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A man can swim in still water with velocity $v_{0}$ . He wishes to cross a river of flow velocity $\frac{v_{0}}{2}$ and width d, such that he reaches just opposite point on the other bank and comes back, at the point from where he started. The time taken by him in the round tripz

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$\frac{2 d}{v_{0} \sqrt{3}}$

$\frac{4 d}{v_{0} \sqrt{3}}$

$\frac{2 d}{v_{0}}$

$\frac{4 d}{v_{0}}$

answer is D.

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Detailed Solution

$i = \frac{d}{\sqrt{v^{2} - u^{2}}} = \frac{d}{\sqrt{v_{0}^{2} - \frac{v_{0}^{2}}{4}}} = \frac{2 d}{v_{0} \sqrt{3}}$

$∴$ Total time $= \frac{4 d}{v_{0} \sqrt{3}}$

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