A river is flowing wih velocity `2 m//s`. A boat is moving downstream. Velocity of boat in still water is `3 m//s`. A person standing on boat throws a ball vertically upwards w.r.t. himself with a velocity to `10 m//s`. At the topmost point the velocity of ball w.r.t. man standing on boat, w.r.t. river and w.r.t. ground respectively are

Options

A. `5, 3, 0 m//s`
B. `0, 3, 5 m//s`
C. `0, 5, 3 m//s`
D. None of these

Explanation

To solve the problem, we need to find the velocities of the ball at the topmost point with respect to the man on the boat, the river, and the ground.

### Step-by-Step Solution:

1. **Understanding the velocities:**
- The velocity of the river (Vr) = 2 m/s (downstream).
- The velocity of the boat in still water (Vb) = 3 m/s (downstream).
- The velocity of the boat with respect to the ground (Vbg) = Vr + Vb = 2 m/s + 3 m/s = 5 m/s (downstream).

2. **Velocity of the ball with respect to the man on the boat:**
- The man throws the ball vertically upwards with a velocity of 10 m/s relative to himself.
- At the topmost point of its trajectory, the vertical component of the ball's velocity becomes 0 m/s.
- Therefore, the velocity of the ball with respect to the man on the boat (Vbm) = 0 m/s.

3. **Velocity of the ball with respect to the river:**
- When the ball is thrown, it has a horizontal velocity equal to the velocity of the boat with respect to the ground, which is 5 m/s (since the ball is moving with the boat).
- The river is moving at 2 m/s downstream.
- Thus, the velocity of the ball with respect to the river (Vbr) = Vbg - Vr = 5 m/s - 2 m/s = 3 m/s.

4. **Velocity of the ball with respect to the ground:**
- The ball maintains its horizontal velocity of 5 m/s (in the direction of the river) since there are no horizontal forces acting on it after it is thrown.
- Therefore, the velocity of the ball with respect to the ground (Vbg) = 5 m/s.

### Final Results:
- Velocity of the ball with respect to the man on the boat: **0 m/s**
- Velocity of the ball with respect to the river: **3 m/s**
- Velocity of the ball with respect to the ground: **5 m/s**

### Summary:
The final answer is:
- With respect to the man on the boat: **0 m/s**
- With respect to the river: **3 m/s**
- With respect to the ground: **5 m/s**