A swimmer crosses the river along the line making an angle of 45^o with the direction of flow. Velocity of the river water is 5 m/s. Swimmer takes 12 seconds to cross
the river of width 60 m. The velocity of the swimmer with respect to water will be 

Time taken by man to cross the river

$\begin{array}{l}=\frac{\text{ width of river }}{v_y}\\ 12=\frac{60}{v_y}\Rightarrow v_y=5\mathrm{m}/\mathrm{s}\end{array}$

Let the x component of velocity of man w.r.t. river is v_x Since velocity of man w.r.t. ground makes an angle of 45^o with river flow x component of velocity of man w.r.t. ground
= y component of velocity of man w.r.t. ground

$\begin{array}{l}{\overrightarrow{v}}_r+{\overrightarrow{v}}_x={\overrightarrow{v}}_y\\ v_x=0\end{array}$

So velocity of man w.r.t. water = v_y= 5 m/s