# Sticky Collisions

Sticky collisions are called perfectly inelastic collision. The equations for conservation of momentum simplify a bit when the objects start or end stuck together.

m1u1 + m2u2 = m1v1 + v2m2
m1u1 + m2u2 = (m1 + m2)v

## Explosions!

Sticky collisions also work in reverse.
The sticky collision equation is just flipped.

(m1 + m2)u = m1v1 + m2v2

Example: A 100.0kg goalie throws a 1.1kg soccer ball while jumping forward at 3.2m/s. If the ball flies out of the goalie's hands at 10.0m/s what speed is the goalie?

solution

initial momentum = final momentum

(goalie and ball) = goalie + ball

$$(m_{1}+m_{2})u=m_{1}v_{1}+m_{2}v_{2}$$ $$(100.0+1.1)(3.2)=(100.0)v_{1}+(1.1)(10.0)$$ $$323.52=(100.0)v_{1}+11$$ $$3.13\small\frac{m}{s}=\normalsize v_{1}$$