JUMPING OFF THE GROUND (10 points possible)

A person of mass m jumps off the ground. Suppose the person pushes off the ground with a constant force of magnitude F for T seconds.

What was the magnitude of the displacement of the center of mass of the person while they were in contact with the ground? Express your answer in terms of m, F, T, and g as needed.

To solve this problem, we need to consider the principles of Newton's laws of motion.

When the person jumps off the ground, they exert a constant force of magnitude F on the ground for T seconds. According to Newton's third law, the ground exerts an equal and opposite force on the person.

Since the person is pushing off the ground with a constant force F, the net force acting on them is zero (assuming no other external forces are acting). Therefore, according to Newton's second law, the person's acceleration is zero.

The center of mass of an object remains at rest or moves with constant velocity when the net external force acting on it is zero. In this case, since the person's acceleration is zero, the net external force acting on them is zero. Hence, the center of mass of the person remains at rest or moves with constant velocity.

During the time T when the person is pushing off the ground, there is no displacement of the center of mass. Therefore, the magnitude of the displacement of the center of mass of the person while they were in contact with the ground is zero.

In summary, the magnitude of the displacement of the center of mass of the person while they were in contact with the ground is zero.