A river is of width 120m which flows at a speed pf `8ms^(-1)`. If a man swims with a speed of `5ms^(-1)` at an angle of `127^(@)` with the stream, his drift on reaching other bank is

Options

A. 50 m
B. 150 m
C. 200 m
D. 300 m

Answer

To solve the problem, we need to determine the drift of the man as he swims across the river. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Problem
We have a river that is 120 meters wide and flows at a speed of 8 m/s. A man swims at a speed of 5 m/s at an angle of 127° with respect to the direction of the river flow. We need to find out how far downstream (drift) he will end up when he reaches the opposite bank.

### Step 2: Resolve the Swimming Velocity
The swimming velocity of the man can be resolved into two components:
- **Vertical Component (across the river)**: This is the component of his swimming speed that helps him cross the river.
- **Horizontal Component (along the river)**: This is the component of his swimming speed that contributes to the drift downstream.

The angle with respect to the river flow is given as 127°. To find the angle with respect to the perpendicular direction (which is 90°), we calculate:
- Angle with respect to vertical = 127° - 90° = 37°.

Now, we can resolve the velocity:
- Vertical component \( V_{y} = V_{man} \cdot \cos(37°) \)
- Horizontal component \( V_{x} = V_{man} \cdot \sin(37°) \)

Where \( V_{man} = 5 \, m/s \).

Using trigonometric values:
- \( \cos(37°) \approx \frac{4}{5} \)
- \( \sin(37°) \approx \frac{3}{5} \)

Calculating the components:
- \( V_{y} = 5 \cdot \cos(37°) = 5 \cdot \frac{4}{5} = 4 \, m/s \)
- \( V_{x} = 5 \cdot \sin(37°) = 5 \cdot \frac{3}{5} = 3 \, m/s \)

### Step 3: Calculate the Time to Cross the River
The time taken to cross the river can be calculated using the width of the river and the vertical component of the man's swimming speed:
\[ \text{Time} = \frac{\text{Width of the river}}{V_{y}} = \frac{120 \, m}{4 \, m/s} = 30 \, s \]

### Step 4: Calculate the Drift
During the time the man is swimming across the river, he will also be carried downstream by the river's current. The effective horizontal speed (downstream) is the sum of the river's speed and the man's horizontal component:
\[ V_{effective} = V_{river} - V_{x} = 8 \, m/s - 3 \, m/s = 5 \, m/s \]

Now, we can calculate the drift:
\[ \text{Drift} = V_{effective} \cdot \text{Time} = 5 \, m/s \cdot 30 \, s = 150 \, m \]

### Final Answer
The drift on reaching the other bank is **150 meters**.

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