Force/Energy Problem: Jump from Window

[arizona_cards_11]

Question

A 75kg man jumpst from a window 1.0m above the side walk.

a) What is his speed just before his feet strike the pavement?

b) If the man jumps with his knees and ankles locked, the only cushion for his fall is approximately 0.50 cm in the pads of his feet. Calculate the average force exerted on him by the ground in this situation.

Work

a) MEi = MEf

PEi + KEi = PEf + KEf ===> mgh + (.5)mv^2 = mgh + (.5)mv^2

After plugging in values:

736 + 0 = 0 + 37.5v^2 ===> V^2 = 19.6 ===> V = 4.43 m/s

b) I'm not sure how to approach this problem. I assume I'm basically trying to find the normal force of the man...but I don't know what the height really has to do with the problem unless I'm supposed to use energies to relate to the force in some way.

 

[Kerbox]

You are given the initial velocity from the previous question, and the distance of acceleration by the thickness of his foodpads. I suppose they want you to calculate the constant acceleration needed for this, and then relate that to the force using Newtons second law.

- Kerbox

 

[kyle8921]

To calculate the average force exerted on the man by the ground, we can use Newton's second law, which states that force equals mass times acceleration (F=ma). In this case, we know the mass of the man (75kg) and the acceleration due to gravity (9.8 m/s^2). However, we need to calculate the deceleration the man experiences when his feet hit the ground. We can do this by using the equation v^2 = u^2 + 2as, where u is initial velocity (4.43 m/s, calculated in part a), a is acceleration (-9.8 m/s^2) and s is the distance the man's feet travel before coming to a stop (0.005 m).

Plugging in values and solving for a, we get a = -2029.4 m/s^2. This is the deceleration the man experiences when his feet hit the ground. Now, we can calculate the average force using F=ma.

F = (75kg)(-2029.4 m/s^2) = -152205 N

Note that the force is negative because it is acting in the opposite direction of the man's initial velocity. This means that the man experiences a very large force (152205 N) when his feet hit the ground, which could result in serious injury. It is important for individuals to properly bend their knees and absorb the impact of a fall to reduce the force exerted on their body.