A man can swim in still water with a speed of `2 ms^-1`. If he wants to cross a river of water current speed `sqrt(3) ms^-1` along the shortest possible path, then in which direction should he swim ?

Options

A. a. At an angle `120^@` to the water current.
B. b. At an angle `150^@` to the water current.
C. c. At an angle `90^@` to the water current.
D. d. None of these

Explanation

To solve the problem, we need to determine the angle at which the man should swim in order to cross the river in the shortest possible path, given his swimming speed and the speed of the river current.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of the man in still water, \( V_m = 2 \, \text{m/s} \)
- Speed of the river current, \( V_r = \sqrt{3} \, \text{m/s} \)

2. **Understand the Problem:**
- The man needs to swim at an angle to the current so that his resultant path is directly across the river. This means that the component of his swimming speed that counters the current must equal the speed of the current.

3. **Set Up the Components:**
- Let \( \theta \) be the angle at which the man swims relative to the direction directly across the river (perpendicular to the current).
- The component of the man's swimming speed that counters the current is \( V_m \sin \theta \).
- The component of the man's swimming speed that goes across the river is \( V_m \cos \theta \).

4. **Set Up the Equation:**
- For the man to swim directly across the river, the component of his speed that counters the current must equal the speed of the current:
\[ V_m \sin \theta = V_r \]
- Substituting the known values:
\[ 2 \sin \theta = \sqrt{3} \]

5. **Solve for \( \sin \theta \):**
- Rearranging the equation gives:
\[ \sin \theta = \frac{\sqrt{3}}{2} \]
- This implies:
\[ \theta = 60^\circ \]

6. **Determine the Angle with the Current:**
- The angle we need is the angle between the direction of swimming and the direction of the current. Since the swimmer is swimming at an angle \( \theta \) upstream to counter the current, the angle with respect to the current is:
\[ \text{Angle with current} = 90^\circ + \theta = 90^\circ + 60^\circ = 150^\circ \]

### Final Answer:
The man should swim at an angle of **150 degrees** to the direction of the water current.