A battalion of soldiers is ordered to swim across a river `500 m` wide. At what minimum rate should they swim perpendicular to river flow in order to avoid being washed away by the waterfall 300 m downstream. The speed of current being 3m/sec:

Options

A. `10 m//s`
B. `5 m//s`
C. `4 m//s`
D. `3 m//s`

Explanation

To solve the problem, we need to determine the minimum rate at which the soldiers should swim perpendicular to the river flow to avoid being swept away by the waterfall.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Width of the river (D) = 500 m
- Distance downstream to the waterfall (L) = 300 m
- Speed of the river current (Vc) = 3 m/s

2. **Calculate the Time to Reach the Waterfall:**
- The time (T) taken to drift downstream to the waterfall can be calculated using the formula:
\[ T = \frac{L}{Vc} \]
- Substituting the values:
\[ T = \frac{300 \, \text{m}}{3 \, \text{m/s}} = 100 \, \text{s} \]

3. **Determine the Required Swimming Speed:**
- The soldiers need to cross the river in the same time (T) it takes to drift downstream to the waterfall. The speed (Vm) at which they need to swim perpendicular to the river can be calculated using the formula:
\[ Vm = \frac{D}{T} \]
- Substituting the values:
\[ Vm = \frac{500 \, \text{m}}{100 \, \text{s}} = 5 \, \text{m/s} \]

4. **Conclusion:**
- Therefore, the minimum rate at which the soldiers should swim perpendicular to the river flow is **5 m/s**.

### Final Answer:
The minimum rate at which the soldiers should swim perpendicular to the river flow is **5 m/s**.

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