Question

A man who can swim at the rate of $2km/hr$ (in still river) crosses a river to a point exactly opposite on the other bank by swimming in a direction of ${120}^{\circ }$ to the flow of the water in the river. The velocity of the water current in $km/hr$ is,

Answer 1

Given,
$V_m=\text{Velocity of man}=2km/hr$.
$V_r=\text{Velocity of river}$,
$\theta ={120}^{\circ }$
$V_{mr}=V_m-V_r$
Taking components, $V_{mr}\cos {120}^{\circ }=V_m\cos {90}^{\circ }-V_r\cos 0^{\circ }$
$2\times (-\frac{1}{2})=-V_r$
So, $V_r=1km/hr$