Question

A ball P of mass 0.25kg, loses one-third of its velocity when it makes a head-on-collision

with an identical ball Q at rest. After the collision, Q moves off with a speed of 2ms-¹ in
the original direction of P. calculate the initial velocity of P.

Answer 1

Let's call the initial velocity of ball P as "v". After the collision, the velocity of P becomes 2/3 of its initial velocity (v) and the velocity of Q becomes 2 m/s in the direction of P.

From the law of conservation of momentum, we know that the total momentum before the collision is equal to the total momentum after the collision.

So, the initial momentum of P (0.25 kg * v) is equal to the final momentum of P (0.25 kg * 2/3 v) + the final momentum of Q (0.25 kg * 2 m/s).

Solving for v, we get:
0.25 kg * v = 0.25 kg * 2/3 v + 0.25 kg * 2 m/s

v = 6 m/s

Therefore, the initial velocity of ball P was 6 m/s.