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

H=Total distance travelled before it stops rebounding or coming to test =`h+h_(1)+h_(2)+……`
`=h+2e^(2)h+2e^(4)h+….`
`H=h+2e^(2)h[1+e^(2)+….]`
`S alpha =a/(1-r)=1/(1-e^(2)`
`H=h+2r^(2)h[1/1-e^(2)]=h[(1+e^(2))/(1+e^(2))]`