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. (a)`2 ms^(-1)`
B. (b)`4 ms^(-1)`
C. (c)`6 ms^(-1)`
D. (d)`8 ms^(-1)`

Explanation

To solve the problem, we need to find the speed of the flow of the water when the swimmer crosses the river in the shortest possible time. Let's break down the solution step by step.

### Step 1: Understand the Given Information
- The speed of the swimmer in still water (V_swimmer) = 3 m/s
- The average speed of the swimmer while crossing the river (V_average) = 5 m/s

### Step 2: Set Up the Relationship
When the swimmer crosses the river in the shortest possible time, the swimmer's velocity (V_swimmer) and the velocity of the river (V_river) can be related using the Pythagorean theorem. The average speed is the resultant of these two velocities.

### Step 3: Use the Pythagorean Theorem
The relationship can be expressed as:
\[ V_{average}^2 = V_{swimmer}^2 + V_{river}^2 \]

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ 5^2 = 3^2 + V_{river}^2 \]
\[ 25 = 9 + V_{river}^2 \]

### Step 5: Solve for V_river
Now, isolate \( V_{river}^2 \):
\[ V_{river}^2 = 25 - 9 \]
\[ V_{river}^2 = 16 \]

Taking the square root of both sides gives:
\[ V_{river} = \sqrt{16} \]
\[ V_{river} = 4 \, \text{m/s} \]

### Conclusion
The speed of the flow of water is **4 m/s**.

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