A river is flowing from West to East at a speed of 5 m/min. A man on the South bank of the river, capable of swimming at 10 m/min in still water, wants to swim across the river in the shortest time. He should swim in a direction
A.
due North
B.
30° East of North
C.
30° West of North
D.
60° East of North
Show answer and solution
Correct option: A
Solution
To minimize crossing time, the man must maximize the component of his velocity perpendicular to the river (i.e., toward the North). This component equals v·cosθ, where θ is the angle from North. This is maximized when θ = 0°, meaning he swims due North. The river current will carry him downstream (eastward), but that only affects where he lands, not the time taken. Since the question asks only about shortest time (not shortest path), swimming due North is optimal.
[1983]
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