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Question

A ball rolls horizontally off the top of a stairway with a speed of 1.5 ms1. The steps are 0.2 m high and 0.2 m wide. If the balls hits the edge of nth step first, then n is equal to

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Solution

Total height through which the ball will fall down vertically before it strikes the nth step h=0.2×n=0.2n
Using second equation of motion, we get
h=12gt2
0.2n=5t2 (i)
Horizontal distance travelled by the ball before striking the nth step
R=0.2×n=0.2n
Now, 0.2n=ux×t
0.2n=1.5×t (ii)
Equating (i) and (ii), we get
5t2=1.5tt=0.3
Substituting in (i), n=5×0.32×10.2=2.25
Ball will first hit the 3rd step first.

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