A skydiver jumps out of a plane. Does the mechanical energy of the jumper change while she is falling? Ignore the effects of air resistance.

If friction is ignored, the total mechanical energy (kinetic + potential) does not change.

However, this is s stupid question. Would a skydiver jump without a parachute? You need the air resistance to stay alive.

yes

No, the mechanical energy of the skydiver does not change while she is falling, assuming we ignore the effects of air resistance. Mechanical energy is the sum of potential energy and kinetic energy, and in this case, the only forces acting on the skydiver are gravity and air resistance (which we are ignoring). Gravity converts the potential energy of the skydiver at the beginning into kinetic energy as she falls, and this conversion maintains a constant total mechanical energy throughout the fall.

To determine whether the mechanical energy of the skydiver changes while she is falling, we need to understand the concept of mechanical energy. Mechanical energy refers to the sum of kinetic energy and potential energy in a system.

When the skydiver jumps out of the plane, she initially has potential energy but no kinetic energy. As she starts to fall, her potential energy decreases while her kinetic energy increases. This happens because potential energy is associated with an object's position or height, whereas kinetic energy is associated with an object's motion.

In the absence of air resistance, the total mechanical energy (the sum of potential and kinetic energy) of the skydiver remains constant throughout the fall. As potential energy decreases, kinetic energy increases such that the sum of the two remains unchanged.

This relationship can be expressed mathematically using the principle of conservation of mechanical energy:

Potential Energy + Kinetic Energy = Constant

So, in conclusion, in the absence of air resistance, the mechanical energy of the skydiver does not change while she is falling.