In the figure shown a river of width `4m` is flowing with speed of `5m//s`. A swimmer whose swimming speed relative to the water is `4m/s`, starts swimming from a point `A` on a bank. On the other bank `B` is a point which is directly opposite to `A`. What minimum distance (in m) the swimmer will have to walk on the other bank to reach the point `B`.

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem, we need to determine the minimum distance the swimmer will have to walk on the other bank to reach point B after swimming across the river.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Width of the river (distance to swim across) = \(4 \, \text{m}\)
- Speed of the river = \(5 \, \text{m/s}\)
- Speed of the swimmer relative to the water = \(4 \, \text{m/s}\)

2. **Determine the Time Taken to Swim Across the River:**
- The time taken to swim across the river can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is the width of the river (4 m) and the speed of the swimmer relative to the water is 4 m/s.
- Therefore, the time taken to swim across is:
\[ \text{Time} = \frac{4 \, \text{m}}{4 \, \text{m/s}} = 1 \, \text{s} \]

3. **Calculate the Drift Caused by the River:**
- While the swimmer is swimming across, the river is also flowing. The swimmer will be carried downstream due to the river's current.
- The distance drifted downstream (BC) can be calculated using:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- The speed of the river is 5 m/s and the time taken to swim across is 1 s.
- Thus, the distance drifted downstream is:
\[ BC = 5 \, \text{m/s} \times 1 \, \text{s} = 5 \, \text{m} \]

4. **Conclusion:**
- The swimmer will have to walk the distance BC on the other bank to reach point B. Therefore, the minimum distance he will have to walk is:
\[ \text{Distance BC} = 5 \, \text{m} \]

### Final Answer:
The minimum distance the swimmer will have to walk on the other bank to reach point B is **5 meters**.

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