Projectile Motion Calculator - Kinematic Equations with Air Resistance

📊 Input Variables

Enter any 2 known values to solve for all other variables:

Ideal Physics

With Air Resistance

🎯 IDEAL PHYSICS MODE - No Air Resistance

Mass (m) kg

Radius (r) m

Projectile Type preset

Base Drag Coefficient (Cd) dimensionless

Air Density (ρ) kg/m³

Temperature °C

Altitude m

Initial Velocity (v₀) m/s

Launch Angle (θ) degrees

Initial Height (h₀) m

Horizontal Range (R) m

Maximum Height (H) m

Total Flight Time (t) s

📋 Calculated Results

Enter 2 known variables and click calculate to see results...

🌪️ Drag Coefficient vs. Velocity

Drag coefficient variation with velocity - showing subsonic, transonic, and supersonic regions

📚 Physics Equations Reference

Ideal: v = v₀ + gt

Ideal: x = v₀t + ½gt²

Ideal: v² = v₀² + 2gx

Air Resistance: F_drag = ½ρv²C_dA

Air Resistance: F_net = mg + F_drag

Numerical: Runge-Kutta 4th Order Integration

Ideal Physics: Uses analytical kinematic equations (no air resistance)
Air Resistance: ρ = air density, v = velocity, C_d = drag coefficient, A = cross-sectional area
Default Values: Baseball (m=0.145kg, r=0.037m, C_d=0.47) at sea level (ρ=1.225 kg/m³)

🎯 Example Problems

Click an example to load preset values:

🚀 Projectile Motion Calculator

📈 Trajectory Visualization

📊 Input Variables

📋 Calculated Results

🌪️ Drag Coefficient vs. Velocity

📚 Physics Equations Reference

🎯 Example Problems