A ball of mass m is thrown straight up. It goes to a maximum height and then returns. Finally it strikes ground. In the whole process.

Options

A. The momentum of the ball remains conserved
B. The momentum of the earth remains conserved.
C. The momentum of the ball and earth system remains conserved
D. none of the above

Answer

To solve the problem, we need to analyze the momentum of the ball and the Earth during the entire process of the ball being thrown upwards, reaching its maximum height, and then falling back down to the ground.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a ball of mass \( m \) thrown straight up against the gravitational pull of the Earth.
- The Earth has a much larger mass compared to the ball.

2. **Identifying Forces**:
- As the ball is thrown upwards, it experiences a gravitational force \( F = mg \) acting downwards (where \( g \) is the acceleration due to gravity).
- The Earth also experiences an equal and opposite force due to Newton's third law, but because of its massive size, the effect on the Earth's motion is negligible.

3. **Momentum of the Ball**:
- When the ball is thrown upwards, it has an initial momentum given by \( p_{initial} = m \cdot u \) (where \( u \) is the initial velocity).
- As the ball rises, it slows down due to gravity until it reaches its maximum height (where its velocity becomes zero) and then starts to fall back down.

4. **Momentum Change**:
- When the ball is at its maximum height, its momentum is \( p_{max\ height} = 0 \).
- As it falls back down, its momentum becomes \( p_{final} = m \cdot v \) (where \( v \) is the final velocity just before hitting the ground).

5. **Momentum of the Earth**:
- The Earth experiences a change in momentum due to the force exerted by the ball. However, because of its large mass, the change in velocity of the Earth is extremely small and often negligible.

6. **Conservation of Momentum**:
- If we consider the ball and the Earth as a single system, the internal forces (gravitational attraction between the ball and Earth) do not change the total momentum of the system.
- Thus, the momentum of the ball and Earth system remains conserved throughout the process.

7. **Conclusion**:
- The momentum of the ball and Earth system remains conserved, even though the individual momenta of the ball and the Earth are not conserved due to external forces acting on them.

### Final Answer:
The momentum of the ball and Earth system remains conserved.