Projectiles: Target Intercept & Kinematics Studio

An interactive 2D projectile kinematics virtual laboratory and inquiry simulator created for The Thinking Experiment (PhysicsKit).

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🎯 Pedagogical Pillars

1. Feed the Monkey (Classic Intercept Challenge)

• The Setup: A banana cannon aims directly at a monkey hanging from a tree branch. As the cannon fires, the sound startles the monkey, which releases the branch and begins free-falling at $t = 0$.
• The Theorem: Both the projectile and the falling target accelerate downward at the identical gravitational rate ($a_y = -g$). Over flight duration $t$, both objects drop by the exact same vertical distance: $$\Delta y_{\text{drop}} = \frac{1}{2}gt^2$$
• The Conclusion: Aiming directly along the visual line of sight guarantees an intercept at any launch speed $v_0$ sufficient to reach the target before it hits the ground.

2. Mark Rober's Automated Dartboard

• Replicates Mark Rober's viral engineering challenge:
  • Launch position: $x_0 = 0\text{ m}$, $y_0 = 1.8\text{ m}$, $v_0 = 15.0\text{ m/s}$, launch angle $\alpha = 40.0^\circ$.
  • Motorized target board at distance $x = 5.0\text{ m}$.
  • Students calculate required board height and check ceiling clearance ($h_{\max} \le H_{\text{ceiling}}$).

3. Classroom Kinematics & Cornell T-Chart Engine

• Horizontal Channel ($a_x = 0$): $v_x = v_0 \cos\theta = \text{const}$, $x = x_0 + v_{0x}t$
• Vertical Channel ($a_y = -g$): $v_y = v_{0y} + gt$, $y = y_0 + v_{0y}t + \frac{1}{2}gt^2$ (with $g = -9.8,\text{m/s}^2$)
• Time as the Scalar Bridge: Visual connecting bridge illustrating how time links the two independent 1D motions.

For complete mathematical derivations, the algebraic proof of the Monkey-Hunter theorem, and worked examples, see PHYSICS.md.

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🎨 Design System Compliance

This simulation adheres strictly to The Thinking Experiment brand standards:

• Teal Headers / Primary: #0f7e9b / #095f76
• Amber Accents / Highlights: #d67b19
• Background: Pure White (#ffffff) with Blueprint Grid (#e9f4fb)
• Typography: Sans-serif (Inter, IBM Plex Sans)
• Prohibited: No Purple (#59118e) or Gold (#ffc61e)

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🚀 Running Locally

# Clone the repository
git clone https://github.com/Thinking-Experiment-Sims/projectiles-inquiry-lab.git
cd projectiles-inquiry-lab

# Start local server
python3 -m http.server 8000

Open http://localhost:8000 in your web browser.

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📱 Embedding in Canvas LMS

<iframe 
  src="https://thinking-experiment-sims.github.io/projectiles-inquiry-lab/" 
  width="100%" 
  height="800" 
  style="border: 1px solid #c8dbe3; border-radius: 8px;"
  loading="lazy"
  allowfullscreen>
</iframe>

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📁 Repository Structure

projectiles-inquiry-lab/
├── index.html                       # Main interactive lab interface
├── styles.css                        # The Thinking Experiment CSS stylesheet
├── Unit_1_Packet_6_Projectiles.pdf   # Accompanying classroom packet
├── src/
│   ├── app.js                       # Canvas rendering, drag handlers, UI state
│   └── physics.js                   # Analytical 2D projectile kinematics engine
├── tests/
│   └── physics.test.js              # Automated unit tests for trajectories
├── PHYSICS.md                       # Comprehensive theoretical physics guide
└── README.md                        # Project documentation

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📄 License & Attribution

Authored by Vladimir Lopez for The Thinking Experiment (PhysicsKit).
Open-source under the MIT License for educational use in physics classrooms worldwide.