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The work done on the body of the jumper by the force F during the jump is the product of the force F and the distance c over which this force acts (see Appendix A). At the full height of the jump H (before the jumper starts falling back to ground), the velocity of the jumper is zero. At this point, the kinetic energy is fully converted to potential energy as the center of mass of the jumper is raised to a height (c + H). It is a common mistake to assume that the height to which a person can jump on the moon increases in direct proportion to the decrease in weight. That is, if a person can jump to a height of 60 cm on Earth, that same person can jump up 6. Note that the ratio H /H 11 is true only for a particular choice of F in the calculation (see Exercise 3-2). The additional height is attained by using part of the kinetic energy of the run to raise the center of gravity o the ground. Let us calculate the height attainable in a running jump if the 1 2 jumper could use all his/her initial kinetic energy ( mv ) to raise his/her body 2 o the ground. If this energy were completely converted to potential energy by raising the center of gravity to a height H, then 1 2 MgH mv (3. Then we must remember that the center of gravity of a person is already about 1 m above the ground. With little extra eort, the jumper can alter the position of his body so that it is horizontal at its maximum height. Thus, our nal estimate for the maximum height of the running high jump is v2 H + 1. Obviously, it is not possible for a jumper to convert all the kinetic energy of a full-speed run into potential energy. In the unaided running high jump, only the force exerted by the feet is available to alter the direction of the running start. The situation is quite dierent in pole vaulting, where, with the aid of the pole, the jumper can in fact use most of the kinetic energy to raise his/her center of gravity. These gures would agree even more closely had we included in our estimate the fact that the jumper must retain some forward velocity to carry him/her over the bar.

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