Question

A swimmer crosses a river of width d flowing at velocity V while swimming he heads himself always at an angle of $120^{\circ}$ with the river flow and on reaching the other end he find a drift of $\frac{d}{2}$ in the direction of flow of river. The speed of the swimmer with respect to river is:

• A. $(2-\sqrt{3}) V$
• B. $2(2-\sqrt{3}) V$
• C. $4(2-\sqrt{3}) V$
• D. $\sqrt{41}$

Answer 1

Answer: (C)

$t =\frac{ d }{ V _{ r } \cos 30} =\frac{2 d }{\sqrt{3} V _{ r }}$
Now, drift $\frac{ d }{2} =\left( V - V _{ r } \sin 30\right) t$
$ =\left[ V -\frac{ V _{ r }}{2}\right]\left[\frac{2 d }{\sqrt{3} V _{ r }}\right]$

$\sqrt{3} V_{r}=4 V-2 V_{r}$
$V_{r}=\left[\frac{4}{2+\sqrt{3}}\right] V=4(2-\sqrt{3}) V$