A ball rolls of the top of a stair way with a horizontal velocity $u\ ms^{- 1}$. If the steps are $h$ metre and $b$ metre wide, the ball hits the edge of $n$th step, the time taken by the ball is

Question

Dr. Abubacker · Accepted Answer

(b) The ball reaches $n$th step in time $t$, then $bn = ut$
or $t = bn/u$,
$nh = \frac{1}{2}gt^{2} = \frac{1}{2}g 	imes \frac{b^{2}n^{2}}{u^{2}}$; so $n = \frac{2u^{2}h}{gb^{2}}$
Time taken to travel vertical distance $nh$ is
$t = \sqrt{\frac{2nh}{g}} = \sqrt{\frac{2h}{g} 	imes \frac{2u^{2}h}{gb^{2}}} = \frac{2uh}{gb}$

Q. A ball rolls of the top of a stair way with a horizontal velocity $u\ ms^{- 1}$. If the steps are $h$ metre and $b$ metre wide, the ball hits the edge of $n$th step, the time taken by the ball is

Explanation

Reviewed by Dr. Abubacker

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