The width of a river is `2sqrt3km`.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`

Explanation

To find the displacement of the boat as it crosses the river, we can follow these steps:

### Step 1: Understand the Problem
The boat is rowed perpendicular to the banks of the river, which means it moves straight across the river. The width of the river is given as \(2\sqrt{3} \, \text{km}\), and the drift due to the river's flow is \(2 \, \text{km}\).

### Step 2: Identify the Coordinates
Let's set up a coordinate system:
- The starting point \(O\) of the boat can be considered at the origin \((0, 0)\).
- As the boat rows across the river, it moves vertically to the point \(A\) at \((0, 2\sqrt{3})\) (the width of the river).
- Due to the drift, the boat ends up at point \(P\) which is horizontally displaced by \(2 \, \text{km}\). Therefore, the coordinates of point \(P\) will be \((2, 2\sqrt{3})\).

### Step 3: Calculate the Displacement
The displacement \(D\) is the straight-line distance from the starting point \(O\) to the final point \(P\). We can use the distance formula to find this:

\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of points \(O\) and \(P\):

\[ D = \sqrt{(2 - 0)^2 + (2\sqrt{3} - 0)^2} \]

Calculating each term:

\[ D = \sqrt{2^2 + (2\sqrt{3})^2} \]

\[ D = \sqrt{4 + 4 \cdot 3} \]

\[ D = \sqrt{4 + 12} \]

\[ D = \sqrt{16} \]

\[ D = 4 \, \text{km} \]

### Conclusion
The displacement of the boat is \(4 \, \text{km}\).

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