A particle falls from a height h on a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle on rebounding has stopped

Options

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

Answer

A

Explanation

The total distance travelled is
`s=h+2e^(2)h+2e^(2)h+2e^(6)h+.....`
`s=h+2h(e^(0)+e^(4)+e^(6)+...)`
By using binomial expansion we can write it as
`S=h+2h(e^(2)/(1-e^(2)))=h(1+(2e^(2))/(1-e^(2)))=h((1-e^(2)+2e^(2))/(1-e^(2)))rArr s=h(1+e^(2))/(1-e^(2))`