The ratio of time taken to fallen successive equal individual is
$1 : (\sqrt{2} - 1) : (\sqrt{3} - \sqrt{2}) : (\sqrt{4} - \sqrt{3})$

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Solution

$t_{1} = \sqrt{\frac{2 s}{g}}$

Now, time taken to reach B from start-

$t_{1} + t_{2} = \sqrt{\frac{4 s}{g}} = \sqrt{2} t_{1}$

$⟹ t_{2} = (\sqrt{2} - 1) t_{1}$

Now, time taken to reach C from start-

$t_{1} + t_{2} + t_{3} = \sqrt{\frac{6 s}{g}} = \sqrt{3} t_{1}$

$⟹ t_{3} = (\sqrt{3} - \sqrt{2}) t_{1}$

Now, time taken to reach D from start-

$t_{1} + t_{2} + t_{3} + t_{4} = \sqrt{\frac{8 s}{g}} = \sqrt{4} t_{1}$

$⟹ t_{4} = (\sqrt{4} - \sqrt{3}) t_{1}$

Hence,

$t_{1} : t_{2} : t_{3} : t_{4} = 1 : (\sqrt{2} - 1) : (\sqrt{3} - \sqrt{2}) : (\sqrt{4} - \sqrt{3})$

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