Trajectory of a projectile WITH air resistance?

[bolshevik]

ok. I'm a sophomore in high school who knows nothing about differential equations except for what wikipedia and some other sources said. I seem to simply have the need to figure this out. I've been to wikipedia, which didn't help. Could someone please provide a walkthrough on how to the math for trajectory with air resistance? This is starting to get on my nerves.
Thanks.

 

[rcgldr]

The main issue is that drag is a fuction of the object itself, speed, and altitude (air is less dense at higher altitudes). It's complex enough that tables of coefficients need to be used with equations to calculate drag. Once you can calculate the drag for a given position and velocity, you can calculate the deceleration due to drag, and the acceleration due to gravity. Then given an initial position and velocity, and calculated accelerations, numerical integration can be used to determine new positions and velocities, then new accelerations, in very small steps of time.

http://en.wikipedia.org/wiki/External_ballistics

http://en.wikipedia.org/wiki/Numerical_ordinary_differential_equations

http://en.wikipedia.org/wiki/Predictor-corrector_method