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 :-

Options

A. Height of 100m
B. Height of 150m
C. Heighest point
D. The ground

Answer

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 the Motion**:
- When a stone is thrown upwards, it moves against the force of gravity. Initially, it has a certain velocity (let's denote it as \( v_0 \)) when thrown.

2. **Maximum Height**:
- The stone will rise to a maximum height of 200 meters. At this point, the stone's velocity becomes zero momentarily before it starts falling back down.

3. **Velocity During Ascent**:
- As the stone ascends, its velocity decreases due to the acceleration due to gravity acting downwards. The stone's velocity at any point during its ascent can be expressed as:
\[ v = v_0 - gt \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)) and \( t \) is the time since it was thrown.

4. **Relative Velocity**:
- The relative velocity of the stone with respect to the Earth is the velocity of the stone minus the velocity of the Earth (which is stationary). Therefore, the relative velocity \( v_{rel} \) is simply the velocity of the stone itself since the Earth’s velocity is zero:
\[ v_{rel} = v \]

5. **When is Relative Velocity Maximum?**:
- The relative velocity of the stone with respect to the Earth is maximum when the stone is at the point of release (the ground) because this is when the stone has its maximum initial velocity \( v_0 \). As the stone rises, its velocity decreases until it reaches zero at the maximum height.

6. **Conclusion**:
- Therefore, the relative velocity of the stone with respect to the Earth will be maximum at the time of release, which is at the ground level.

### Final Answer:
The relative velocity of the stone with respect to the Earth will be maximum at the ground level (when it is thrown).