Question

How should a man cross the river in order that he takes (i) shortest time and, (ii) shortest path?

Answer 1

Answer: To cross a river by the shortest path, man's velocity (relative to the ground) is perpendicular to the flow. To cross a river in minimum time, man's speed relative to the water should be perpendicular to the river flow.

Explanation: (i) Shortest time : To cross the river by the shortest time, he has to be rowed perpendicular to the river.

As a result of the river velocity the person will reach a point say C from A. (drawn the current).

(ii) Shortest path : To cross by shortest path, i.e., from A to B the boat should be rowed at an angle