# A ball with a mass of 2 kg is rolling at 9 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

Jan 29, 2016

${v}_{A} = 4.5 \frac{m}{s} ^ 2$ and ${v}_{B} = 2.25 \frac{m}{s} ^ 2$

#### Explanation:

In an elastic collision no energy is lost. We can therefore know that the combined momentum of the two objects will be the same after the collision, although the collision will transfer half its momentum from the moving ball to the resting ball.

Before the collision the momentum of ball $A$ is
${M}_{A} = {v}_{A} \cdot {m}_{A} = 9 \cdot 2 = 18$

The momentum of ball $B$ is ${M}_{B} = 0$ because its velocity is zero.
After the collision ${M}_{A} = {M}_{B} = \frac{18}{2} = 9$
${M}_{A} = 2 \cdot {v}_{A}$

$\therefore {v}_{A} = 4.5 \frac{m}{s} ^ 2$

${M}_{B} = 4 \cdot {v}_{B}$

$\therefore {v}_{B} = \frac{9}{4} = 2.25 \frac{m}{s} ^ 2$