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Question

# A particle falls from a height 'h' upon a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution the total distance travelled before rebounding has stopped is :-

A
h(1+e21e2)
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B
h(1e21+e2)
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C
h2(1e21+e2)
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D
h2(1+e21e2)
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Solution

## The correct option is A h(1+e21−e2)As ball dropped fro height 'h', then it will strike the floor with velocity (v)=√2ghnow after striking the floor it will bounce back with velocity (u)=evnow it will travel total 2h1 distance before again striking the ground. where h1=e2v22g again the ball will bounce back with e2v velocity and now it will travel 2h2 distance before striking the ground,where h1=e4v22g and this process continues for long time till ball comes to the rest.So total distance travelled=h+2h1+2h2+..... =v22g+2e2v22g+2e4v22g+2e6v22g+........ =v22g+2e2v22g(1+e2+e4+e6+....) =v22g+e2v2g(11−e2) =(1−e2+2e21−e2)v22g =(1+e21−e2)v22g =(1+e21−e2)h

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