Design the implementation for this scene using the provided Manim patterns:

SCENE CONTEXT:
\nContinuity: Uses the established principles to solve a concrete example involving projectile motion, tied visually to the basketball shot introduced earlier.  \nVisual_Focus: Step-by-step animated walkthrough of calculating the ball’s range, maximum height, and flight time, overlayed on footage of the basketball shot.  \nLearning_Objective: Show how to apply formulas to predict projectile behavior and understand the significance of angle, speed, and gravity in determining the outcome.  \nContent: Present given values: initial speed and launch angle. Demonstrate calculations: splitting velocity components, calculating time of flight using vertical motion, finding horizontal distance traveled. Show these results correspond visually to the ball’s actual path in slow motion, emphasizing how theory predicts reality.  \nTransition_To_Next: Preview that understanding projectile motion goes beyond sports—this knowledge informs fields like engineering and space exploration, setting up for a broader conclusion.  \n

TOPIC: Projectile motion
SCENE NUMBER: 3
PREVIOUS SCENE STATE: Elements: ['\\n\\nSCENE CONTEXT'], State: Scene 2 completed

RELEVANT MANIM PATTERNS:
Pattern: step_by_step_derivation
Description: Show mathematical derivation step by step
Use case: Step-by-step mathematical derivations
Template:

        # Starting equation
        eq1 = MathTex(r"{start_eq}").to_edge(UP, buff=1.0)
        
        # Transformation steps
        eq2 = MathTex(r"{step1_eq}").next_to(eq1, DOWN, buff=1.2)
        eq3 = MathTex(r"{step2_eq}").next_to(eq2, DOWN, buff=1.2)
        eq4 = MathTex(r"{final_eq}").next_to(eq3, DOWN, buff=1.2)
        
        # Step labels
        label1 = Text("{step1_label}").scale(0.5).next_to(eq2, RIGHT, buff=1.0)
        label2 = Text("{step2_label}").scale(0.5).next_to(eq3, ...

Pattern: equation_introduction
Description: Introduce mathematical equation with fade-in and highlight
Use case: Introducing key formulas and concepts
Template:

        # Title at top
        title = Text("{title}").scale(0.8).to_edge(UP, buff=0.5)
        
        # Main equation in center
        equation = MathTex(r"{equation}").scale(1.2)
        
        # Label below equation  
        label = Text("{label}").scale(0.6).next_to(equation, DOWN, buff=1.0)
        
        # Highlight box around equation
        highlight = SurroundingRectangle(equation, color=YELLOW, buff=0.2)
        
        # Animation sequence
        self.play(Write(title))
  ...

Implementation Plan:

1. CONTINUITY PLAN:
- Elements to carry forward from previous scene: [list specific visual elements]
- New elements to introduce: [list new elements]
- Transition method: [how to smoothly connect]

2. VISUAL LAYOUT (No overlaps):
| Element | Type | Zone | Position Method | Purpose |
|---------|------|------|----------------|---------|
| 1       |      |      |                |         |
| 2       |      |      |                |         |
| 3       |      |      |                |         |

3. ANIMATION SEQUENCE:
| Step | Action | Element(s) | Timing | Notes |
|------|--------|------------|--------|-------|
| 1    |        |            |        |       |
| 2    |        |            |        |       |
| 3    |        |            |        |       |
| 4    |        |            |        |       |
| 5    |        |            |        |       |

4. SCENE END STATE:
- Elements remaining on screen: [for next scene continuity]
- Key visual/conceptual state: [what should be remembered]

5. MANIM PATTERN TO USE:
- Primary pattern: step_by_step_derivation
- Customizations needed: [how to adapt the pattern]

Be specific about transitions and maintaining visual continuity.