Projectile motion simulator comparing three physical regimes: vacuum (no air), Stokes drag (linear in velocity, F=bv, laminar flow), and Newton drag (quadratic, F=½ρCdAv², turbulent regime). In vacuum the optimal angle for maximum range is exactly 45°. With drag the optimum drops to 30–38° depending on drag magnitude. The simulator numerically integrates the equations of motion with RK4 and shows both the multi-trajectory angle sweep and the live comparison between all three regimes.

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Ballistics & Projectile Motion 🏹

UK
Range (vacuum)
Range (drag)
Max Height
Flight Time
Opt. angle (drag)

Vacuum
Newton drag
Angle sweep
Projectile
Launch angle
45°
Speed (m/s)
40
Drag Cd
0.47