Kinetic Energy During Takeoff
During take-off, the body parts move with different accelerations. In the initial stage of a take-off, the upper part of the body is being accelerated but the bottom part (feet and shanks) stays relatively motionless. It is believed that the kinetic energy of the upper segments of the body is redistributed among all the body parts. (see "Work and Power Production in the Vertical Jump Under Various Loads Fixed to the Upper Body or Ankles". C. Corwin, V. Zatsiorsky, V. Fortney, Dept. of Kinesiology, The Pennsylvania State University, University Park, PA 16802.)
The human body during vertical jumps could be conveniently viewed as a two mass system, the upper body and the lower body. The upper body is accelerated and it's kinetic energy "pulls" the lower body up and off the ground.
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Both of the guys in the picture below started on the same command to go. We can see the difference how much slower "pushing" is than "pulling." This is the importance of the upper body leading the way which pulls the lower body. The arms must accelerate, leading the way, instead of the head being pushed by the lower body.