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I would like to use something like a kinematic equation to know where the person will be in the jump at a given time. However since I think acceleration is not constant because of the jump force it doesn't seem I can use that equation.

It seems like this is a summation of forces with a kinematic equation but it has been a few years since I've had to do this kind of thing. Any help is greatly appreciated!

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You are correct to say that the acceleration during the jump will not be constant. However, once the jumper is in the air, only gravity (ignoring air resistance and other effects) acts to accelerate the body. The details of the jump are not important to applying kinematic equations to the motion, so long as you know the initial velocity (angle and magnitude).

Also, note that this assumes you're working with a point mass, i.e. no rotation or internal energy, which isn't strictly accurate for the real world. Insofar is you can approximate things to this ideal case, the kinematic equations will track the center of mass of the jumper. Of course, real long jumpers rotate their bodies so their feet land farther from the starting point than their center of mass, but if you're only concerned with where the center of mass is, not the jump distance that would be measured in a competition, kinematics will serve you acceptably well.

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when we toss a ball vertically into the air from our palm, we do work on it. in this way we provide it the necessary energy for it to reach a certain height. similar is your jump. here your feet provide the required force on the floor and the floor pushes you back with an equal and opposite force(Newton's 3rd law). this enables you to attain a certain height above ground. this problem is very easy when we apply conservation of energy principle. the KE that you gain when you jump up = your PE when you have reached the maximum height. equating these two energies we get v=(2gh)^(1/2). why do you think acceleration is not constant? always remember that when a resultant unbalanced external force acts on a body it accelerates. here at height h your body weight mg is the resultant force. thus g here is acceleration which is constant.

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I wasn't sure that the force from jumping would be constant. But I wouldn't really know. – Xavier Jun 11 '11 at 14:52
Highly unlikely to be constant. The angle of the joints changes throughout the motion, and the degree of contraction of the various muscle fibers is changing as well. Also you can jump higher if during the takeoff you are pushing your arms upward, i.e. you are changing the relationship between your center of gravity and yout feet. – Omega Centauri Jun 11 '11 at 15:52

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