Question

A river is flowing from west to east with a speed 5 $m{s}^{-1}$. A swimmer can swim in still water at a speed of 10 $m{s}^{-1}$. If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim?

• A. 30${}^{\circ }$ east of north
• B. 60${}^{\circ }$ east of north
• C. 30${}^{\circ }$ west of north
• D. 60${}^{\circ }$ west of north

Answer 1

Answer: (C)

30${}^{\circ }$ west of north

Here, Velocity of swimmer in still water, $v_s=10m{s}^{-1}$
Velocity of water flowing in river, $v_r=5m{s}^{-1}$
From figure, $sin\theta =\frac{v_r}{v_s}=\frac{5}{10}=\frac{1}{2}$
$\theta =si{n}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$ west of north