posted by lau .
The feet of a standing person of mass m exert a force equal to mg on the floor, and the floor exerts an equal and opposite force upwards on the feet, which we call the normal force. During the extension phase of a vertical jump, the feet exert a force on the floor that is greater than mg, so the normal force is greater than mg. We can use this result and Newton's second law to calculate the acceleration of the jumper: a = Fnet / m = (n - mg)/ m.
Using energy ideas, we know that work is performed on the jumper to give him or her kinetic energy. But the normal force can't perform any work here because the feet don't undergo any displacement. How is energy transferred to the jumper?
The jumper is not a rigid body.
The problem discussed the "extension phase".
During that phase the force is moving the center of mass of the jumper up (not the feet but somewhere around the belly button), thereby creating a force times the displacement of the CG of the person.
(It is hard to jump up without crouching down first :)