A stone is dropped from the top of a tall cliff and n seconds later another stone is thrown vertically downwards with a velocity u. Then the second stone overtakes the first, below the top of the cliff at a distance given by

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$\frac{g}{2} {[\frac{n (\frac{g n}{2} - u)}{(g n - u)}]}^{2}$

$g {[\frac{(g n - u)}{(g n - u / 2)}]}^{2}$

$\frac{g}{2} {[\frac{n (g n - u / 2)}{(g n - u)}]}^{2}$

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answer is A.

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Detailed Solution

Let second stone overtakes the first, at time ' t ' after the first stone was thrown

$∴ \frac{1}{2} g t^{2} = u (t - n) + \frac{1}{2} g {(t - n)}^{2}$

On solving, $t = (\frac{u n - g n^{2} / 2}{g n - u})$

And required distance $= \frac{1}{2} g t^{2}$

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