# Looking for the right equation that will account for drag and air density [closed]

I didn't see anything about posting homework questions so here it goes. I need to find either the velocity or acceleration or the time(all 3 eventually) for an object that is falling 1000 meters. Here's the catch, I need this equation to account for air density (which I have changing recursively in excel) and drag. I'm using a drag coefficient of 0.4. I'm having a hard time finding an equation for any one of those three variables that doesn't have another one of those three variables (velocity, accleration, time) in the equation. Edit:

The recursive relation for density is:

Density=DensityOriginal*e^-lapserate*heightofFall

where lapse rate=0.0001036

I'm having no problems with this.

I need to find those 3 variables independently of each other solely because they are all unknowns.

I have not taken calculus 3 yet and do not know how to solve differential equations.

Known variables

Air Density: Changes recursively

Fall distance:$1000 \rm m$

Mass:$10\:\rm{kg}$

Cross sectional area of a sphere: (4)$\pi(10\:\rm{cm})^2 =0.12566 \rm m^2$

Terminal velocity $\approx 11\:\rm{m/s}$

Recursive relation for density: $d=d_0e^{-\lambda h}$ ($\lambda$ is lapse rate, $h$ is height of fall)

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 physics.stackexchange.com/faq we do have something against homework. Homework questions are only allowed if they ask for specific concepts. – Manishearth♦ Mar 19 '12 at 5:21 It would be better if you stated the recursive relation. – Manishearth♦ Mar 19 '12 at 5:22 I'm not looking for answers just for help. The recursive calculation for air density is Density=DensityOriginal*e^-lapserate*heightofFall. – Tyler Pfaff Mar 19 '12 at 5:36 Hi Tyler, and welcome to Physics Stack Exchange! As Manishearth said, questions asking how to do a problem are not appropriate here, but I suspect that with just a little editing you could turn this into a good conceptual question for the site. For starters, what model are you using for density? What have you been able to do, and exactly what step do you get stuck on? Why do you need an equation for one of $v,a,t$ that is independent of the other two? – David Zaslavsky♦ Mar 19 '12 at 5:44 Wouldn't it make more sense to chuck Excel, formulate a differential equation, and solve it? The recursive relation you've given is perfect for this, IMO. – Manishearth♦ Mar 19 '12 at 5:45