A swimmer can swim in still water with a speed of 5 ms^-1. While crossing a river his average speed is 3 ms^-1. If he crosses the river taking shortest possible path, what is the speed of flow of water ? (in ms^-1)

In order to cross the river taking shortest path, the resultant velocity v of the swimmer must be perpendicular to the velocity v_w of water, as shown in figure. It follows from the figure that ${\mathrm{v}}_{\mathrm{s}}^2={\mathrm{v}}^2+{\mathrm{v}}_{\mathrm{w}}^2 \mathrm{or} {\mathrm{v}}_{\mathrm{w}}^2={\mathrm{v}}_{\mathrm{s}}^2-{\mathrm{v}}^2=25-9=16 \mathrm{or} {\mathrm{v}}_{\mathrm{w}}=4 {\mathrm{ms}}^{-1}$.