A stone is thrown upwards and it rises to a height 0f 200m. The relative velocity of the stone with respect to the earth will be maximum at :-

Explanation

To solve the problem, we need to analyze the motion of the stone thrown upwards and determine when its relative velocity with respect to the Earth is maximum.

### Step-by-Step Solution:

1. **Understanding Relative Velocity**:
The relative velocity of the stone with respect to the Earth can be defined as:
\[ v_{rel} = v_{stone} - v_{earth} \]
Since the Earth is stationary, we can simplify this to:
\[ v_{rel} = v_{stone} \]

2. **Motion of the Stone**:
When the stone is thrown upwards, it rises to a maximum height of 200 m. As it rises, its velocity decreases due to the acceleration due to gravity acting downwards. At the maximum height, the velocity of the stone becomes zero.

3. **Velocity at Different Points**:
- **At the moment of projection**: The stone has a maximum upward velocity.
- **At the maximum height (200 m)**: The stone's velocity is zero.
- **Just before hitting the ground**: The stone is falling back down, and its velocity increases again due to gravity.

4. **Identifying Maximum Relative Velocity**:
The relative velocity of the stone with respect to the Earth will be maximum at two points:
- At the moment of projection (when it is thrown upwards).
- Just before it hits the ground (when it is falling back down).

5. **Conclusion**:
Since the question asks for when the relative velocity is maximum, we can conclude that the relative velocity of the stone with respect to the Earth is maximum just before it hits the ground.

### Final Answer:
The relative velocity of the stone with respect to the Earth will be maximum just before hitting the ground.

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