A ball is dropped from a height 'h' on to a floor of coefficient of restitution 'e'. The total distance covered by the ball just before second hit is

Options

A. `h[1+e^(2)]`
B. `he^(2)`
C. `h[1-2e^(2)]`
D. `h[1+2e^(2)]`

Answer

D

Explanation

Let 2 m be the mass of the shell before collision. At the highest point in its path, its vertical velocity is zero and has only the horizontal velocity `v cos theta`.

From the conservation of linear momentum,
Momentum berore collision = Momentum after collision.
`:. 2 m ( v cos theta ) = mv' - m ( v cos theta )`
`:. 3 mv cos theta = mv' ` `:. v' = 3v cos theta`