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Question

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

Moderate
Solution

If the ball hits the nth step, then horizontal distance traversed = nb.
Vertical distance traversed = nh.
Here, velocity along horizontal direction = u.
Velocity along vertical direction = 0.

nb=ut  ......(i) nh=0+12gt2   ......(ii)
From eqn. (i),
t=nbu,nh=12gnbu2n=2hu2gb2

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