Question

A person wants to reach the exactly opposite point on the bank of a river. He can swim with a speed of $5m/s$. He swims at an angle of ${45}^{\circ }$ with the bank of the river facing the south-west direction. What is the speed and direction of the flow of the river?

• A. $5\sqrt{2}m/s$ in the east direction.
• B. $\frac{5}{\sqrt{2}}m/s$ in the east direction.
• C. $5\sqrt{2}m/s$ in the west direction.
• D. $\frac{5}{\sqrt{2}}m/s$ in the west direction.

Answer 1

The correct option is B $\frac{5}{\sqrt{2}}m/s$ in the east direction.


As we can see the image to reach the exactly opposite end, the river should flow towards the east direction. For the person to reach the exact opposite point on the bank, the magnitude of $x$ component of the velocity of man w.r.t. river should be equal to the magnitude of velocity of the river.
Hence, speed of river, $v_r=5\cos {45}^{\circ }=\frac{5}{\sqrt{2}}$
Hence the correct option is (b).