Question

Water in a river flows from wets to east at $4km/h$. A man on the north bank capable of swimming at km/h crossed the river in the shortest possible time. Then he should swim along?
(A) North
(B) south
(C) ${{30}^{0}}$west of north
(D) ${{30}^{0}}$east of north

Answer 1

In this problem the water is also moving and when the man attempts to swim across the river, then the movement of the water will affect his motion. The man wanted to cover the distance in the shortest possible time and as such he did not attempt to move directly to the opposite bank. So, we can make use of vectors to arrive at the meaningful solution.

Complete answer:
Let us first represent the velocity vectors of the man, and the river.

We can see here in order to move to the opposite side the man should move in the direction perpendicular to the motion of the water. And when he moves such, ultimately his motion will be in the direction of the resultant vector. Thus, the man should swim towards the south.

Hence, the option B is the correct answer.

Note: we were to tell only the direction of the motion. Had we been asked to find the resultant velocity for that we should have been given the velocity of the man and then we would have used the triangle law of vector addition to find the resultant velocity. These kinds of problems are solved by using vector algebra and using laws of vector addition.