The width of a river is `2sqrt(3)` km. A boat is rowed in direction perpendicular to the banks of river. If the drift of the boat due to flow is 2 km, the displacement of the boat is

Options

A. 3 km
B. 6 km
C. 5 km
D. 4 km

Answer

To solve the problem, we need to find the displacement of the boat as it crosses the river while being affected by the flow of the river. The width of the river and the drift due to the current will help us form a right triangle, where we can use the Pythagorean theorem to find the displacement.

### Step-by-Step Solution:

1. **Identify the given values:**
- Width of the river (W) = \(2\sqrt{3}\) km
- Drift of the boat (D) = 2 km

2. **Visualize the scenario:**
- The boat is rowed straight across the river, which means it moves perpendicular to the banks.
- Due to the river's current, the boat drifts downstream while crossing.

3. **Set up the right triangle:**
- The width of the river (W) is one leg of the triangle.
- The drift (D) is the other leg of the triangle.
- The displacement (d) of the boat is the hypotenuse of the triangle.

4. **Apply the Pythagorean theorem:**
- According to the Pythagorean theorem:
\[ d^2 = W^2 + D^2 \]
- Substitute the values:
\[ d^2 = (2\sqrt{3})^2 + (2)^2 \]
- Calculate \(W^2\) and \(D^2\):
\[ (2\sqrt{3})^2 = 4 \times 3 = 12 \]
\[ (2)^2 = 4 \]
- Now substitute these values back into the equation:
\[ d^2 = 12 + 4 = 16 \]

5. **Calculate the displacement (d):**
- Take the square root of both sides:
\[ d = \sqrt{16} = 4 \text{ km} \]

6. **Conclusion:**
- The displacement of the boat is \(4\) km.

### Final Answer:
The displacement of the boat is \(4\) km.

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