# 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.

m

_{1}u

_{1}+ m

_{2}u

_{2}= m

_{1}v

_{1}+ v

_{2}m

_{2}

m

_{1}u

_{1}+ m

_{2}u

_{2}= (m

_{1}+ m

_{2})v

## Explosions!

Sticky collisions also work in reverse.

The sticky collision equation is just flipped.

_{1}+ m

_{2})u = m

_{1}v

_{1}+ m

_{2}v

_{2}

**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

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