# Using thermodynamics and Kinematics together to solve a parachuter problem?

I need to find a parachutist's displacement after a given height (nearly 37000m) and at a given latitude. I have his mass, area, parachute area, drop height, parachute deployment height, data about the atmosphere, and other assorted values. I don't have velocity and Temperature so I'm stuck. Please help.

My issues:

finding pressure change without temperature: $V(dP/dt) = nR(PV/NR)$ (doing that would result in the original pressure for pressure change...)?

using pressure change to find density change: again, no temperature, and if you substitute temp for PV/NR you end up canceling the pressure terms making using the pressure derivative futile? $Density = (P*Mw)/(RT)$

using density change to find drag change: No velocity given so what do I do? $Drag = Cd*A*.5*r*v^2$, where $r = drag$

using drag to net force to find acceleration: $drag/m = a$?

repeat last few steps for the parachute:...

Find how fast the earth rotates, and use the two velocities (earth/person) to find salient times: ?

Use the above to find: total displacement

Note I'd need to stick to the above process and I didn't give values because I'd prefer to get help with strategies.

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If it's a standard atmosphere, then you have both pressure and temperature as those are relatively well known. en.wikipedia.org/wiki/U.S._Standard_Atmosphere or en.wikipedia.org/wiki/International_Standard_Atmosphere depending on your location and standard. –  tpg2114 Dec 11 '12 at 11:18
Pressure, Volume, molar weight of atmosphere, number of moles, gas constant, drag coefficients, and avg density are given (among some others). –  ThroatOfWinter57 Dec 11 '12 at 12:00
So if you have pressure and density (or number of moles and molecular weight) and gas constant, you have enough state variables to compute any other state variable you want, such as temperature. –  tpg2114 Dec 11 '12 at 12:02
True, but the problem here is that pressure, density, and temperature are all changing, and those rates are not given (this is a related rates problem for calculus.) I'll try just finding Temp though. But, what can I do about not having velocity? –  ThroatOfWinter57 Dec 11 '12 at 12:03
Certainly some things were given to you as a function of altitude, or you were told what assumptions you could make (such as standard atmosphere). Which means you can take derivatives of the ideal gas law to find what you need as things change and you know the initial value because you have the state variables at some point. For example, if you know how pressure changes with altitude you can chain it together with how temperature changes with pressure to get temperature change with altitude. –  tpg2114 Dec 11 '12 at 12:07
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