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Question

A particle falls from a height 'h' upon a fixed horizontal plane and rebounds. If e=0.2is the coefficient of restitution. Find the total distance travelled before rebounding has stopped.

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Solution

h1=e2v22gh1=e2v22g
h2=[e4v2]2gh2=[e4v2]2g
Total distance :
h+2h1+2h2+2h3+..........h+2h1+2h2+2h3+..........
v22gv22g+2e2v22g+2e2v22g+2(e4v22g)+2(e4v22g)+2(e6v2)2g+2(e6v2)2g+.............+.............
v22g+e2v22gv22g+e2v22g[1+e2+e4+......][1+e2+e4+......]
v22g+e2v2g[11e2]v22g+e2v2g[11−e2]
[1e2+2e2]v22g(1e2)=[1+e21e2]v22g[1−e2+2e2]v22g(1−e2)=[1+e21−e2]v22g
=(1+e21e2)=(1+e21−e2)hh

1144070_1204921_ans_f9121e6793c44dac884a6d8abb30f742.JPG

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