A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in shortest time. He should swim in a direction

The situation is shown in figure. Let u be the velocity of the river and v be the velocity of the man. Let d be the width of the river and $\mathrm{\theta }$, the angle made by o with north. Here the river will be crossed by the component of velocity along the width of the river, i.e., from south of north.

Now, $\mathrm{t}=\frac{\mathrm{distance}}{ \mathrm{velocity} \mathrm{component} }=\frac{\mathrm{d}}{\mathrm{vcos}\mathrm{\theta }}$
For shortest time $\cos \mathrm{\theta }=1,\mathrm{i.}\mathrm{e}., \mathrm{\theta }=0^{\circ }$
So the man should swim along the north.