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Projectile Time, Height and Range

A ball rolls ...

Question

A ball rolls off the top of a staircase with a horizontal velocity u. If each step has a height h and a width b, then the ball will just bit the nth step, if n equals

A

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B

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C

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D

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Solution

The correct option is A
$R = u \sqrt{\frac{2 H}{g}} w h e r e R = n b; H = n h \Rightarrow n b = u \sqrt{\frac{2 n h}{g}} \Rightarrow n = \frac{u^{2} 2 h}{g b^{2}}$

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