A boy swims in a straight line to reach the other side of a river. His velocity is $5{\text{ms}}^{-1}$  and the angle of swim with shore is ${30}^0$ . Flow of river opposes his movement at $2{\text{ms}}^{-1}$  if width of river is $200m$ , where does he reach the other bank

Velocity of river ${\overrightarrow{v}}_r=-2\hat{i}$ 

Velocity of swimmer w. r. t river is

   ${\overrightarrow{v}}_s=5\cos 30\hat{i}+5+\sin 30\hat{j}$

      $=4.33\hat{i}+2.5\hat{j}$

Using ${\overrightarrow{v}}_R={\overrightarrow{v}}_s+{\overrightarrow{v}}_r$  we get

${\overrightarrow{v}}_R=2.33\hat{i}+2.5\hat{j}$

Time taken by swimmer $=\frac{\text{Distance}\text{along}\text{y-axis}}{\text{y}\text{component}\text{of}\text{velocity}}$

$=\frac{200}{2.5}=80s$

Distance moved along $x-axis,$

$OF=x$ component of relative $\times$  time

$=2.33\times 80=186.4m$