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# A ball rolls off top of a stair way with horizontal velocity $u\; m/s$ If height of each step is h and width of each step is b the ball will hit the edge of $n^{th}$ step if $n$ is equal to

If the ball hits the $n^{th}$ step vertical distance travelled in $nh$ horizontal distance travelled is $nb$
Let $t$ be the time of fall
Initaial vertical velocity $=0$
Therefore $nb=ut$----(1)
$nh=0+\large\frac{1}{2}$$gt^2$-----(2)
from (1) and (2)
$n= \large\frac{2hu^2}{gb^2}$
Hence d is the correct answer.

edited Jan 26, 2014 by meena.p

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