The speed of a swimmer in still water is $20 {\mathrm{ms}}^{-1}$. The speed of river water is $10 {\mathrm{ms}}^{-1}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by  

Given, speed of river, ${\mathrm{v}}_{\mathrm{R}} = 10 {\mathrm{ms}}^{-1}$ 

Speed of swimmer in still water, ${\mathrm{v}}_{\mathrm{SN}} = 20 {\mathrm{ms}}^{-1}$

For the shortest path to cross the river, he should swim at an angle (90^o + 8) with the stream flow. From the above figure,

${\mathrm{v}}_{\mathrm{SN}} = {\mathrm{v}}_{\mathrm{R}} + {\mathrm{v}}_{\mathrm{S}}$

So, angle $\mathrm{\theta }$ is given by 

                         $\sin \theta =\left|\frac{{\mathbf{v}}_R}{{\mathbf{v}}_{SN}}\right|=\frac{10}{20}=\frac{1}{2}\Rightarrow \theta =30°$ 

As the river is flowing in east direction, so he should swim towards west.