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Q.

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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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

$S_{1 st} = S_{2 nd}$

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

$t = \frac{n (u - \frac{gn}{2})}{u - gn}$

$S_{1} = \frac{1}{2} g [t]^{2}$

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