The kick is modelled with the impulse–momentum theorem: a short foot–donut contact delivers an impulse J proportional to the force slider, which instantly sets the donut's launch velocity v₀ = J / m for its mass m = 0.72 kg:
J = F × 0.0145 (impulse, kg·m/s)
v₀ = J / m
vₓ = v₀·cosθ, vᷲ = v₀·sinθ
While airborne, gravity (g = 9.81 m/s²) is the only force, giving standard projectile-motion parabolas whose range and peak height you can read off the live panel. Each surface sets a friction coefficient μ and a coefficient of restitution e used two ways: when the donut lands with vertical speed it bounces with vᷲ′ = −e·vᷲ; once it settles onto the ground it rolls with rolling-friction deceleration a = −μg opposing its motion, so ice barely slows it while rubber stops it quickly.
Hitting the crate is a genuine 1D momentum-conserving collision between the donut (m₁ = 0.72 kg) and the crate (m₂ = 1.1 kg, initially at rest), solved with the standard two-body restitution formulas:
v₁′ = [(m₁−e·m₂)v₁ + (1+e)m₂v₂] / (m₁+m₂)
v₂′ = [(m₂−e·m₁)v₂ + (1+e)m₁v₁] / (m₁+m₂)
- Momentum & kinetic energy — tracked live for the donut alone; watch KE drop across a lossy (low-e) crate hit and momentum split between donut and crate.
- Trail — dashed line traces the flight path; a solid line marks the rolling phase along the ground.
- Crate — slides on its own friction (μ = 0.6) after impact, then stops; reset to put it back.