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A swimmer crosses a river of width $d$ flowing at velocity $v$ . While swimming, he heads himself always at an angle of $120 °$ with the river flow and on reaching the other end he finds a drift of $d / 2$ in the direction of flow of river. The speed of the swimmer with respect to the river is

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$(2 - \sqrt{3}) v$

$4 (2 - \sqrt{3}) v$

$2 (2 - \sqrt{3}) v$

$(2 + \sqrt{3}) v$

answer is C.

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Detailed Solution

$t = \frac{d}{v_{r} \cos 30 °} = \frac{2 d}{\sqrt{3} v_{r}}$

A swimmer crosses a river of width d flowing at velocity v. While swimming he heads himself always at an angle of 120^o with the river flow and on reaching to the

Now drift,
$\frac{d}{2} = (v - v_{r} \sin 30 °) t = (v - v_{r} / 2) (\frac{2 d}{\sqrt{3} v_{r}})$
$∴ \sqrt{3} v_{r} = 4 v - 2 v_{r}$
$∴ v_{r} = (\frac{4}{2 + \sqrt{3}}) v$
$= 4 (2 - \sqrt{3}) v$

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