When jumping straight down, you can be seriously injured if you land stiff-legge

Question

When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. Suppose you have of mass m and you jump off a wall of a height h . (a) With what speed, v, will you hit the ground? Assume you simply step off the wall so your initial y-velocity is zero. Ignore air resistance. (Express your answer in terms of the symbols given.) (b) Suppose that the time interval starting when your feet first touch the ground until your body fully stops is . Calculate the (average) net force acting on you during that interval. (Again, express your answer in terms of the symbols given.) (c) Suppose your mass is 61 kg and the height of the wall is 1.00 m. If you land stiff-legged, the time it takes you to stop may be as short as 2 ms, while if you bend your knees, it might be as long as 0.1 s. Calculate the average net force (in newtons) that would act on you in those two cases. (d) The net force on you while you are stopping includes both the force of gravity and the force of the ground pushing up on you. Which of these plays a larger role if you are injured? To answer that, for each of the two cases in part (c), calculate the upward force the ground exerts on you (in newtons) and compare its magnitude to the force of gravity on you.

Explanation / Answer

force = mass * change_in_velocity/change_in_time This is just an application of Newton's Second Law: F=ma, just remember that acceleration is really the change in velocity divided by time. the net force will be the force of the ground minus the force of gravity (you should draw a free-body diagram to confirm this). So the force of the ground will be equal to the net force, plus the force of gravity. Gravitational force is going to be mg (m is the mass of the person and g = 9.8 m/s^2). So just add mg to both of your answers to get the answers

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