A boat travels from south bank to north bank of a river with a maximum speed of `8km//h`. A river current flows from west to east with a speed of `4km//h`. To arrive at a point opposite to the point of start, the boat should start at an angle:

Options

A. `tan^(-1)(1//2)` W of N
B. `tan^(-1)(1//2)` N of W
C. `30^(@` W of N
D. `30^(@` N of W

Explanation

To solve the problem of the boat traveling across a river with a current, we need to determine the angle at which the boat should head to reach a point directly opposite its starting position on the north bank.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Speed of the boat (Vb) = 8 km/h (maximum speed)
- Speed of the river current (Vr) = 4 km/h (flowing from west to east)

2. **Understand the Motion**:
- The boat is moving from the south bank to the north bank.
- The river current will push the boat eastward while it is trying to move northward.

3. **Set Up the Components**:
- Let θ be the angle at which the boat must head relative to the north direction.
- The northward component of the boat's velocity (Vb) is given by:
\[ Vb_y = Vb \cdot \cos(θ) = 8 \cdot \cos(θ) \]
- The eastward component of the boat's velocity is given by:
\[ Vb_x = Vb \cdot \sin(θ) = 8 \cdot \sin(θ) \]

4. **Condition for Reaching the Opposite Point**:
- To arrive directly opposite the starting point, the eastward component of the boat's velocity must equal the speed of the river current:
\[ Vb_x = Vr \]
- Therefore, we can set up the equation:
\[ 8 \cdot \sin(θ) = 4 \]

5. **Solve for θ**:
- Rearranging the equation gives:
\[ \sin(θ) = \frac{4}{8} = \frac{1}{2} \]
- The angle θ that satisfies this equation is:
\[ θ = 30^\circ \]

6. **Determine the Direction**:
- Since the boat is heading north but needs to compensate for the eastward current, the angle of 30° is measured from the north towards the west. This means the boat should head "30° west of north".

### Final Answer:
The boat should start at an angle of **30° west of north**.