A woman (mass= 50.5 kg) jumps off of the ground, and comes back down to the ground at a velocity of -8.4 m/s.

Rather than landing stiff-legged, it would be much safer for the woman to land with bent knees, which would bring her to a stop in about 0.27 seconds. Show the average net force that would act on her with this longer stopping time.



Hint: You will need to find the change in the woman's momentum before and after she lands, and set that equal to our impulse formula ( p = F*t) to find the average force during the impact

Approximately .

Explanation:

By the Impulse-Momentum Theorem, the change in this woman's momentum  will be equal to the impulse that is applied to her.

The momentum of an object is equal to the product of its mass and velocity . That is: .

Let and represent the velocity of the woman before and after the landing. Let represent the woman's mass.

Therefore, the change in this woman's momentum would be:

.

On the other hand, impulse is equal to force multiplied by the duration of the force. Let represent the average force on the woman. The impulse on her during the landing would be .

Apply the Impulse-Momentum Theorem.

Impulse is equal to the change in momentum:

.

After landing, the woman comes to a stop. Her velocity would become zero. Therefore, .

.

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