From what maximum height can a 61 kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.65 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is 170*10^6 N/m^2, and its smallest cross-sectional area is 2.5*10^ -4 m^2. I really need help with this problem!!!

I will be happy to critique your work. Find the breaking force first.

Then breaking force*distance= KE of fall.

ok so would the equation look like this: 170*10^6 *.65=mgh, which would be (61)(9.8)(h)

is this correct?

To determine the maximum height from which a 61 kg person can jump without breaking the lower leg bone, we need to consider the vertical displacement of the person during the jump and the force exerted on the bone.

Let's start by calculating the force exerted on the bone. We can use the equation:

Force = Pressure * Area

Given:
Pressure = 170 * 10^6 N/m^2
Area = 2.5 * 10^-4 m^2

Substituting the values, we find:

Force = (170 * 10^6 N/m^2) * (2.5 * 10^-4 m^2)
= 42,500 N

Now, let's consider the vertical displacement of the person during the jump. We know that the center of mass (CM) moves a distance of 0.65 m from the standing to the seated position, which is equivalent to the displacement of the person during the jump.

Using the work-energy principle, we can relate the force exerted on the bone, the displacement, and the gravitational potential energy (GPE) of the person during the jump:

Force * Displacement = GPE

GPE = m * g * h

Where:
m = mass of the person = 61 kg
g = acceleration due to gravity = 9.8 m/s^2
h = maximum height from which the person can jump without breaking the bone

Rearranging the equation, we have:

h = (Force * Displacement) / (m * g)

Substituting the given values, we find:

h = (42,500 N * 0.65 m) / (61 kg * 9.8 m/s^2)
= 0.43 m

Therefore, the maximum height from which a 61 kg person can jump without breaking the lower leg bone is approximately 0.43 meters.