A boatman moves his boat with a velocity 'v' (relative to water) in river and finds to his surprise that velocity of river 'u' (with respect to ground) is more than 'v'. He has to reach a point directly opposite to the starting point on another bank by travelling minimum possible distance. Then

Options

A. he must steer the boat (with velocity v) at certain angle with river flow so that he can reach the opposite point on other bank directly.
B. his velocity 'v' must be towards directly opposite point, So, that he can travel rest of distance by walking on other bank to reach the directly opposite point.
C. boatman should maintain velocity v of boat at certain angle greater than `90^(@)` with direction of river flow to minimize drifting and then walk rest of distance on other bank.
D. boat velocity 'v' should be at an angle less than `90^(@)` with direction of river flow to minimize the drift and then walk to the point.

Answer

To solve the problem, we need to analyze the motion of the boatman in the river. The goal is to reach a point directly opposite the starting point on the other bank while minimizing the distance traveled.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- Let the velocity of the boat relative to the water be \( v \).
- Let the velocity of the river (current) relative to the ground be \( u \).
- Given that \( u > v \), the river flows faster than the boat can move.

2. **Setting Up the Coordinate System**:
- Assume the river flows horizontally from left to right.
- The boatman starts at point \( O \) on the left bank and wants to reach point \( A \) directly opposite on the right bank.

3. **Analyzing the Boat's Motion**:
- The boat must be directed at an angle \( \theta \) with respect to the river flow to counteract the current and reach point \( A \).
- The boat's velocity can be broken down into two components:
- A component against the current (upstream) to counteract the river's velocity.
- A vertical component to cross the river.

4. **Using Velocity Components**:
- The upstream component of the boat's velocity can be expressed as \( v \cos(\theta) \).
- The vertical component (across the river) is \( v \sin(\theta) \).

5. **Condition for Reaching Point A**:
- To reach point \( A \), the upstream component must equal the river's velocity:
\[ v \cos(\theta) = u \]
- This means \( \theta \) must be such that the boat's upstream motion can counter the river's flow.

6. **Finding the Angle**:
- Rearranging the equation gives:
\[ \cos(\theta) = \frac{u}{v} \]
- Since \( u > v \), \( \cos(\theta) \) will be negative, indicating that \( \theta \) must be greater than 90 degrees.

7. **Conclusion**:
- The boatman should steer the boat at an angle greater than 90 degrees with respect to the direction of the river flow to reach the opposite bank directly.

### Final Answer:
The correct option is that the boatman should maintain a velocity \( v \) of the boat at an angle greater than 90 degrees with the direction of river flow.

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