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Question

A ball is projected in a direction inclined to the horizontal and it bounces on a horizontal plane. If the range of first rebound is R and coefficient of restitution is e, then range of the next rebound is


A
R=eR
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B
R=e2R
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C
R=Re
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D
R=R
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Solution

The correct option is A R=eR

As we know that,
Range =ux×T
here, ux is horizontal component of velocity
ux=ucosθ
uy=usinθ= vertical component of velocity
Time of flight, T=2usinθg
T=2uyg
Hence, Range R=uxT
R=2uxuyg
After rebound, horizontal component will not change but vertical component of velocity will be decreased by e times, therefore, uy=e×uy
Therefore new range, R=2ux×uyg
R=2euxuyg=e.2uxuyg=eR

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