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Question

A ball is moving with a speed of 4 m/s towards a heavy wall. The wall is also moving towards the ball with velocity of 1 m/s. If the coefficient of restitution is 0.5, find the velocity of the ball immediately after the collision. (Assume that the wall maintains the same speed even after the collision.)

A
3.5 m/s along initial direction.
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B
1.5 m/s opposite to initial direction.
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C
2.5 m/s opposite to initial direction.
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D
3.5 m/s opposite to initial direction.
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Solution

The correct option is D 3.5 m/s opposite to initial direction.
Before collision

Taking velocity positive along the positive X axis and vice versa.

Given:
u1=4 m/s; u2=1 m/s

After collision


We know,
Coefficient of restitution, e=velocity of separationvelocity of approach
=v2v1u1u20.5=1(v1)4(1)
v1=3.5 m/s
Velocity of the ball is 3.5 m/s opposite to initial direction.
The correct option is (d)

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