Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms^{-1}collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

#### Solution 1

Initial momentum of each ball before collision

= 0.05 x 6 kg ms^{-1} = 0.3 kg ms^{-1}

Final momentum of each ball after collision

= – 0.05 x 6 kg ms^{-1} = – 0.3 kg ms^{-1} Impulse imparted to each ball due to the other

= final momentum – initial momentum = 0.3 kg m s-1 – 0.3 kg ms^{-1}

= – 0.6 kg ms^{-1} = 0.6 kg ms^{-1 }(in magnitude)

The two impulses are opposite in direction.

#### Solution 2

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 kg m/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 kg m/s

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

= *p*_{f} – *p*_{i}

= –0.3 – 0.3 = –0.6 kg m/s

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