A swimmer can swim in still water with a speed of 3 `ms^(-1)` While crossing a river his average speed is 5 `ms^(-1)` If crosses the river in the shortest possible time, what is the speed of flow of water ?

Options

A. `2 ms^(-1)`
B. `4 ms^(-1)`
C. `6 ms^(-1)`
D. `8 ms^(-1)`

Explanation

To solve the problem, we need to find the speed of the flow of the river based on the swimmer's speed in still water and the average speed while crossing the river.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of the swimmer in still water (V_swimmer) = 3 m/s
- Average speed while crossing the river (V_crossing) = 5 m/s

2. **Understand the Relationship:**
- When the swimmer crosses the river, his effective speed (V_crossing) is the resultant of his swimming speed and the speed of the river (V_river).
- This can be visualized as a right triangle where:
- One side is the speed of the swimmer in still water (3 m/s).
- The other side is the speed of the river (unknown).
- The hypotenuse is the average speed while crossing (5 m/s).

3. **Apply Pythagorean Theorem:**
- According to the Pythagorean theorem:
\[ V_crossing^2 = V_swimmer^2 + V_river^2 \]
- Substituting the known values:
\[ 5^2 = 3^2 + V_river^2 \]
- This simplifies to:
\[ 25 = 9 + V_river^2 \]

4. **Solve for V_river:**
- Rearranging the equation gives:
\[ V_river^2 = 25 - 9 \]
\[ V_river^2 = 16 \]
- Taking the square root of both sides:
\[ V_river = \sqrt{16} = 4 \text{ m/s} \]

5. **Conclusion:**
- The speed of the flow of the river is **4 m/s**.