Question

A river is flowing from $W$ to $E$ with a speed $5m/min$. A man can swim in still water at a velocity $10m/min$. In which direction should a man swim to take the shortest path to reach the south bank?

• A. ${30}^{\circ }$ East of South
• B. ${60}^{\circ }$ East of North
• C. South
• D. ${30}^{\circ }$ West of South

Answer 1

The correct option is D ${30}^{\circ }$ West of South

Let $v_{river}$ be the velocity of the river and $v_s$ be the velocity of the man swimming.
$v_s=10m/min\times sin\theta =v_{river}=5m/min$
$v_{s}sin\theta =v_{river}$
$10sin\theta =5$
$sin\theta =\frac{5}{10}=\frac{1}{2}$
$\theta ={30}^o$
Thus, the man should swim at ${30}^o$ west of south to take the shortest path to reach the south bank