Question

A river is flowing from East to West at a speed of $5m/min$. A man on south bank of river, capable of swimming $10m/min$ in still water, wants to swim across to river in the shortest time. He should swim

• A. Due North
• B. Due North- East
• C. Due North-East with double the speed of river
• D. None of the above

Answer 1

The correct option is A

Due North

Step 1: Given data

Speed of river $=5m/min$

Speed of man $=10m/min$

Step 2: Finding the direction of the swimmer

Here, $AC$ is the shortest distance for the person to cross the river from the south bank of the river.

The component of velocity of the person along the shortest path $=v_{man}\cos \theta$

Now, the time taken by the person to cross the river along shortest path is given as;

$t=\frac{AC}{v_{man}\cos \theta }$

The time will be minimum when the denominator will be maximum.

That is basically, $\cos \theta =$ maximum

Maximum value of $\cos \theta =1$

Therefore

$\cos \theta =1$

$\cos \theta =\cos 0°$

$\theta =0°$

That is in the north direction.

Thus,

The direction in which the swimmer should move will be in north direction.

Therefore, he should swim due North direction.

Hence, the correct option is A.