A ball is projected in a direction inclined to the vertical and bounces on a smooth horizontal plane. The range of one rebound is `R`. If the coefficient of restitution is `e`, then range of the next rebound is

Options

A. Angle of projection `alpha = tan^(-1)(4)`
B. Angle of projection `alpha = tan^(-1) (4e)` where e is the impact coefficient
C. Angle of projection is `45^@`
D. Angle of rebound is same as angle of projection

Answer

B

Explanation

Before collision, `" "u_x = u cos theta, u_(y) = u sin theta` After collision,
`u_(x) = u cos theta, u_(y) = eu sin theta`
`implies H = (u^2 sin^2 theta)/(g)` " "As `H = R_2 implies (sin theta)/(2) = 2 e cos theta implies tan theta = 4e`.