A person about to jump from a 1.6m high platform wants to limit the average stopping force on landing to 12 times her weight. By how much will it be necessary to lower herself by flexing her knees? Give an algebraic rather than numerical answer. Compare that work with the original potential energy she had before she jumped.
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The ground exerts an average stopping force on the person. This stopping force is the result of changing the momentum of the person from some initial momentum Pi to zero at a certain time interval ?t.
From the impulse equation we know that this force is:
F = ?P/?t = (Pf-Pi)/?t
Pi represents the final momentum (that is zero).
F = ?P/?t = (0-Pi)/?t = -Pi/?t
The negative sign just indicates that the force direction is against the direction of the initial momentum. If we define any physical quantity pointing down as negative, then the force is actually positive. If the person does not bend her knees, then ?t is very small, since the entire body changes its momentum at the ...
The solution looks at limiting one's average stopping force by controlling how one lowers oneself from a specified height, in an algebraic method. Certain assumptions are made, such as all released energy being turned to kinetic energy, and the release of impact on the ground after the jump, and a full answer is given.