A ball rolls off the top of a staircase with a horizontal velocity `u m//s`. If the steps are h meter high and b meter wide, the ball will hit the edge of the nth steps, if:

Options

A. `n = (2 h u)/(g b^2)`
B. `n = (2 h u^2)/(g b)`
C. `n = (2 h u^2)/(g b^2)`
D. `n = (h u^2)/(g b^2)`

Answer

C

Explanation

( c) If the ball hits the `nth` step, then horizontal distance traversed `= nh`. Here, velocity along horizontal direction `= u.n = ut` (i) Initial velocity along vertical direction is `0`.
`nh = 0 + (1)/(2) "gt"^2`...(ii)
From `t = (nb)/(v)`, putting `t` in (ii), we get
`n h = (1)/(2) g xx ((n b)/(u))^2` or `n = (2 h u ^2)/(g b^2)`.
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