Question

A river is flowing from west to east at a speed of $5$ meters per minute. A man on the south bank of the river, capable of swimming at $10$ meters per minute in still waters, wants to swim across the river in the shortest time, he should swim in a direction :

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

Answer 1

Answer: (A)

due north

To reach the opposite bank of the river in minimum time, the swimmer should swim at right angles to the direction of flow of river. He should swim in a direction due north
Let the width of the river be $d$. If the man swims at an angle $\theta$ with the direction of flow of water, his velocity component perpendicular to the direction of flow of water is $10\sin \theta$
Time taken to reach the opposite bank: $t=\frac{d}{10\sin \theta }$
$\therefore$ t will be minimum when $\sin \theta$ is maximum i.e $\theta ={90}^{\circ }$