Two billiard balls each of mass 0.05 kg moving in opposite directions

Question.
Iwo billiard balls each of mass $0.05 \mathrm{~kg}$ moving in opposite directions with speed $6 \mathrm{~m} \mathrm{~s}^{-1}$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

solution:

Mass of each ball = 0.05 kg

Initial velocity of each ball = 6 m/s

Magnitude of the initial momentum of each ball, $p_{i}=0.3 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

After collision, the balls change their directions of motion without changing the magnitudes of their velocity.

Final momentum of each ball, $p_{f}=-0.3 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

Impulse imparted to each ball = Change in the momentum of the system

$=p_{f}-p_{i}$

$=-0.3-0.3=-0.6 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

The negative sign indicates that the impulses imparted to the balls are opposite in direction.