Question

A river is flowing from west to east with a speed of $5\, m / \min$. A man can swim in still water with a velocity $10\, m / \min$. In which direction should the man swim so, as to take the shortest possible path to go to the south ?

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

Answer 1

Answer: (A)

$30^{\circ}$ east of south

Answer 2

Let the swimmer swims at an angle $\theta$ with the vertical.

$\therefore \sin \theta =\frac{v_{r}}{v_{s}}=\frac{5}{10}=\frac{1}{2}=\sin 30^{\circ}$
$\theta =30^{\circ}$
The swimmer should swim $30^{\circ}$ east of south to take the shortest possible path to go to the south.