Question

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. Finally, he will swim in a direction

• A. $ta{n}^{-1}\left(B\right)$ E of N
• B. $ta{n}^{-1}\left(B\right)$ N of E
• C. ${30}^{\circ }$ E of N
• D. ${60}^{\circ }$ E of N

Answer 1

The correct option is C ${30}^{\circ }$ E of N

We have,

River speed $=5m/min$

And Man speed $=10m/min$

So,

Let the width of river $=xmtr$

He travels due north then his rtesultant velocity acts 30 degree north of east and the distance to be covered to reach the other bank increase to $\frac{x}{\cos {30}^o}$

And resultant velociity $=11.2m/min$

So time taken $\frac{x}{9.7}\text{mins}$

If the travels due 30 degree north of east then his resultant velocity (Due to velocity of downstream of water ) acts due north.

The distance be covered to reach the other bank will be x mtrs.

And the resultant velocity is $8.7mtr/min.$

So time taken is $\frac{x}{8.7}\text{mins}\text{.}$

Then, $30$ degree east of north

So at least time he should travel due to north.

Hence, this is the answer.