A swimmer crosses a river of width d flowing at velocity v. While swimming, he keeps himself always at an angle of `120^(@)` with the river flow and on reaching the other end. He finds a drift of d/2 in the direction of flow of river. The speed of the swimmer with respect to the river is :

Options

A. `(2-sqrt(3))v`
B. `2(2-sqrt(3))v`
C. `4(2-sqrt(3))v`
D. `(2+sqrt(3))v`

Explanation

To solve the problem, we need to analyze the swimmer's motion across the river while considering the river's current. Let's break it down step by step.

### Step 1: Understand the Problem
The swimmer is crossing a river of width \( d \) while swimming at an angle of \( 120^\circ \) with respect to the flow of the river, which has a velocity \( v \). The swimmer experiences a drift of \( \frac{d}{2} \) downstream due to the river's current.

### Step 2: Define the Components of Velocity
Let the speed of the swimmer with respect to the river be \( V_s \). The swimmer's velocity can be broken down into two components:
- The component along the river flow (x-direction): \( V_s \cos(120^\circ) \)
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