Question

The stream of a river is flowing at a speed of $2km/h$. A swimmer can swim at a speed of $4km/h$ in still water. What should be the direction of the swimmer with respect to the flow of the river to cross the river with minimum drift?

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${90}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is B ${120}^{\circ }$

Let $v_r$ be the velocity of river and $v_{sr}$ be the velocity of swimmer w.r.t river.
According to question,
$v_r=2km/h$ and $v_{sr}=4km/h$
Also, angle of swimmer with the flow of river (down the stream) is $\alpha$ as shown in the figure below


From diagram,
$\sin \theta =\frac{v_r}{v_{sr}}=\frac{2km/h}{4km/h}=\frac{1}{2}$
$⟹\theta ={30}^{\circ }$
Hence, $\alpha ={90}^{\circ }+{30}^{\circ }={120}^{\circ }$