A partical 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

Particle falls from height h then formula for height covered by it in nth rebound is given by
`h_(n)= h e^(2n)`
where e = coefficient of restitution, n = No. of rebound Total distance travelled by particle before rebounding has stopped
`H= h+ 2h_(1) + 2h_(2) + 2h_(3)+ 2h_(n) +` .....
`=h + 2 he^(2) + 2h e^(4) + 2h e^(6) + 2 he^(8) +`....
`=h + 2h(e^(2) + e^(4) + e^(6) + e^(8) +`....)
`=h + 2h [(e^(2))/(1- e^(2))]= h [1+ (e^(2))/(1-e^(2))]= h ((1+e^(2))/(1-e^(2)))`