📐 How the Physics Simulator Works
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Projectile Motion Without Air Resistance: Uses closed-form kinematics equations (SUVAT formulas) for exact calculations of time of flight, range, and maximum height. The range formula is: R = (v₀² × sin(2θ)) / g. Perfect for physics homework, AP Physics, and engineering courses.
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Projectile Motion With Air Resistance: Uses Euler numerical integration (dt=0.005s) to solve quadratic drag equations: Fdrag = 0.5·ρ·Cd·A·v², where ρ = air density, Cd = drag coefficient, A = cross-sectional area, v = velocity. Essential for realistic ballistics calculations, sports physics analysis, and understanding terminal velocity.
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30+ Sports & Object Presets: Instant physics simulation for basketball free throws, soccer goal kicks, golf drives, baseball home runs, tennis serves, volleyball spikes, ping pong shots, arrow trajectories, frisbee flights, and more. Each preset includes real-world mass, drag coefficient, and cross-sectional area values.
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Multi-Planet Gravity Simulation: Calculate projectile motion on 17 celestial bodies including Mercury (3.7 m/s²), Venus (8.87 m/s²), Earth gravity (9.81 m/s²), Moon gravity (1.62 m/s²), Mars gravity (3.71 m/s²), Jupiter (24.79 m/s²), Saturn, Uranus, Neptune, Europa, Titan, Pluto, Ceres, Sun, and White Dwarf. Perfect for space mission planning and astrophysics education.
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Fun Scenario Challenges: Pre-configured physics puzzles including Medieval Trebuchet (50 kg stone), Napoleon's Cannon (120 m/s), Moon Golf Record (400m range), Mars Rover Jump, Angry Birds trajectory, Superhero Throw, Everest Summit (8,848m altitude with thin air), and White Dwarf extreme gravity. Great for engaging students in physics learning!
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Privacy & Free Access: All projectile motion calculations run 100% locally in your browser. No server uploads, no data collection, no registration required. Works offline after initial load. Completely free physics calculator for students, teachers, and professionals.
🎓 Educational Use Cases
- Physics Students: Verify homework answers for range, time of flight, and apex calculations. Visualize how launch angle affects trajectory.
- Teachers & Professors: Demonstrate parabolic motion, compare vacuum vs. air resistance trajectories, show gravity differences across planets.
- Sports Coaches: Analyze optimal basketball shooting angles, golf ball trajectories, soccer free kicks, and baseball pitch physics.
- Engineering Students: Study ballistics, rocketry, fluid dynamics (drag coefficients), and numerical simulation methods.
- AP Physics / IB Physics: Interactive tool for kinematics, dynamics, 2D motion, energy conservation, and projectile motion labs.
🔑 Key Features of This Calculator
✓ Real-time trajectory visualization on interactive canvas
✓ Instant range and time of flight calculator
✓ Air resistance simulation with adjustable parameters
✓ Velocity and energy charts (kinetic + potential)
✓ Auto-scaling for large trajectories
✓ Multiple shot comparison overlay
🔍 Common Projectile Motion Formulas
Without Air Resistance (Vacuum):
• Range: R = (v₀² × sin(2θ)) / g
• Time of Flight: T = (2v₀ × sin(θ)) / g
• Maximum Height: H = (v₀² × sin²(θ)) / (2g)
• Horizontal Velocity: vx = v₀ × cos(θ) [constant]
• Vertical Velocity: vy = v₀ × sin(θ) - g×t
With Air Resistance (Realistic):
• Drag Force: Fd = 0.5 × ρ × Cd × A × v²
• Requires numerical integration (Euler, Runge-Kutta)
• Range is significantly reduced compared to vacuum
• Terminal velocity: vterm = √(2mg / ρCdA)
💡 Pro Tip: Use "Keep Shots" to overlay multiple trajectories and compare how changing velocity, angle, or air resistance affects the projectile path. Perfect for physics lab reports and presentations!