Question

A man can row a boat at $4\text{km/h}$ in still water. If he is crossing a river which is $4\text{km}$ wide, and the speed of current is $2\text{km/h}$, then in what direction should his boat be headed if he wants to reach a point on the other bank, directly opposite to the starting point?

• A. ${30}^{\circ }$ with direction of river flow
• B. ${60}^{\circ }$ with direction of river flow
• C. ${120}^{\circ }$ with direction of river flow
• D. ${150}^{\circ }$ with direction of river flow

Answer 1

The correct option is C ${120}^{\circ }$ with direction of river flow

Let direction perpendicular to the river flow be $y-$axis and direction along the river flow be $x-$axis.



Given that |${\overrightarrow{v}}_{br}|=4\text{km/h}$
And velocity of river, ${\overrightarrow{v}}_r=2\hat{i}\text{km/h}$
$\theta ={\sin }^{-1}\left(\frac{v_r}{v_{br}}\right)={\sin }^{-1}\left(\frac{2}{4}\right)={\sin }^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$

Hence, to reach the point directly opposite to starting point he should head the boat at an angle of ${30}^{\circ }$ with the y-axis or ${90}^{\circ }+{30}^{\circ }={120}^{\circ }$ with the x-axis, i.e.; along the river flow.