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A ball rolls off top of a staircase with...

A ball rolls off top of a staircase with a horizontal velocity `u m s^-1`. If the steps are `h` metre high and `b` mere wide, the ball will just hit the edge of `n th` step. Find the value of `n`.

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Refer to figure For `n^(th)` step
net vertical displacement=nh
net horizonatal displacement`=nomega`
Let t be the time taken by the ball to reach the nth step. Then

or `nomega=ut` or `t=(nomega)/(u)`
Also `y=u_yt+1/2"gt"^2`
or `nh=0+1/2"gt"^2=1/2g((nomega)/(u))^2` or `n=(2hu^2)/(gomega^2)`
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