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Question

# A ball is dropped onto a fixed horizontal surface from height h0. The coefficient of restitution is e. Find the total distance D travelled by the ball before it comes to rest on the surface.

A

h0(1e2)(1+e2)

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B

h0(1+e2)(1e)

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C

h0(1+e2)(1+e)

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D

h0(1+e2)(1e2)

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Solution

## The correct option is D h0(1+e2)(1−e2) Let hi(I=1,2,3,⋯⋯.) be the height of rebound after the ith impact. Then e=hihi−1 which gives hn=e2nh0 (n=1.2.3⋯⋯⋯.) D=h0+2( h1+h2+h3+h4+h5+⋯⋯) =h0{10+2(e2+e4+e6+e8+e10+⋯⋯⋯)}D=h0(1+e21−e2)

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