The Key is the System
The law of conservation of momentum states that the total momentum of a closed system remains constant. The trick is understanding what constitutes our "system" in this case.
* The ball alone is NOT a closed system. The Earth exerts a gravitational force on the ball, and the ball exerts an equal and opposite force on the Earth (Newton's Third Law).
* The correct closed system is the ball AND the Earth.
How it Works
1. Initial Momentum: Initially, the ball has some small momentum, while the Earth has an enormous but essentially negligible momentum due to its massive size.
2. As the ball falls:
* The ball's momentum increases downwards.
* Simultaneously, the Earth's momentum increases upward (though incredibly small).
3. Conservation: The increase in the ball's momentum is exactly balanced by the minuscule increase in the Earth's momentum. This keeps the total momentum of the ball-Earth system constant throughout the fall.
An Analogy
Imagine two ice skaters standing still, one much heavier than the other. If the heavier skater pushes the lighter skater, the lighter skater will move much faster. The heavier skater will also move, but much more slowly. The total momentum of the system (both skaters) remains zero.
In Conclusion
While it might seem like the ball's momentum increases "out of nowhere," the Earth's momentum also changes to perfectly balance it. The law of conservation of momentum is upheld, but we must consider the entire system involved to see it.
