A ball falls from a height h upon a fixed horizontal plane, e is the coefficient of restitution, the whole distance described by the ball before it comes to rest 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

Total distance travelled by ball before it stops rebounding -
`H=h_0+2h_1+2h_3+ "- - - -"=`
`=h_0+2e^2h_(0)+2e^(4)h_(0)+ "- - - -"`
`H=h_0[1+2e^2][1+^2+e^4+"- - - -"]`
`h_0[1+2e^2] [1/(1-e^2)]`
`H=h_0[(1+e^2)/(1-e^2)]=h[(1+e^2)/(1-e^2)]`