When jumping straight down, you can be seriously injured if you land sti-legged.

Question

When jumping straight down, you can be seriously injured if you land sti-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 o a wall of a height h.

a. With what speed, v, will you hit the ground? Assume you simply step o 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 rst touch the ground until you stop is ? t.
Calculate the (average) net force acting on you during that interval. (Again, express your answer in
terms of the symbols given.)

c. Suppose h = 1 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 that would act on
you in the 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. Which of these does you the injury? For the two cases in part c, calculate the
upward force the ground exerts on you

Explanation / Answer

a.)   For a height h, assuming gravitational acceleration is g. the velocity with which you will hit the ground

        is given by the eqn v2=u2+2gh.   Since u is initial velocity and =0 as mentioned in the q, final velocity

        v = (2gh).

b.)    We know that Force = p/t. therefore if your mass is m, p = -mv = -m(2gh) / t, the minus just indicates that the force is acting to reduce momentum i.e to stop you. We generally neglect gravitationa force when the magnitude of F is very large

c.) for h=1m , stiff-legged landing--> force = p/t = -m(2g)/(2x10-3) = 20002g x m - mg

     for bent knee landing                   force = -m(2g)/0.1    =     102g x m - mg

d.)    the upward force injures you , upward force = 20002g x m for stiff landing

                                                     upward force = 102g x m for bent knee landing

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