A ball rolls of the top of a stair way with a horizontal velocity u m `s^(-1)`. If the steps are h metre high and b metre wide, the time taken by the ball to hit the edge of `n^(th)` step, is

Options

A. `(hu)/(gb)`
B. `(2hu)/(gb)`
C. `(2hu^2)/(gb)`
D. `(hu^2)/(2gb)`

Answer

B

Explanation

The ball reaches `n^(th)` step in time t, then bn = ut or t=bn/u ,
Also , `nh=1/2 g t^2 = 1/2 g xx (b^2n^2)/u^2, therefore n=(2u^2h)/(gb^2)`
Time taken to travel vertical distance nh is
`t=sqrt((2nh)/g)=sqrt((2h)/gxx(2u^2h)/(gb^2))=(2uh)/(gb)`