Question

The speed of a swimmer in still water is $20\text{m/s}$. The speed of river water is $10\text{m/s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north, is given by

• A. $30°$ west
• B. $0°$
• C. $60°$ west
• D. $45°$ west

Answer 1

The correct option is A ${30}^{\circ }$ west

Given:
Speed of swimmer w.r.t river, $V_{SR}=20\text{m/s}$

Speed of river flow, $V_{RG}=10\text{m/s}$


From above diagram,

${\overrightarrow{V}}_{SG}={\overrightarrow{V}}_{SR}+{\overrightarrow{V}}_{RG}$

So,
$\sin \theta =\frac{|{\overrightarrow{V}}_{RG}|}{|{\overrightarrow{V}}_{SR}|}$

$\sin \theta =\frac{10}{20}=\frac{1}{2}$

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

Hence, option $\left(\text{A}\right)$ is the right choice.