Change in Momentum during the Impact with the Ground

When a body of mass m falls from a height h1 and rises to a height h2, the magnitude of the change in momentum during the impact with the ground can be calculated by considering the principles of conservation of energy and momentum.

Principle of Conservation of Energy:
According to the principle of conservation of energy, the total mechanical energy of the system remains constant. In this case, the mechanical energy of the system consists of the potential energy and kinetic energy of the body.

Principle of Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. In this case, the only external force acting on the body is due to the impact with the ground.

Calculation of Change in Momentum:
1. Initial State:
- The body is at a height h1 above the ground.
- Its initial velocity is zero, so its initial momentum is also zero.

2. Falling:
- As the body falls, its potential energy is converted into kinetic energy according to the law of conservation of energy.
- The body gains momentum as it accelerates due to the force of gravity.
- At the moment of impact with the ground, the body's kinetic energy is maximized while its potential energy is zero.

3. Rising:
- After the impact, the body rebounds and rises to a height h2.
- Its kinetic energy decreases as it rises, and its potential energy increases.
- The body loses momentum as it decelerates due to the upward force applied by the ground.

4. Final State:
- The body reaches a height h2 above the ground.
- Its final velocity is zero, so its final momentum is also zero.

5. Change in Momentum:
- The change in momentum of the body during the impact with the ground can be calculated as the difference between its initial and final momenta.
- Since the initial and final momenta are both zero, the change in momentum is also zero.

Conclusion:
The magnitude of the change in momentum during the impact with the ground is zero. This implies that the momentum of the body is conserved in this system, as there are no external forces acting on it during the fall and rise.