A river `500m` wide is flowing at a rate of `4 m//s.` A boat is sailing at a velocity of `10 m//s` with respect to the water, in a direction perpendicular to the river. The time taken by the boat to reach the opposite bank

Options

A. 30 s
B. 40 s
C. 50 s
D. 60 s

Explanation

To solve the problem, we need to determine the time taken by the boat to reach the opposite bank of the river. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Problem
The river is 500 m wide, and the boat is moving perpendicular to the flow of the river. The velocity of the river is 4 m/s, and the velocity of the boat with respect to the water is 10 m/s.

### Step 2: Identify the Relevant Velocities
- Velocity of the river (V_r) = 4 m/s (this will affect the boat's downstream drift but not the time to cross).
- Velocity of the boat (V_b) = 10 m/s (perpendicular to the river).

### Step 3: Calculate the Time to Cross the River
Since the boat is moving perpendicular to the river, we can calculate the time taken to cross the river using the formula:

\[ \text{Time} (t) = \frac{\text{Distance}}{\text{Velocity}} \]

In this case, the distance to cross is the width of the river, which is 500 m, and the velocity of the boat is 10 m/s.

\[ t = \frac{500 \text{ m}}{10 \text{ m/s}} = 50 \text{ seconds} \]

### Step 4: Conclusion
The time taken by the boat to reach the opposite bank is 50 seconds.

### Final Answer
The time taken by the boat to reach the opposite bank is **50 seconds**.

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