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Work, Energy And Power

Question
CBSEENPH11017325

A body is dropped from a height h on an inelastic floor of the coefficient of restitution e. Find the total distance travelled by the body before it comes to rest.

Solution
The body is dropped from height h.
Let h1, h2, h3..........be the heights attained by the body after first, second, .... collision.
Total distance travelled by the body just before coming to rest is,
straight S equals straight h subscript 0 plus 2 straight h subscript 1 plus 2 straight h subscript 2 plus 2 straight h subscript 3.......... 
 equals straight h subscript 0 plus 2 straight e squared straight h subscript 0 plus 2 straight e to the power of 4 straight h subscript 0 plus 2 straight e to the power of 6 straight h subscript 0........ 
 equals straight h subscript 0 plus 2 straight h subscript 0 straight e squared left parenthesis 1 plus straight e squared plus straight e to the power of 4........ right parenthesis 
 equals straight h subscript 0 plus 2 straight h subscript 0 fraction numerator straight e squared over denominator 1 minus straight e squared end fraction
equals straight h subscript 0 fraction numerator 1 plus straight e squared over denominator 1 minus straight e squared end fraction