# Could someone help me out please?

honeydukes
Hello!

I am doing a project with a few other people. It is sort of a mock trial. None of us are physics wiz's. We need to know the speed a body would impact the ground from a fall of 100 meters. We figured out that it would be 99 miles per hour/44 meters per second WITHOUT air resistance. But we need to know what it would be WITH air resistance. The person is about 5'10 and weighs about 150lbs/68kg. Your help would be much appreciated! Thanks!

Geoff St. Germaine
honeydukes said:
Hello!

I am doing a project with a few other people. It is sort of a mock trial. None of us are physics wiz's. We need to know the speed a body would impact the ground from a fall of 100 meters. We figured out that it would be 99 miles per hour/44 meters per second WITHOUT air resistance. But we need to know what it would be WITH air resistance. The person is about 5'10 and weighs about 150lbs/68kg. Your help would be much appreciated! Thanks!

You'll need to add a drag term to your force balance equation. IIRC from my undergraduate mechanics, there can be a viscous drag, which is proportional to the velocity, or a quadratic drag, which is proportional to the square of the velocity. I think that above a few meters per second, the quadratic drag term is used in a typical approximate calculation. So, the drag force should be $$f = -cv^2$$. You can approximate the drag coefficient with something like $$c= \frac{1}{2} C_D S\rho$$. $$C_D$$ is a dimensionless term related to the geometry of the falling object, S is the cross-sectional area of the falling obect and $$\rho$$ is the density of air.