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

Concept:

To find the velocity of the stream, we decompose the swimmer's velocity into components parallel and perpendicular to the flow of water.

Let V_w be the speed of the water (stream), and V_s be the speed of the swimmer.

The component of the swimmer's velocity in the opposite direction of the flow is given by:

V_s (opposite) = V_s × cos(180° - θ)

where θ is the angle between the swimmer’s direction and the flow of the water.

Calculation:

Given θ = 120°, V_s = 0.5 m/s

⇒ V_s (opposite) = 0.5 × cos(180° - 120°)

⇒ V_s (opposite) = 0.5 × cos(60°)

We know, cos(60°) = 0.5

⇒ V_s (opposite) = 0.5 × 0.5

⇒ V_s (opposite) = 0.25 m/s

So, the velocity of the flow (stream), V_w, will also be 0.25 m/s, so that the person can oppose the stream and reach the opposite side directly without being drifted by the stream.

∴ The velocity of the stream is 0.25 m/s.