A person aiming to reach exactly opposite point on the bank of a stream is swimming with a speed of 0.6 m/s at an angle of `120^(@)` with the direction of flow of water . The speed of water in the stream is

Options

A. 0.3 m/s
B. 0.5 m/s
C. 1.0 m/s
D. 0.433 m/s

Answer

To solve the problem, we need to analyze the swimmer's velocity and how it relates to the flow of the stream. Here’s a step-by-step solution:

### Step 1: Understand the swimmer's velocity
The swimmer swims with a speed of \(0.6 \, \text{m/s}\) at an angle of \(120^\circ\) with respect to the direction of the stream.

### Step 2: Resolve the swimmer's velocity into components
To find the effective velocity of the swimmer in the direction opposite to the flow of the stream, we need to resolve the swimmer's velocity into two components:
- One component in the direction opposite to the flow of the stream.
- The other component perpendicular to the flow of the stream.

The angle between the swimmer's direction and the direction opposite to the flow of the stream is \(180^\circ - 120^\circ = 60^\circ\).

Using the cosine of this angle, we can find the component of the swimmer's velocity in the direction opposite to the flow of the stream:

\[ V_{opposite} = V_{swimmer} \cdot \cos(60^\circ) \]

Where:
- \(V_{swimmer} = 0.6 \, \text{m/s}\)
- \(\cos(60^\circ) = \frac{1}{2}\)

### Step 3: Calculate the component of the swimmer's velocity
Substituting the values:

\[ V_{opposite} = 0.6 \cdot \frac{1}{2} = 0.3 \, \text{m/s} \]

### Step 4: Determine the speed of the stream
Since the swimmer aims to reach the point directly opposite on the bank, the effective velocity of the swimmer in the direction opposite to the flow of the stream must equal the speed of the stream.

Thus, the speed of the stream \(V_{stream}\) is equal to the component of the swimmer's velocity in the opposite direction:

\[ V_{stream} = V_{opposite} = 0.3 \, \text{m/s} \]

### Final Answer
The speed of the water in the stream is \(0.3 \, \text{m/s}\).

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