Generate Manim code for Scene 1 using the implementation plan and pattern.

IMPLEMENTATION PLAN:
[['Design the implementation for this scene using the provided Manim patterns:\n\nSCENE CONTEXT:\n\\nContinuity: [Starting point - how to hook the audience]\\nVisual_Focus: [Main visual element]\\nLearning_Objective: [What viewers should learn]\\nContent: [What concepts/information to present]\\nTransition_To_Next: [How this prepares for scene 2]\\n\n\nTOPIC: Projectile motion\nSCENE NUMBER: 1\nPREVIOUS SCENE STATE: \n\nRELEVANT MANIM PATTERNS:\nPattern: concept_comparison\nDescription: Side-by-side comparison of two concepts\nUse case: Comparing and contrasting concepts\nTemplate:\n\n        # Title\n        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)\n        \n        # Left side concept\n        left_title = Text("{left_title}").scale(0.7).shift(LEFT*3 + UP*1.5)\n        left_content = Text("{left_content}").scale(0.6).shift(LEFT*3)\n        left_box = SurroundingRectangle(\n            VGroup(left_title, left_content), \n            color=BLUE, buff=0.3\n        )\n        \n        # Right side concept  \n        right_title = Text("{right_title}").scale(0.7).shift(RI...\n\nPattern: equation_introduction\nDescription: Introduce mathematical equation with fade-in and highlight\nUse case: Introducing key formulas and concepts\nTemplate:\n\n        # Title at top\n        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)\n        \n        # Main equation in center\n        equation = MathTex(r"{equation}").scale(1.2)\n        \n        # Label below equation  \n        label = Text("{label}").scale(0.6).next_to(equation, DOWN, buff=1.0)\n        \n        # Highlight box around equation\n        highlight = SurroundingRectangle(equation, color=YELLOW, buff=0.2)\n        \n        # Animation sequence\n        self.play(Write(title))\n  ...\n\nImplementation Plan:\n\n1. CONTINUITY PLAN:\n- Elements to carry forward from previous scene: [list specific visual elements]\n- New elements to introduce: [list new elements]\n- Transition method: [how to smoothly connect]\n\n2. VISUAL LAYOUT (No overlaps):\n| Element | Type | Zone | Position Method | Purpose |\n|---------|------|------|----------------|---------|\n| 1       |      |      |                |         |\n| 2       |      |      |                |         |\n| 3       |      |      |                |         |\n\n3. ANIMATION SEQUENCE:\n| Step | Action | Element(s) | Timing | Notes |\n|------|--------|------------|--------|-------|\n| 1    |        |            |        |       |\n| 2    |        |            |        |       |\n| 3    |        |            |        |       |\n| 4    |        |            |        |       |\n| 5    |        |            |        |       |\n\n4. SCENE END STATE:\n- Elements remaining on screen: [for next scene continuity]\n- Key visual/conceptual state: [what should be remembered]\n\n5. MANIM PATTERN TO USE:\n- Primary pattern: concept_comparison\n- Customizations needed: [how to adapt the pattern]\n\nBe specific about transitions and maintaining visual continuity.', 'Certainly! Below is a detailed implementation plan for **Scene 1** on **Projectile Motion**, designed using the provided **concept_comparison** Manim pattern and tailored to your scene context:\n\n---\n\n### Implementation Plan for Scene 1: Projectile Motion\n\n---\n\n#### 1. CONTINUITY PLAN:\n\n- **Elements to carry forward from previous scene:**  \n  - None (This is Scene 1; starting fresh to hook the audience)\n\n- **New elements to introduce:**  \n  - Title: “Projectile Motion: Understanding the Basics”  \n  - Left concept: **Horizontal motion** (constant velocity)  \n  - Right concept: **Vertical motion** (constant acceleration due to gravity)  \n  - Visual comparison layout to clearly differentiate the two components of projectile motion\n\n- **Transition method:**  \n  - Fade in the title to hook the audience.  \n  - Present the two components side-by-side with subtle slide-in animations from left and right, visually emphasizing how projectile motion is decomposed into two independent motions.\n  - This sets up the viewer to understand the next step on how these combine, preparing for Scene 2.\n\n---\n\n#### 2. VISUAL LAYOUT (No overlaps):\n\n| Element          | Type           | Zone       | Position Method                | Purpose                                                    |\n|------------------|----------------|------------|-------------------------------|------------------------------------------------------------|\n| 1. Title         | Text           | Top Center | `.to_edge(UP, buff=0.5)`      | Introduce topic to the viewer and create focus             |\n| 2. Left concept   | Text + Box     | Left side  | Shifted `LEFT*3 + UP*1.5`      | Explain horizontal motion - constant velocity               |\n| 3. Left content   | Text           | Left side  | Shifted `LEFT*3`               | Supporting info for horizontal motion                       |\n| 4. Right concept  | Text + Box     | Right side | Shifted `RIGHT*3 + UP*1.5`     | Explain vertical motion - constant acceleration due to gravity |\n| 5. Right content  | Text           | Right side | Shifted `RIGHT*3`              | Supporting info for vertical motion                         |\n\n---\n\n#### 3. ANIMATION SEQUENCE:\n\n| Step | Action                                         | Element(s)                       | Timing    | Notes                                                          |\n|-------|------------------------------------------------|--------------------------------|-----------|----------------------------------------------------------------|\n| 1     | Fade in the title                              | Title                          | 1.5 sec   | Capture attention                                              |\n| 2     | Animate slide-in of left_title and left_content from left off-screen | Left title & content            | 1.5 sec   | Establish horizontal motion concept                           |\n| 3     | Animate slide-in of right_title and right_content from right off-screen | Right title & content           | 1.5 sec   | Establish vertical motion concept                             |\n| 4     | Show surrounding rectangles (boxes) around left and right groups | left_box & right_box            | 1 sec     | Visually group concepts                                        |\n| 5     | Pause for emphasis                             | All current elements           | 2 secs    | Allow viewer to absorb comparison                             |\n\n---\n\n#### 4. SCENE END STATE:\n\n- **Elements remaining on screen:**  \n  - Title  \n  - Both left and right concept groups boxed and fully visible\n\n- **Key visual/conceptual state:**  \n  - Clear understanding that projectile motion splits into independent horizontal and vertical components.  \n  - Audience is primed to see how these combine (next scene will likely show trajectory and associated equations).\n\n---\n\n#### 5. MANIM PATTERN TO USE:\n\n- **Primary pattern:** `concept_comparison`\n\n- **Customizations needed:**  \n  - Customize left and right text to define **Horizontal motion** vs **Vertical motion** specifically.  \n  - Use colors to enhance understanding: e.g., use BLUE for horizontal motion box and RED for vertical motion box to visually differentiate.  \n  - Add a subtle slide-in animation for left and right groups instead of just fade in, to add dynamic engagement as this is the hook scene.  \n  - Adjust text scaling slightly to match the density of information (left/right content could have bullet points or succinct phrases).  \n\n---\n\n### Concrete example of content to fill into the pattern:\n\n```python\ntitle = Text("Projectile Motion: Understanding the Basics").scale(0.8).to_edge(UP, buff=0.5)\n\n# Left side concept: Horizontal motion\nleft_title = Text("Horizontal Motion").scale(0.7).shift(LEFT*3 + UP*1.5)\nleft_content = Text(\n    "• Constant velocity\\n• No acceleration", \n    font_size=24\n).shift(LEFT*3)\nleft_box = SurroundingRectangle(\n    VGroup(left_title, left_content), \n    color=BLUE, buff=0.3\n)\n\n# Right side concept: Vertical motion\nright_title = Text("Vertical Motion").scale(0.7).shift(RIGHT*3 + UP*1.5)\nright_content = Text(\n    "• Accelerated motion\\n• Acceleration = g (~9.8 m/s²)", \n    font_size=24\n).shift(RIGHT*3)\nright_box = SurroundingRectangle(\n    VGroup(right_title, right_content), \n    color=RED, buff=0.3\n)\n\n# Animation idea: title fades in, left group slides in from left, right group slides in from right, then boxes appear\n```\n\n---\n\n### Summary:\n\n- Start with a strong, clear title as a hook.  \n- Emphasize decomposition of projectile motion into two fundamentally different but simultaneous motions.  \n- Use color-coded boxes with succinct bullet points to visually anchor these concepts.  \n- Slide in from sides adds visual interest and sets stage to later unify the concepts (likely Scene 2).  \n\nThis respects your scene context and produces a strong continuity and learning objective alignment.\n\n---\n\nIf you want, I can provide the full Manim scene code snippet based on this plan next. Would you like that?']]

MANIM PATTERN TO ADAPT:

        # Title
        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)
        
        # Left side concept
        left_title = Text("{left_title}").scale(0.7).shift(LEFT*3 + UP*1.5)
        left_content = Text("{left_content}").scale(0.6).shift(LEFT*3)
        left_box = SurroundingRectangle(
            VGroup(left_title, left_content), 
            color=BLUE, buff=0.3
        )
        
        # Right side concept  
        right_title = Text("{right_title}").scale(0.7).shift(RIGHT*3 + UP*1.5)
        right_content = Text("{right_content}").scale(0.6).shift(RIGHT*3)
        right_box = SurroundingRectangle(
            VGroup(right_title, right_content),
            color=GREEN, buff=0.3
        )
        
        # Animation
        self.play(Write(title))
        self.wait(1)
        self.play(Write(left_title), Create(left_box))
        self.wait(1)
        self.play(Write(left_content))
        self.wait(1)
        self.play(Write(right_title), Create(right_box))
        self.wait(1)
        self.play(Write(right_content))
        self.wait(2)
                

CONTINUITY REQUIREMENTS:
- Previous scene ended with: []
- Must smoothly transition from: Starting fresh

STRICT REQUIREMENTS:
- Use the provided pattern as a base, customize for this specific scene
- Ensure smooth transitions if elements carry over from previous scenes
- Position all elements without overlaps using .to_edge(), .shift(), .next_to() with buff>=1.0
- Create meaningful pauses between animation steps (self.wait(1) minimum)
- Add educational value through progressive revelation
- Use colors: BLUE, RED, GREEN, WHITE, YELLOW, ORANGE, PURPLE, GRAY (no quotes)
- Class name: Scene1(Scene)

TEMPLATE CUSTOMIZATION:
Replace template placeholders with:
{'title': '\\n\\nSCENE CONTEXT:\\n\\\\nContinuity: [Starting point - how to hook the audience]\\\\nVisual_Focus: [Main visual element]\\\\nLearning_Objective: [What viewers should learn]\\\\nContent: [What concepts/information to present]\\\\nTransition_To_Next: [How this prepares for scene 2]\\\\n\\n\\nTOPIC: Projectile motion\\nSCENE NUMBER: 1\\nPREVIOUS SCENE STATE: \\n\\nRELEVANT MANIM PATTERNS:\\nPattern: concept_comparison\\nDescription: Side-by-side comparison of two concepts\\nUse case: Comparing and contrasting concepts\\nTemplate:\\n\\n        # Title\\n        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)\\n        \\n        # Left side concept\\n        left_title = Text("{left_title}").scale(0.7).shift(LEFT*3 + UP*1.5)\\n        left_content = Text("{left_content}").scale(0.6).shift(LEFT*3)\\n        left_box = SurroundingRectangle(\\n            VGroup(left_title, left_content), \\n            color=BLUE, buff=0.3\\n        )\\n        \\n        # Right side concept  \\n        right_title = Text("{right_title}").scale(0.7).shift(RI...\\n\\nPattern: equation_introduction\\nDescription: Introduce mathematical equation with fade-in and highlight\\nUse case: Introducing key formulas and concepts\\nTemplate:\\n\\n        # Title at top\\n        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)\\n        \\n        # Main equation in center\\n        equation = MathTex(r"{equation}").scale(1.2)\\n        \\n        # Label below equation  \\n        label = Text("{label}").scale(0.6).next_to(equation, DOWN, buff=1.0)\\n        \\n        # Highlight box around equation\\n        highlight = SurroundingRectangle(equation, color=YELLOW, buff=0.2)\\n        \\n        # Animation sequence\\n        self.play(Write(title))\\n  ...\\n\\nImplementation Plan:\\n\\n1. CONTINUITY PLAN:\\n- Elements to carry forward from previous scene: [list specific visual elements]\\n- New elements to introduce: [list new elements]\\n- Transition method: [how to smoothly connect]\\n\\n2. VISUAL LAYOUT (No overlaps):\\n| Element | Type | Zone | Position Method | Purpose |\\n|---------|------|------|----------------|---------|\\n| 1       |      |      |                |         |\\n| 2       |      |      |                |         |\\n| 3       |      |      |                |         |\\n\\n3. ANIMATION SEQUENCE:\\n| Step | Action | Element(s) | Timing | Notes |\\n|------|--------|------------|--------|-------|\\n| 1    |        |            |        |       |\\n| 2    |        |            |        |       |\\n| 3    |        |            |        |       |\\n| 4    |        |            |        |       |\\n| 5    |        |            |        |       |\\n\\n4. SCENE END STATE:\\n- Elements remaining on screen: [for next scene continuity]\\n- Key visual/conceptual state: [what should be remembered]\\n\\n5. MANIM PATTERN TO USE:\\n- Primary pattern: concept_comparison\\n- Customizations needed: [how to adapt the pattern]\\n\\nBe specific about transitions and maintaining visual continuity.\', \'Certainly! Below is a detailed implementation plan for **Scene 1** on **Projectile Motion**, designed using the provided **concept_comparison** Manim pattern and tailored to your scene context:\\n\\n---\\n\\n### Implementation Plan for Scene 1: Projectile Motion\\n\\n---\\n\\n#### 1. CONTINUITY PLAN:\\n\\n- **Elements to carry forward from previous scene:**  \\n  - None (This is Scene 1; starting fresh to hook the audience)\\n\\n- **New elements to introduce:**  \\n  - Title: “Projectile Motion: Understanding the Basics”  \\n  - Left concept: **Horizontal motion** (constant velocity)  \\n  - Right concept: **Vertical motion** (constant acceleration due to gravity)  \\n  - Visual comparison layout to clearly differentiate the two components of projectile motion\\n\\n- **Transition method:**  \\n  - Fade in the title to hook the audience.  \\n  - Present the two components side-by-side with subtle slide-in animations from left and right, visually emphasizing how projectile motion is decomposed into two independent motions.\\n  - This sets up the viewer to understand the next step on how these combine, preparing for Scene 2.\\n\\n---\\n\\n#### 2. VISUAL LAYOUT (No overlaps):\\n\\n| Element          | Type           | Zone       | Position Method                | Purpose                                                    |\\n|------------------|----------------|------------|-------------------------------|------------------------------------------------------------|\\n| 1. Title         | Text           | Top Center | `.to_edge(UP, buff=0.5)`      | Introduce topic to the viewer and create focus             |\\n| 2. Left concept   | Text + Box     | Left side  | Shifted `LEFT*3 + UP*1.5`      | Explain horizontal motion - constant velocity               |\\n| 3. Left content   | Text           | Left side  | Shifted `LEFT*3`               | Supporting info for horizontal motion                       |\\n| 4. Right concept  | Text + Box     | Right side | Shifted `RIGHT*3 + UP*1.5`     | Explain vertical motion - constant acceleration due to gravity |\\n| 5. Right content  | Text           | Right side | Shifted `RIGHT*3`              | Supporting info for vertical motion                         |\\n\\n---\\n\\n#### 3. ANIMATION SEQUENCE:\\n\\n| Step | Action                                         | Element(s)                       | Timing    | Notes                                                          |\\n|-------|------------------------------------------------|--------------------------------|-----------|----------------------------------------------------------------|\\n| 1     | Fade in the title                              | Title                          | 1.5 sec   | Capture attention                                              |\\n| 2     | Animate slide-in of left_title and left_content from left off-screen | Left title & content            | 1.5 sec   | Establish horizontal motion concept                           |\\n| 3     | Animate slide-in of right_title and right_content from right off-screen | Right title & content           | 1.5 sec   | Establish vertical motion concept                             |\\n| 4     | Show surrounding rectangles (boxes) around left and right groups | left_box & right_box            | 1 sec     | Visually group concepts                                        |\\n| 5     | Pause for emphasis                             | All current elements           | 2 secs    | Allow viewer to absorb comparison                             |\\n\\n---\\n\\n#### 4. SCENE END STATE:\\n\\n- **Elements remaining on screen:**  \\n  - Title  \\n  - Both left and right concept groups boxed and fully visible\\n\\n- **Key visual/conceptual state:**  \\n  - Clear understanding that projectile motion splits into independent horizontal and vertical components.  \\n  - Audience is primed to see how these combine (next scene will likely show trajectory and associated equations).\\n\\n---\\n\\n#### 5. MANIM PATTERN TO USE:\\n\\n- **Primary pattern:** `concept_comparison`\\n\\n- **Customizations needed:**  \\n  - Customize left and right text to define **Horizontal motion** vs **Vertical motion** specifically.  \\n  - Use colors to enhance understanding: e.g., use BLUE for horizontal motion box and RED for vertical motion box to visually differentiate.  \\n  - Add a subtle slide-in animation for left and right groups instead of just fade in, to add dynamic engagement as this is the hook scene.  \\n  - Adjust text scaling slightly to match the density of information (left/right content could have bullet points or succinct phrases).  \\n\\n---\\n\\n### Concrete example of content to fill into the pattern:\\n\\n```python\\ntitle = Text("Projectile Motion: Understanding the Basics").scale(0.8).to_edge(UP, buff=0.5)\\n\\n# Left side concept: Horizontal motion\\nleft_title = Text("Horizontal Motion").scale(0.7).shift(LEFT*3 + UP*1.5)\\nleft_content = Text(\\n    "• Constant velocity\\\\n• No acceleration", \\n    font_size=24\\n).shift(LEFT*3)\\nleft_box = SurroundingRectangle(\\n    VGroup(left_title, left_content), \\n    color=BLUE, buff=0.3\\n)\\n\\n# Right side concept: Vertical motion\\nright_title = Text("Vertical Motion").scale(0.7).shift(RIGHT*3 + UP*1.5)\\nright_content = Text(\\n    "• Accelerated motion\\\\n• Acceleration = g (~9.8 m/s²)", \\n    font_size=24\\n).shift(RIGHT*3)\\nright_box = SurroundingRectangle(\\n    VGroup(right_title, right_content), \\n    color=RED, buff=0.3\\n)\\n\\n# Animation idea: title fades in, left group slides in from left, right group slides in from right, then boxes appear\\n```\\n\\n---\\n\\n### Summary:\\n\\n- Start with a strong, clear title as a hook.  \\n- Emphasize decomposition of projectile motion into two fundamentally different but simultaneous motions.  \\n- Use color-coded boxes with succinct bullet points to visually anchor these concepts.  \\n- Slide in from sides adds visual interest and sets stage to later unify the concepts (likely Scene 2).  \\n\\nThis respects your scene context and produces a strong continuity and learning objective alignment.\\n\\n---\\n\\nIf you want, I can provide the full Manim scene code snippet based on this plan next. Would you like that?\']]', 'equation': 'E = mc^2', 'label': "Einstein's Mass-Energy Equation", 'step1_text': 'Step 1', 'step2_text': 'Step 2', 'step3_text': 'Step 3'}

Generate complete Python code with proper imports: