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## Homework Statement

One of my classes involves constructing a differential equation to model the freefall of the red bull sky diver Felix Baumgartner. I need to construct the correct differential equation to find v(t) and y(t) at any given time t. As stated above, I need to take the two forces (drag and gravity) as varying with height. I'm simply interested in how to construct the model, I can worry about solving it on my own.

## Homework Equations

ma = [itex]F_{g}[/itex] - [itex]F_{d}[/itex]

v' = vdv/dy

## The Attempt at a Solution

ma = mvdv/dy = GMm/(R + [itex]y^{2}[/itex]) - 1/2[itex]C_{d}[/itex]A[itex]\rho[/itex][itex]v^{2}[/itex]

where R, G, M, and m are the usual gravitational constants, [itex]C_{d}[/itex] is the drag coefficient, A is the cross sectional area of the diver, and rho is the density of the air.

I'm a little perplexed because I believe rho should be a function of y as well. I was wondering if I should just treat the drag force as 1/2k[itex]v^{2}[/itex] and solve accordingly. I also might need to add the linear term for the drag force although it gets dominated once v gets larger. Any thoughts as to how bad I butchered this model are appreciated.

Thanks