Two balls X and Y are moving towards each other with speeds of 5 m s-1 and 15 m s-1 respectively.

Question 20

Two balls X and Y are moving towards each other with speeds of 5 m s^-1 and 15 m s^-1

respectively.

They make a perfectly elastic head-on collision and ball Y moves to the right with a speed of 7 m s^-1.

What is the speed and direction of ball X after the collision?

A 3 m s^-1 to the left

B 13 m s^-1 to the left

C 3 m s^-1 to the right

D 13 m s^-1 to the right

Reference: Past Exam Paper – March 2019 Paper 12 Q8

Solution:

Answer: B.

For a perfectly elastic head-on collision,

Relative velocity of separation = Relative velocity of approach

Initially, the two balls are moving towards each other.

Relative velocity of approach = 5 + 15 = 20 m s^-1

After the collision, ball Y moves to the right at a speed of 7 m s^-1.

The relative velocity of separation should be equal to the relative velocity of approach (= 20 m s^-1). 

Ball Y is moving to the right at 7 m s^-1. So, ball X should move in such a way to increase the increase the relative velocity of separation.

Ball X should move in the opposite direction (i.e. to the left).

v + 7 = 20

Velocity v = 20 – 7 = 13 m s^-1