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. a 75-kg man just before contact with the ground has a speed of 6.4 m/s. (a) in a stiff-legged landing he comes to a halt in 2.0 ms. find the average net force that acts on him during this time. (b) when he bends his knees, he comes to a halt in 0.10 s. find the average net force now. (c) during the landing, the force of the ground on the man points upward, while the force due to gravity points downward. the average net force acting on the man includes both of these forces. taking into account the directions of the forces, find the force of the ground on the man in parts (a) and (b).

(a) 240,000 N

We can solve the problem by using the impulse theorem, which states that the impulse exerted on the man is equal to its change in momentum:

where

F is the average net force exerted on the man

is the contact time

m = 75 kg is the man's mass

v=0 m/s is the final speed of the man

u = 6.4 m/s is his initial speed

Solving the formula for F, we find

And the negative sign simply means that the force (upward) is opposite to the initial velocity of the man (downward).

(b) 4800 N

The problem can be solved exactly as the previous part, but this time the time of contact is

So the average force is

(c) 239,265 N and 4065 N

The force found in part (a) and (b) corresponds to the net force, which is the difference between the force exerted by the ground on the man (N, upward), and the weight of the man (W, downward):

For part (a), we can find N as

While for part (b), we find

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