Q#20 (Past Exam Paper – March 2019 Paper 12 Q8)
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
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
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