Question

A man can row a boat at $4\text{km/hr}$ in still water. He is crossing a river where the current velocity is $2\text{km/hr}$ . 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. ${120}^{\circ }$ with the direction of flow
• B. ${150}^{\circ }$ with the direction of flow
• C. ${60}^{\circ }$ with the direction of flow
• D. ${90}^{\circ }$ with the direction of flow

Answer 1

The correct option is A ${120}^{\circ }$ with the direction of flow


Let, $V_r=\text{Velocity of river}$
$V_{br}=\text{Velocity of boat w.r.t river}$

To reach at a point directly opposite to A, the component of $V_{br}$ in the horizontal direction must be equal to $V_r$ in magnitude.

$\Rightarrow V_{br}\sin \theta =V_r$

$\sin \theta =\frac{V_r}{V_{br}}=1/2$

$\Rightarrow \theta ={30}^{\circ }$

Hence, to reach the point directly opposite to the starting point he should head the boat at an angle $\beta ={90}^{\circ }+{30}^{\circ }={120}^{\circ }$ with the river flow.

Therefore, option $\left(\text{A}\right)$ is correct.