Question

A river is flowing from west to east with a speed $5ms^{- 1}$. A swimmer can swim in still water at a speed of $10ms^{- 1}$. 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. $30^{o}$east of north
• B. $60^{o}$east of north
• C. $30^{o}$west of north
• D. $60^{o}$west of north

Answer 1

Answer: (C)

$30^{o}$west of north

Answer 2

Here,

Velocity of swimmer in still water, $v_{s} = 10ms^{- 1}$

Velocity of water flowing in river, $v_{r} = 5ms^{- 1}$

From figure,

$\sin\theta = \frac{v_{r}}{v_{s}} = \frac{5}{10} = \frac{1}{2}$

$\theta = \sin^{- 1}\left( \frac{1}{2} \right) = 30{^\circ}$west of north

Alternative solutions

$v = \sqrt{v_{s}^{2} - v_{r}^{2}} = \sqrt{(10)^{2} - (5)^{2}} = 5\sqrt{3}ms^{- 1}$

$\tan\theta = \frac{v_{r}}{v} = \frac{5}{5\sqrt{3}} = \frac{1}{\sqrt{3}}$

Or $\theta = \tan^{- 1}\left( \frac{1}{\sqrt{3}} \right) = 30{^\circ}$west of north