A swimmer wants to cross a 200 m wide river which is flowing at a speed of 2 m/s. the velocity of the swimmer with respect to the river is 1 m/s. how far from the point directly opposite to the starting point does the swimmer reach the opposite bank ?

Options

A. 200 m
B. 400 m
C. 600 m
D. 800 m

Answer

To solve the problem of how far the swimmer reaches from the point directly opposite to the starting point, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Width of the river (D) = 200 m
- Velocity of the river (Vr) = 2 m/s
- Velocity of the swimmer with respect to the river (Vs) = 1 m/s

2. **Calculate the Time Taken to Cross the River:**
The time (t) taken by the swimmer to cross the river can be calculated using the formula:
\[ t = \frac{D}{Vs} \]
Substituting the values:
\[ t = \frac{200 \text{ m}}{1 \text{ m/s}} = 200 \text{ seconds} \]

3. **Calculate the Distance Drifted Downstream:**
While the swimmer is crossing the river, the river is also flowing downstream. The distance (d) drifted downstream can be calculated using the formula:
\[ d = Vr \times t \]
Substituting the values:
\[ d = 2 \text{ m/s} \times 200 \text{ seconds} = 400 \text{ m} \]

4. **Conclusion:**
The swimmer reaches a point 400 m downstream from the point directly opposite to the starting point.

### Final Answer:
The swimmer reaches the opposite bank 400 meters downstream from the point directly opposite to the starting point.

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