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

A particle falls from a height h on a fixed horizontal plane and rebou

1.	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
Answer» (a) `(h(1+e)^(2))/((1-e)^(2)` (B) `(h(1+e))/((1-e))` (c) `(h(1+e^(2)))/((1-e^(2)))` (d) `(h(1-e)^(2))/((1+e)^(2)` Solution :The totaldistance 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))`