Question

A 0.16-kg billiard ball moving right at 2.5 m/s collided with a second identical billiard ball moving 1.5 m/s in the opposite direction. After collision, the first ball rebounds with a speed of 0.5m/s

Answer 1

Answer: 1.5 m/s

Explanation:

In this problem we have to find the velocity of the second billiard ball after the collision.

According to the conservation of momentum law:

"If two objects or bodies are in a closed system and both collide, the total momentum of these two objects before the collision will be the same as the total momentum of these same two objects after the collision".

This means the initial momentum $p_{o}$ must be equal to the final momentum $p_{f}$:  

$p_{o}=p_{f}$ (1)

Where:

$p_{o}=m_{1}V_{o}+m_{2}U_{o}$ (2)

$p_{f}=m_{1}V_{f}+m_{2}U_{f}$ (3)

$m_{1}=m_{2}=0.16 kg$ are the masses of each ball

$V_{o}=2.5 m/s$ is the initial velocity of ball 1 (in the right direction)

$U_{o}=-1.5 m/s$ is the initial velocity of ball 2 (in the opposite direction)

$V_{f}=-0.5 m/s$  is the final velocity of ball 1 (in the opposite direction)

$U_{f}$ is the final velocity of ball 2

Substituting (2) and (3) in (1):

$m_{1}V_{o}+m_{2}U_{o}=m_{1}V_{f}+m_{2}U_{f}$ (4)

Isolating $U_{f}$ and remembering $m_{1}=m_{2}$:

$U_{f}=V_{o}-V_{f}+U_{o}$ (5)

$U_{f}=2.5 m/s-(-0.5 m/s)-1.5 m/s$ (6)

Finally:

$U_{f}=1.5 m/s$ This is the final velocity of ball 2, directed to the right