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 :

Options

A. `h((1+e^2)/(1-e^2))`
B. `h((1-e^2)/(1+e^2))`
C. `h/(2)((1-e^2)/(1+e^2))`
D. `h/(2)((1+e^2)/(1-e^2))`

Answer

a

Explanation

Here total distance travelled is giving by
`S=h+2e^2h+2e^4h+2e^6h+`
or `S=h+2e^2h[1+e^2+e^4+e^6+…]`
This gives infinite G.P. with common ratio `e^2`.
`S=h+2e^h[(1)/(1-e^2)]=h[1+(2e^2)/(1-e^2)]`
=`h[(1+e^2)/(1-e^2)]`.