A ball is thrown horizontally from a height h above a staircase as shown in the figure. If the coefficient of restitution for any collision between the ball and the staircase is e, then the value of h for which the ball will bounce the same height above each step, is

Options

A. `(4d)/(3)`
B. 2d
C. `(3d)/(4)`
D. `(3d)/(2)`

Answer

C

Explanation

Kinetic energy of a body of mass m moving with velocity `vec(v)_(1)` w.r.t. an observer moving with `vec(v)_(2)`
`KE_(1//2)=(m)/(2)|vec(v)_(1)-vec(v)_(2)|^(2)`
`implies KE _(1//2)` depends on velocity of observer implies statement -2 is false
`KE_("loss")=(1)/(2)(m_(1)m_(2))/(m_(1)+m_(2))|vec(v)_(1)-vec(v)_(3)|^(2)`
where `vec(v)_(1)` is velocity of first particle & `vec(v)_(3)` is velocity of other particle & it is independent of velocity of observer.