Two boats A and B having same speed relative to river are moving in a river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current. Boat B moves normal to the river as observed by the observer on the ground.

Options

A. To a ground observer Boat B moves faster than A
B. To a ground observer boat A moves faster than B
C. to the given moving observer boat B moves faster than A
D. To the given moving observer the speeds of boat A and B are same

Explanation

To solve the problem, we need to analyze the motion of both boats A and B in relation to the river current and the observers.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two boats, A and B, moving in a river with the same speed relative to the river.
- Boat A moves perpendicular (normal) to the river current as observed by an observer who is moving with the velocity of the river current.
- Boat B moves perpendicular (normal) to the river current as observed by an observer on the ground.

2. **Defining the Velocities**:
- Let the speed of both boats relative to the river be \( v \).
- Let the speed of the river current be \( u \).

3. **Analyzing Boat A**:
- For the observer moving with the river current, Boat A moves directly across the river. Its velocity relative to this observer is \( v \) (perpendicular to the current).
- However, from the perspective of a ground observer, Boat A also has a component of velocity in the direction of the river current due to the river's flow.
- The resultant velocity of Boat A as seen by the ground observer can be calculated using the Pythagorean theorem:
\[ V_A = \sqrt{v^2 + u^2} \]
- This is because Boat A has a velocity \( v \) across the river and \( u \) downstream due to the river current.

4. **Analyzing Boat B**:
- For Boat B, which moves perpendicular to the river as observed from the ground, its velocity relative to the ground is simply \( v \) (perpendicular to the current) since it is not affected by the river's current in the direction of its motion.
- The velocity of Boat B remains \( v \) as it moves straight across the river.

5. **Comparing the Velocities**:
- From the ground observer's perspective:
- The velocity of Boat A is \( V_A = \sqrt{v^2 + u^2} \).
- The velocity of Boat B is \( V_B = v \).
- Since \( \sqrt{v^2 + u^2} > v \) (because \( u > 0 \)), it follows that:
\[ V_A > V_B \]

6. **Conclusion**:
- To a ground observer, Boat A moves faster than Boat B.

### Final Answer:
To a ground observer, Boat A moves faster than Boat B.