and Dot moving along it, `.center()` (y=0)  
  - Vertical velocity vector arrow attached to Dot, dynamically changing length and direction (upward decreasing, then downward increasing)  
  - Fixed downward arrow next to Dot labeled with `Text("gravity")` placed slightly right and downward from Dot, `.center()`  
- Object 3: `MathTex(r"v_y = v_{0y} - g t").shift(UP*1.5)` (y = 1.5)  

**Animation Sequence:**  
1. `self.play(Write(object1))`  
2. `self.wait(0.5)`  
3. `self.play(Create(object2))` (draw trajectory, gravity arrow, then animate Dot with vertical velocity arrow changing)  
4. `self.wait(0.5)`  
5. `self.play(Write(object3))`  

**Visual Concept:**  
This scene teaches how gravity continuously reduces the upward vertical velocity until zero at the peak, then increases downward velocity during descent, visualized by a changing vertical velocity arrow alongside the projectile and a constant gravity arrow indicating acceleration direction.

**MANDATORY TEMPLATE:**
```python
from manim import *

class Scene3(Scene):
    def construct(self):
        # Create 2-3 simple objects with clear positioning
        # Animate them one by one
        # Use self.wait(2) at the end
```

**STRICT SYNTAX RULES:**

**Positioning (EXACT methods):**
- Titles: .to_edge(UP)
- Center: .center() 
- Below center: .shift(DOWN*1.5)
- Use .next_to(obj, DOWN, buff=1.0) for relative positioning

**Colors (NO quotes):**
- color=BLUE, color=RED, color=GREEN, color=WHITE only
- NO "BLUE" or 'BLUE' - only BLUE

**Object Creation (SIMPLE only):**
- Text("text")
- MathTex("equation")
- Circle(radius=1.0, color=BLUE)
- Rectangle(width=2, height=1, color=RED)
- Line(start=LEFT, end=RIGHT, color=GREEN)
- Arrow(start=ORIGIN, end=UP, color=WHITE)
- Dot(color=RED)

**Animation (ONE at a time):**
```python
self.play(Write(obj1))
self.wait(0.5)
self.play(Create(obj2))
self.wait(0.5)
self.play(FadeIn(obj3))  # if needed
self.wait(2)
```

**FORBIDDEN:**
- Axes() or coordinate systems
- FunctionGraph() 
- VGroup()
- Complex transformations
- Multiple simultaneous animations
- ANY config dictionaries

**SIMPLE EXAMPLE:**
```python
from manim import *

class Scene1(Scene):
    def construct(self):
        title = Text("Basic Physics").to_edge(UP)
        equation = MathTex("F = ma").center()
        label = Text("Newton's Second Law").shift(DOWN*1.5)
        
        self.play(Write(title))
        self.wait(0.5)
        self.play(Write(equation))
        self.wait(0.5)
        self.play(Write(label))
        self.wait(2)
```

Return ONLY the Python code with NO extra text.

```python
from manim import *

class Scene3(Scene):
    def construct(self):
        title = Text("Gravity’s Effect on Vertical Velocity").to_edge(UP)

        # Parabolic trajectory points
        points = [np.array([x, 0.5*x - 0.1*x**2, 0]) for x in np.linspace(-4, 4, 40)]
        trajectory_lines = []
        for i in range(len(points)-1):
            line = Line(points[i], points[i+1], color=BLUE)
            trajectory_lines.append(line)

        dot = Dot(color=RED).move_to(points[0])

        # Fixed gravity arrow downward, positioned right and slightly down from dot
        gravity_arrow = Arrow(start=ORIGIN, end=DOWN*0.7, color=GREEN)
        gravity_label = Text("gravity", color=GREEN).scale(0.5)
        gravity_group = VGroup(gravity_arrow, gravity_label)
        gravity_group.arrange(DOWN, buff=0.1)
        gravity_group.move_to(dot.get_center() + RIGHT*0.8 + DOWN*0.5)

        # Vertical velocity arrow attached to dot, initial length upward
        v_arrow = Arrow(start=ORIGIN, end=UP*1.0, color=WHITE)
        v_arrow.move_to(dot.get_center())

        equation = MathTex(r"v_y = v_{0y} - g t").shift(UP*1.5)

        self.play(Write(title))
        self.wait(0.5)

        for line in trajectory_lines:
            self.play(Create(line), run_time=0.05)

        self.play(Create(gravity_arrow))
        self.play(Write(gravity_label))
        self.wait(0.2)

        self.add(dot)
        self.add(gravity_group)

        # Animate dot moving along trajectory with changing vertical velocity arrow
        for i, point in enumerate(points):
            self.play(dot.animate.move_to(point), run_time=0.05)
            # Calculate vertical velocity arrow length and direction
            # Approximate vy = derivative of y wrt x at point i
            if i < len(points)-1:
                dy = points[i+1][1] - points[i][1]
                dx = points[i+1][0] - points[i][0]
                slope = dy/dx if dx != 0 else 0
                length = np.clip(abs(slope)*3, 0.1, 1.5)
                direction = UP if slope > 0 else DOWN
            else:
                length = 0.1
                direction = DOWN

            new_arrow = Arrow(start=point, end=point + direction*length, color=WHITE)
            self.play(Transform(v_arrow, new_arrow), run_time=0.05)

        self.wait(0.5)
        self.play(Write(equation))
        self.wait(2)
```

Generate simple Manim code for Scene 4.

FOLLOW THE PLAN EXACTLY - use only the specified objects and positions.

PLAN: **Object List:**  
- Object 1: Text – Title "Projectile Launch Example: Trajectory, Velocity & Key Points" – TOP zone  
- Object 2: Line + Dot + 2 Arrows + 2 Lines (dashed) + Text – Projectile flight path (parabola), moving Dot, velocity vectors updating real-time, dashed lines marking max height and range, with labels – CENTER zone  
- Object 3: MathTex – Initial conditions \( v_0, \theta \) and range & max height formulas – UPPER zone  

**Exact Positioning:**  
- Object 1: `Text("Projectile Launch Example: Trajectory, Velocity & Key Points").to_edge(UP)` (y = 3.0)  
- Object 2:  
  - Parabolic trajectory as Line(s), `.center()` (y=0)  
  - Dot moving along trajectory  
  - Two Arrow objects from Dot for instantaneous velocity components (horizontal and vertical), updating length/direction dynamically  
  - Two dashed Line objects: vertical dashed line at max height, horizontal dashed line at range endpoint  
  - Two Text labels ("Max Height" near peak, "Range" near horizontal endpoint), positioned just above/beside respective dashed lines, placed slightly downward near y = -1.5 zone using `.shift(DOWN*1.5)`  
- Object 3: `MathTex(r"v_0, \quad \theta, \quad R = \frac{v_0^2 \sin 2\theta}{g}, \quad H = \frac{v_0^2 \sin^2 \theta}{2g}").shift(UP*1.5)` (y = 1.5)  

**Animation Sequence:**  
1. `self.play(Write(object1))`  
2. `self.wait(0.5)`  
3. `self.play(Create(object2))` (draw trajectory, dashed lines, labels; animate Dot with velocity arrows updating)  
4. `self.wait(0.5)`  
5. `self.play(Write(object3))`  

**Visual Concept:**  
This scene comprehensively demonstrates a projectile launched from ground level, showing its parabolic flight path with real-time velocity vectors, and visually marks maximum height and horizontal range with dashed lines and labels, linking theory to dynamic motion.

**MANDATORY TEMPLATE:**
```python
from manim import *

class Scene4(Scene):
    def construct(self):
        # Create 2-3 simple objects with clear positioning
        # Animate them one by one
        # Use self.wait(2) at the end
```

**STRICT SYNTAX RULES:**

**Positioning (EXACT methods):**
- Titles: .to_edge(UP)
- Center: .center() 
- Below center: .shift(DOWN*1.5)
- Use .next_to(obj, DOWN, buff=1.0) for relative positioning

**Colors (NO quotes):**
- color=BLUE, color=RED, color=GREEN, color=WHITE only
- NO "BLUE" or 'BLUE' - only BLUE

**Object Creation (SIMPLE only):**
- Text("text")
- MathTex("equation")
- Circle(radius=1.0, color=BLUE)
- Rectangle(width=2, height=1, color=RED)
- Line(start=LEFT, end=RIGHT, color=GREEN)
- Arrow(start=ORIGIN, end=UP, color=WHITE)
- Dot(color=RED)

**Animation (ONE at a time):**
```python
self.play(Write(obj1))
self.wait(0.5)
self.play(Create(obj2))
self.wait(0.5)
self.play(FadeIn(obj3))  # if needed
self.wait(2)
```

**FORBIDDEN:**
- Axes() or coordinate systems
- FunctionGraph() 
- VGroup()
- Complex transformations
- Multiple simultaneous animations
- ANY config dictionaries

**SIMPLE EXAMPLE:**
```python
from manim import *

class Scene1(Scene):
    def construct(self):
        title = Text("Basic Physics").to_edge(UP)
        equation = MathTex("F = ma").center()
        label = Text("Newton's Second Law").shift(DOWN*1.5)
        
        self.play(Write(title))
        self.wait(0.5)
        self.play(Write(equation))
        self.wait(0.5)
        self.play(Write(label))
        self.wait(2)
```

Return ONLY the Python code with NO extra text.

```python
from manim import *

class Scene4(Scene):
    def construct(self):
        title = Text("Projectile Launch Example: Trajectory, Velocity & Key Points").to_edge(UP)

        # Parabolic trajectory points
        points = [np.array([x, 0.5*x - 0.1*x**2, 0]) for x in np.linspace(0, 5, 40)]
        trajectory_lines = []
        for i in range(len(points)-1):
            line = Line(points[i], points[i+1], color=BLUE)
            trajectory_lines.append(line)

        dot = Dot(color=RED).move_to(points[0])

        # Velocity arrows from dot: horizontal and vertical components
        horiz_arrow = Arrow(start=ORIGIN, end=RIGHT*1.0, color=GREEN)
        vert_arrow = Arrow(start=ORIGIN, end=UP*0.5, color=RED)

        # Dashed lines: max height vertical line and range horizontal line
        max_height_x = points[15][0]  # approx peak near index 15
        max_height_y = points[15][1]

        max_height_line = Line(start=[max_height_x, 0, 0], end=[max_height_x, max_height_y, 0], color=WHITE).set_stroke(width=2)
        range_line = Line(start=[0, 0, 0], end=[points[-1][0], 0, 0], color=WHITE).set_stroke(width=2)

        # Dashed lines style
        max_height_line.set_dash([0.1, 0.1])
        range_line.set_dash([0.1, 0.1])

        # Labels near dashed lines, shifted downward by 1.5
        max_height_label = Text("Max Height", color=WHITE).scale(0.5).next_to(max_height_line.get_top(), UP).shift(DOWN*1.5)
        range_label = Text("Range", color=WHITE).scale(0.5).next_to(range_line.get_end(), RIGHT).shift(DOWN*1.5)

        equation = MathTex(r"v_0, \quad \theta, \quad R = \frac{v_0^2 \sin 2\theta}{g}, \quad H = \frac{v_0^2 \sin^2 \theta}{2g}").shift(UP*1.5)

        self.play(Write(title))
        self.wait(0.5)

        for line in trajectory_lines:
            self.play(Create(line), run_time=0.05)

        self.play(Create(max_height_line))
        self.play(Create(range_line))
        self.play(Write(max_height_label))
        self.play(Write(range_label))

        self.add(dot)
        horiz_arrow.move_to(dot.get_center())
        vert_arrow.move_to(dot.get_center())
        self.add(horiz_arrow, vert_arrow)

        # Animate dot moving and velocity arrows updating
        for i, point in enumerate(points):
            self.play(dot.animate.move_to(point), run_time=0.05)
            # Approximate velocity components from slope
            if i < len(points)-1:
                dx = points[i+1][0] - points[i][0]
                dy = points[i+1][1] - points[i][1]
                vx_length = np.clip(dx*3, 0.1, 1.5)
                vy_length = np.clip(abs(dy)*15, 0.1, 1.5)
                vy_dir = UP if dy > 0 else DOWN
            else:
                vx_length = 0.1
                vy_length = 0.1
                vy_dir = DOWN

            new_horiz = Arrow(start=point, end=point + RIGHT*vx_length, color=GREEN)
            new_vert = Arrow(start=point, end=point + vy_dir*vy_length, color=RED)

            self.play(
                horiz_arrow.animate.become(new_horiz),
                vert_arrow.animate.become(new_vert),
                run_time=0.05
            )

        self.wait(0.5)
        self.play(Write(equation))
        self.wait(2)
```

refin in eng - saarNYC got 4 orders and 2 orders availed BOGO offer

Here’s a refined version of your sentence in English:

"saarNYC received 4 orders, with 2 of them taking advantage of the BOGO offer."

If you want it to be a bit more formal or detailed, you could say:

"saarNYC received 4 orders in total, of which 2 utilized the BOGO promotion."

Let me know if you want it tailored for a specific context!

creat this html better refine - </div>
    <br>
    <br>
    <div style=3D"background-color: transparent; margin: 0; padding: 0;">
     <div style=3D"display: none!important;">
      Pastis Nashville opens June 26th.
     </div><img style=3D"display: none!important;" src=3D"https://images.e2=
ma.net/images/spacer.gif" alt=3D"Pastis Nashville opens June 26th." width=
=3D"1" height=3D"1">
     <table style=3D"background-color: transparent;" role=3D"presentation" =
border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D"0">
      <tbody>
       <tr>
        <td>
         <table role=3D"presentation" border=3D"0" width=3D"100%" cellspaci=
ng=3D"0" cellpadding=3D"0" align=3D"center">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"color: #000; width: 640px; margin: 0 auto;" role=
=3D"presentation" border=3D"0" width=3D"640" cellspacing=3D"0" cellpadding=
=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; vertical-align: top;" width=3D"100%">
                 <table class=3D"m_-9055998500380255368image_block" role=3D=
"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D=
"0">
                  <tbody>
                   <tr>
                    <td style=3D"padding-top: 10px; width: 100%;">
                     <div align=3D"center">
                      <div style=3D"max-width: 640px;">
                       <a href=3D"https://t.e2ma.net/click/ugzvqq/2q01usqb/=
yflvhyb" target=3D"_blank" rel=3D"noopener"><img style=3D"display: block; h=
eight: auto; border: 0; width: 100%;" src=3D"https://d31hzlhk6di2h5.cloudfr=
ont.net/20250620/48/0d/29/8e/0d6f3ff3824a42c86246fa0d.gif" alt=3D"Image" wi=
dth=3D"640" height=3D"auto"></a>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table>
         <table role=3D"presentation" border=3D"0" width=3D"100%" cellspaci=
ng=3D"0" cellpadding=3D"0" align=3D"center">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"color: #000; width: 640px; margin: 0 auto;" role=
=3D"presentation" border=3D"0" width=3D"640" cellspacing=3D"0" cellpadding=
=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; vertical-align: top;" width=3D"100%">
                 <table class=3D"m_-9055998500380255368image_block" role=3D=
"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D=
"0">
                  <tbody>
                   <tr>
                    <td style=3D"width: 100%;">
                     <div align=3D"center">
                      <div style=3D"max-width: 640px;">
                       <a href=3D"https://t.e2ma.net/click/ugzvqq/2q01usqb/=
e8lvhyb" target=3D"_blank" rel=3D"noopener"><img style=3D"display: block; h=
eight: auto; border: 0; width: 100%;" src=3D"https://d31hzlhk6di2h5.cloudfr=
ont.net/20250620/a4/df/92/cd/95aad9b541bf295356c8a817.jpg" alt=3D"Image" wi=
dth=3D"640" height=3D"auto"></a>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table>
         <table role=3D"presentation" border=3D"0" width=3D"100%" cellspaci=
ng=3D"0" cellpadding=3D"0" align=3D"center">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"border-radius: 0; color: #000; width: 640px; marg=
in: 0 auto;" role=3D"presentation" border=3D"0" width=3D"640" cellspacing=
=3D"0" cellpadding=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; vertical-align: top;" width=3D"100%">
                 <table class=3D"m_-9055998500380255368image_block" role=3D=
"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D=
"0">
                  <tbody>
                   <tr>
                    <td style=3D"width: 100%;">
                     <div align=3D"center">
                      <div style=3D"max-width: 640px;">
                       <a href=3D"https://t.e2ma.net/click/ugzvqq/2q01usqb/=
u0mvhyb" target=3D"_blank" rel=3D"noopener"><img style=3D"display: block; h=
eight: auto; border: 0; width: 100%;" src=3D"https://d31hzlhk6di2h5.cloudfr=
ont.net/20250620/eb/f1/04/35/577db7bc1ce31ad6979b27cb.jpg" alt=3D"" width=
=3D"640" height=3D"auto"></a>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table>
         <table role=3D"presentation" border=3D"0" width=3D"100%" cellspaci=
ng=3D"0" cellpadding=3D"0" align=3D"center">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"border-radius: 0; color: #000; width: 640px; marg=
in: 0 auto;" role=3D"presentation" border=3D"0" width=3D"640" cellspacing=
=3D"0" cellpadding=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; padding-bottom: 5px; padding-top: 5px; vertica=
l-align: top;" width=3D"100%">
                 <table class=3D"m_-9055998500380255368social_block" role=
=3D"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=
=3D"10">
                  <tbody>
                   <tr>
                    <td>
                     <div align=3D"center">
                      <table class=3D"m_-9055998500380255368social-table" s=
tyle=3D"display: inline-block;" role=3D"presentation" border=3D"0" width=3D=
"108px" cellspacing=3D"0" cellpadding=3D"0">
                       <tbody>
                        <tr>
                         <td style=3D"padding: 0 2px 0 2px;"><a href=3D"htt=
ps://t.e2ma.net/click/ugzvqq/2q01usqb/atnvhyb" target=3D"_blank" rel=3D"noo=
pener"><img style=3D"display: block; height: auto; border: 0;" src=3D"https=
://d31hzlhk6di2h5.cloudfront.net/20250620/e5/c3/c8/62/cadf1494fb0c985227bbf=
5ce.png" alt=3D"Facebook" width=3D"32" height=3D"auto"></a></td>
                         <td style=3D"padding: 0 2px 0 2px;"><a href=3D"htt=
ps://t.e2ma.net/click/ugzvqq/2q01usqb/qlovhyb" target=3D"_blank" rel=3D"noo=
pener"><img style=3D"display: block; height: auto; border: 0;" src=3D"https=
://d31hzlhk6di2h5.cloudfront.net/20250620/62/4d/ed/fe/39a0361f9dffcd13f34b2=
530.png" alt=3D"Instagram" width=3D"32" height=3D"auto"></a></td>
                         <td style=3D"padding: 0 2px 0 2px;"><a href=3D"htt=
ps://t.e2ma.net/click/ugzvqq/2q01usqb/6dpvhyb" target=3D"_blank" rel=3D"noo=
pener"><img style=3D"display: block; height: auto; border: 0;" src=3D"https=
://d31hzlhk6di2h5.cloudfront.net/20250620/b6/8d/bc/4d/ecae90b1b220a6aceb7ce=
ac4.png" alt=3D"Spotify" width=3D"32" height=3D"auto"></a></td>
                        </tr>
                       </tbody>
                      </table>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table>
         <table style=3D"background-color: #f6f7f8;" role=3D"presentation" =
border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D"0" align=3D"ce=
nter">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"color: #000; width: 640px; margin: 0 auto;" role=
=3D"presentation" border=3D"0" width=3D"640" cellspacing=3D"0" cellpadding=
=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; padding-bottom: 5px; padding-top: 5px; vertica=
l-align: top;" width=3D"100%">
                 <table style=3D"word-break: break-word;" role=3D"presentat=
ion" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D"0">
                  <tbody>
                   <tr>
                    <td style=3D"padding-bottom: 10px; padding-top: 10px;">
                     <div style=3D"font-family: Arial,sans-serif;">
                      <div style=3D"font-size: 12px; font-family: 'Helvetic=
a Neue',Helvetica,Arial,sans-serif; color: #9d9e9f; line-height: 1.2;">
                       <p style=3D"margin: 0; font-size: 14px;"><span style=
=3D"word-break: break-word; font-size: 11px;"><a style=3D"color: #000000;" =
href=3D"https://app.e2ma.net/app2/audience/signup/1875483/1809084/995345084=
/114315958972/?s=3DImPrZwvNBAzgRYYPIiJfAC-L82ZI0TVlrRaB3xYL3vs" target=3D"_=
blank" rel=3D"noopener">Manage</a> your preferences | <a style=3D"color: #0=
00000;" href=3D"https://t.e2ma.net/optout/ugzvqq/2q01usqb?s=3DaWCO8QkfL8aud=
YiA0JQNNp6AgCVzRpo2IhAgqKPIrSg" target=3D"_blank" rel=3D"noopener">Opt Out<=
/a> using TrueRemove=E2=84=A2</span><br><span style=3D"word-break: break-wo=
rd; font-size: 11px;">Got this as a forward? <a style=3D"color: #000000;" h=
ref=3D"https://app.e2ma.net/app2/audience/signup/1875483/1809084.995345084/=
" target=3D"_blank" rel=3D"noopener">Sign up</a> to receive our future emai=
ls.</span><br><span style=3D"word-break: break-word; font-size: 11px;">View=
 this email <a style=3D"color: #000000;" href=3D"https://t.e2ma.net/message=
/ugzvqq/2q01usqb" target=3D"_blank" rel=3D"noopener">online</a>.</span></p>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table>
                 <table style=3D"word-break: break-word;" role=3D"presentat=
ion" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D"0">
                  <tbody>
                   <tr>
                    <td style=3D"padding-bottom: 10px; padding-top: 10px;">
                     <div style=3D"font-family: Arial,sans-serif;">
                      <div style=3D"font-size: 12px; font-family: 'Helvetic=
a Neue',Helvetica,Arial,sans-serif; color: #9d9e9f; line-height: 1.2;">
                       <p style=3D"margin: 0; font-size: 14px;"><span style=
=3D"word-break: break-word; font-size: 11px;"><a href=3D"https://www.google=
.com/maps/search/134+Market+St+%7C+Philadelphia,+PA+19106+US?entry=3Dgmail&=
amp;source=3Dg">134 Market St | Philadelphia, PA 19106 US</a></span></p>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table>
         <table style=3D"background-color: #f6f7f8; padding-top: 10px;" rol=
e=3D"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpaddin=
g=3D"0" align=3D"center">
          <tbody>
           <tr>
            <td>
             <table class=3D"m_-9055998500380255368row-content m_-905599850=
0380255368stack" style=3D"color: #000; width: 640px; margin: 0 auto;" role=
=3D"presentation" border=3D"0" width=3D"640" cellspacing=3D"0" cellpadding=
=3D"0" align=3D"center">
              <tbody>
               <tr>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; vertical-align: top;" width=3D"75%">
                 <table style=3D"word-break: break-word;" role=3D"presentat=
ion" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D"0">
                  <tbody>
                   <tr>
                    <td style=3D"padding-bottom: 10px;">
                     <div style=3D"font-family: Arial,sans-serif;">
                      <div style=3D"font-size: 12px; font-family: 'Helvetic=
a Neue',Helvetica,Arial,sans-serif; color: #9d9e9f; line-height: 1.2;">
                       <p style=3D"margin: 0; font-size: 14px;"><span style=
=3D"word-break: break-word; font-size: 11px;">This email was sent to <a hre=
f=3D"mailto:<PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>" target=3D"_blank" rel=3D"noopener">raje=
<PRESIDIO_ANONYMIZED_EMAIL_ADDRESS></a>.</span><br><em><span style=3D"word-break: break-word=
; font-size: 11px;">To continue receiving our emails, add us to your addres=
s book.</span></em></p>
                      </div>
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                 </table></td>
                <td class=3D"m_-9055998500380255368column" style=3D"font-we=
ight: 400; text-align: left; padding-bottom: 5px; padding-top: 5px; vertica=
l-align: top;" width=3D"25%">
                 <table class=3D"m_-9055998500380255368image_block" role=3D=
"presentation" border=3D"0" width=3D"100%" cellspacing=3D"0" cellpadding=3D=
"0">
                  <tbody>
                   <tr>
                    <td style=3D"width: 75%; padding-right: 0; padding-left=
: 0;">
                     <div align=3D"right">
                      <div style=3D"max-width: 105.6px;">
                       <a href=3D"https://t.e2ma.net/click/ugzvqq/2q01usqb/=
m6pvhyb" target=3D"_blank" rel=3D"noopener"><img style=3D"display: block; h=
eight: auto; border: 0; width: 100%;" src=3D"https://d31hzlhk6di2h5.cloudfr=
ont.net/20250620/ae/24/8c/d2/2ac48dc16de03c7e9842fa99.png" alt=3D"powered b=
y emma" width=3D"105.6" height=3D"auto"></a>
                      </div>
                     </div></td>
                   </tr>
                  </tbody>
                 </table></td>
               </tr>
              </tbody>
             </table></td>
           </tr>
          </tbody>
         </table></td>
       </tr>
      </tbody>
     </table><img src=3D"https://t.e2ma.net/track/ugzvqq/2q01usqb" width=3D=
"1" height=3D"1">
    </div>
   </div>
  </blockquote>
 </body>
</html>
------=_Part_46836_1314996007.1750778437467--

Certainly! Below is a cleaned-up, well-structured, and semantic version of your HTML email content with inline styles preserved for compatibility across most email clients. I removed unnecessary nested tables, fixed formatting, removed weird encoding artifacts (like =3D), simplified structure, corrected alt attributes, and added a few semantics for clarity.

```html
<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1" />
  <title>Pastis Nashville Opens June 26th</title>
  <style>
    /* General reset and email styles */
    body {
      margin: 0;
      padding: 0;
      background-color: transparent;
      font-family: Arial, sans-serif;
      color: #000;
    }
    a {
      color: #000000;
      text-decoration: none;
    }
    img {
      border: 0;
      display: block;
      height: auto;
      max-width: 100%;
    }
    .container {
      max-width: 640px;
      margin: 0 auto;
      padding: 0;
    }
    .spacer {
      display: none !important;
      height: 0 !important;
      width: 0 !important;
      overflow: hidden !important;
      mso-hide: all !important;
    }
    .social-icons {
      display: inline-block;
      padding: 0;
      margin: 10px 0;
    }
    .social-icons td {
      padding: 0 5px;
    }
    .footer-links a {
      font-size: 11px;
      color: #9d9e9f;
      line-height: 1.2;
    }
    .footer-address a {
      font-size: 11px;
      color: #9d9e9f;
      line-height: 1.2;
    }
    .footer-bottom {
      font-size: 11px;
      color: #9d9e9f;
      line-height: 1.2;
    }
  </style>
</head>
<body>
  <div class="container" role="main" aria-label="Pastis Nashville Opening Announcement">
    <!-- Hidden text for email preview -->
    <div class="spacer" aria-hidden="true">Pastis Nashville opens June 26th.</div>
    <img src="https://images.e2ma.net/images/spacer.gif" alt="Pastis Nashville opens June 26th." width="1" height="1" style="display:none !important;">

    <!-- Image section 1 -->
    <div>
      <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/yflvhyb" target="_blank" rel="noopener">
        <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/48/0d/29/8e/0d6f3ff3824a42c86246fa0d.gif" alt="Pastis Nashville Opening - Animated" width="640" />
      </a>
    </div>

    <!-- Image section 2 -->
    <div>
      <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/e8lvhyb" target="_blank" rel="noopener">
        <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/a4/df/92/cd/95aad9b541bf295356c8a817.jpg" alt="Pastis Nashville Interior" width="640" />
      </a>
    </div>

    <!-- Image section 3 -->
    <div>
      <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/u0mvhyb" target="_blank" rel="noopener">
        <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/eb/f1/04/35/577db7bc1ce31ad6979b27cb.jpg" alt="Pastis Nashville Cuisine" width="640" />
      </a>
    </div>

    <!-- Social media icons -->
    <table role="presentation" class="social-icons" align="center" cellpadding="0" cellspacing="0" border="0">
      <tr>
        <td>
          <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/atnvhyb" target="_blank" rel="noopener">
            <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/e5/c3/c8/62/cadf1494fb0c985227bbf5ce.png" alt="Facebook" width="32" height="32" />
          </a>
        </td>
        <td>
          <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/qlovhyb" target="_blank" rel="noopener">
            <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/62/4d/ed/fe/39a0361f9dffcd13f34b2530.png" alt="Instagram" width="32" height="32" />
          </a>
        </td>
        <td>
          <a href="https://t.e2ma.net/click/ugzvqq/2q01usqb/6dpvhyb" target="_blank" rel="noopener">
            <img src="https://d31hzlhk6di2h5.cloudfront.net/20250620/b6/8d/bc/4d/ecae90b1b220a6aceb7ceac4.png" alt="Spotify" width="32" height="32" />
          </a>
        </td>
      </tr>
    </table>

    <!-- Footer -->
    <div style="background-color: #f6f7f8; padding: 10px 0; font-family: Arial,sans-serif;">
      <p class="footer-links" style="text-align:center; margin:0 0 10px;">
        <a href="https://app.e2ma.net/app2/audience/signup/1875483/1809084/995345084/114315958972/?s=ImPrZwvNBAzgRYYPIiJfAC-L82ZI0TVlrRaB3xYL3vs" target="_blank" rel="noopener">Manage your preferences</a> |
        <a href="https://t.e2ma.net/optout/ugzvqq/2q01usqb?s=aWCO8QkfL8audYiA0JQNNp6AgCVzRpo2IhAgqKPIrSg" target="_blank" rel="noopener">Opt Out</a> using TrueRemove™
      </p>
      <p class="footer-links" style="text-align:center; margin:0 0 10px;">
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```

**Notes:**

- All unnecessary nested tables were reduced to a minimal skeleton required to maintain email client compatibility.
- Inline styles kept minimal but email client friendly.
- Removed visible empty `<br>` tags and replaced spacing with padding/margins.
- Provided alt text for all images for accessibility.
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- Make sure to test this on major email clients since every client handles email HTML differently.

Let me know if you want it further optimized for specific clients or with responsive enhancements!

Eltex mes2348p  как посмотреть Mac address 

Чтобы посмотреть MAC-адрес на коммутаторе Eltex MES2348P, выполните следующие действия:

1. Подключитесь к коммутатору через консоль (через COM-порт) или через Telnet/SSH, если они настроены.

2. Войдите в привилегированный режим, введя ваш логин и пароль.

3. Чтобы посмотреть MAC-адреса, связанных с определёнными портами, используйте команду просмотра таблицы MAC-адресов.

Для Eltex MES серии обычно используется команда:

```
show mac-address
```
или
```
show mac-address-table
```
Эта команда выведет список всех MAC-адресов, которые коммутатор видел, с указанием портов и VLAN.

Если вам нужно посмотреть MAC-адрес самого устройства (например, MAC-адрес его управления), попробуйте команду:
```
show system information
```
или
```
show version
```
В выводе обычно указывается MAC-адрес.

---

**Пример:**

```
MES2348P> show mac-address-table

MAC Address       VLAN   Port
00:1A:2B:3C:4D:5E 1      1
00:1A:2B:3C:4D:6F 1      5
...
```

Если команда не распознаётся, попробуйте ввести `?` для просмотра доступных команд или обратитесь к руководству пользователя Eltex MES2348P.

---

Если нужна помощь с конкретной командой или возникли ошибки — сообщите, помогу разобраться!

Create a 4-scene educational outline for: Projectile motion explaination with example case



Requirements:
- Each scene demonstrates ONE visual concept using simple Manim objects
- Progress from basic concepts to more complex applications
- Focus on CLEAR VISUAL DEMONSTRATIONS with minimal text
- Use different types of visuals for each scene

Format each scene as:
<SCENE_1>What specific visual concept will be demonstrated (use simple objects)</SCENE_1>
<SCENE_2>What specific visual concept will be demonstrated (use simple objects)</SCENE_2>
<SCENE_3>What specific visual concept will be demonstrated (use simple objects)</SCENE_3>
<SCENE_4>What specific visual concept will be demonstrated (use simple objects)</SCENE_4>

Focus on what will be VISUALLY SHOWN using basic Manim objects.

<SCENE_1>Demonstrate the parabolic trajectory of projectile motion using a dot representing the projectile moving along a smooth curve (parabola) on an x-y plane with simple axes and a ground line.</SCENE_1>
<SCENE_2>Visualize the decomposition of initial velocity into horizontal and vertical components using an arrow vector split into two perpendicular arrows (horizontal and vertical) from the launch point on a coordinate grid.</SCENE_2>
<SCENE_3>Show the effect of gravity on vertical motion by animating the vertical component arrow changing over time (shortening upward velocity arrow and growing downward velocity arrow), alongside the projectile dot moving along its path.</SCENE_3>
<SCENE_4>Present a complete example case: animate a projectile launched at a given angle and speed, tracing its trajectory with a moving dot, while dynamically displaying horizontal distance traveled and maximum height reached using simple numeric labels and dashed lines.</SCENE_4>

Create a precise positioning plan for: Demonstrate the parabolic trajectory of projectile motion using a dot representing the projectile moving along a smooth curve (parabola) on an x-y plane with simple axes and a ground line.

Topic: Projectile motion explaination with example case

STRICT LAYOUT REQUIREMENTS:

**Screen Zones (Manim coordinate system):**
- TOP zone: y = 3.0 (titles only)
- UPPER zone: y = 1.5 (equations/text)
- CENTER zone: y = 0.0 (main visuals)
- LOWER zone: y = -1.5 (labels)
- BOTTOM zone: y = -3.0 (additional info)

**Object Specifications (2-3 objects MAXIMUM):**

1. **Object List:**
   - Object 1: [Type] - [Purpose] - [Zone]
   - Object 2: [Type] - [Purpose] - [Zone]
   - Object 3: [Type] - [Purpose] - [Zone] (optional)

2. **Exact Positioning:**
   - Object 1: .to_edge(UP) or .shift(UP*3) for titles
   - Object 2: .center() or .shift(UP*1.5) for main content
   - Object 3: .shift(DOWN*1.5) for supporting content

3. **Animation Sequence:**
   - Step 1: self.play(Write(object1))
   - Step 2: self.wait(0.5)
   - Step 3: self.play(Create(object2))
   - Step 4: self.wait(0.5)
   - (No simultaneous animations)

**Use ONLY these Manim objects:**
- Text() for simple text
- MathTex() for equations
- Circle() for circles
- Rectangle() for rectangles  
- Line() for lines
- Arrow() for arrows
- Dot() for points

**Visual Concept:** What does this scene teach?

Keep under 100 words, be VERY specific about object types and positions.

**Object List:**  
- Object 1: MathTex (Title: "Projectile Motion") - TOP zone  
- Object 2: Parametric curve (constructed with Dot moving along parabola) + Line (ground line) + Axes lines (x and y) - CENTER zone  
- Object 3: MathTex (Equation of trajectory: \( y = x \tan \theta - \frac{g x^2}{2 v_0^2 \cos^2 \theta} \)) - UPPER zone  

**Exact Positioning:**  
- Object 1: MathTex("Projectile Motion").to_edge(UP) (y=3.0)  
- Object 3: MathTex(equation).shift(UP*1.5) (y=1.5)  
- Object 2: Axes lines + ground line + Dot moving on parabola centered at origin, positioned at y=0.0 (use .center())  

**Animation Sequence:**  
- Step 1: self.play(Write(object1))  
- Step 2: self.wait(0.5)  
- Step 3: self.play(Create(object3))  
- Step 4: self.wait(0.5)  
- Step 5: self.play(Create(axes and ground line))  
- Step 6: self.wait(0.5)  
- Step 7: self.play(MoveAlongPath(dot, parabola_path))  

**Visual Concept:**  
Demonstrates the parabolic path of a projectile by animating a dot moving smoothly along a mathematically accurate trajectory on x-y axes with labeled ground, reinforcing the connection between the equation and the motion.