Question

A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle of 120° with the direction of flow of water. The speed of water is:

• A. 1.0 m/s
• B. 0.5 m/s
• C. 0.25 m/s
• D. 0.43 m/s

Hint:

When a swimmer swims against a current at an angle, the effective speed of the swimmer in the direction of the current depends on the component of their speed in that direction.

Answer 1

The Correct Option is C

Step 1: Resolve the swimming velocity.
The swimmer’s velocity is at an angle of 120° to the direction of the water flow, so the component of the swimmer's velocity in the direction of the water flow is: \[ v_{\text{swim}} = 0.5 \times \cos(120^\circ) = -0.25 \, \text{m/s} \] Step 2: Conclusion.
The velocity of water must balance the swimmer's velocity component to ensure the swimmer reaches the opposite point, thus the speed of water is 0.25 m/s.
Final Answer: \[ \boxed{0.25 \, \text{m/s}} \]