Question

A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is __________.

Hint:

For the "shortest path" (directly opposite), the horizontal component of velocity must be zero: $v_{swimmer} \sin \theta = v_{river}$.

Answer 1

Correct Answer: 5

Step 1: Let $v_s = 10$ m/s be swimmer's speed and $v_r$ be river speed.
Step 2: Angle with flow is 120°, so angle with the normal (upstream) is $120^\circ - 90^\circ = 30^\circ$.
Step 3: To reach directly opposite, the horizontal component of swimmer's velocity must cancel river flow: $v_s \sin 30^\circ = v_r$.
Step 4: $10 \times (1/2) = v_r \implies v_r = 5 \text{ m/s}$.