Presets
Playback
Kick
World and ground
Layers
Model check
The science
What happens to the rock
1. The kick. The foot (effective mass M = 3 kg for a leg and boot) hits the rock (mass m) at speed u. In a collision with restitution ek the rock leaves at v = (1 + ek) M u / (M + m). The impulse is J = m v and, if contact lasts about 12 ms, the mean force is J / 12 ms. That is why kicking a real rock hurts a lot more than kicking a ball: use a soft ball for real life.
2. Flight. Newton's second law with gravity and quadratic air drag: a = -g z^ - k |v| v, with k = rho Cd A / (2 m), drag coefficient Cd = 0.8 for an angular rock and A = pi r2 from the mass at density 2650 kg/m3. The equations are integrated with a 4th-order Runge-Kutta step of 2 ms. Without air the range from launch height h is v cos a (v sin a + sqrt(v2 sin2 a + 2 g h)) / g and the best angle is close to 45 degrees; air drag lowers it.
3. Bouncing. At each landing the normal speed becomes e times its old value and a Coulomb friction impulse mu (1 + e) vn removes horizontal speed (never more than all of it). When a bounce would rise less than half a millimetre the rock is treated as sliding.
4. Sliding. Constant deceleration mu g plus drag until it stops: distance v2 / (2 mu g) without air.
Honest simplifications
The rock is a point mass with a spherical drag area. Spin, the Magnus effect, rolling instead of sliding, ground deformation and wind are not modelled; the tumbling you see is for display. The rock is drawn larger than life by default; the physics always uses its true radius. Ground bounce and friction values are typical textbook figures for each surface, not measurements.
Model checks (run live)
Range without air against the closed form; an energy ledger (drag + bounces + sliding = launch energy); terminal speed against sqrt(2 m g / (rho Cd A)); vertical bounces without air against e2 and the sliding stop distance against v2/(2 mu g); the best angle against 45 degrees.