Plotting Height vs Time for an Object Under Air Resistance

[Opus_723]

If I wanted to make a graph of height versus time for an object under the effects of air resistance av+bv^2 and thrown with a given initial speed, how would I go about doing that? I was also hoping to get a y versus x graph for a projectile under the same drag, but I presume I could find x versus t the same way I end up finding y versus t and then treating the two like a parameterized curve.

I thought about using ma = av+bv^2-mg and taking the integral twice to get height as a function of time, but my limited calculus skills are failing at that. Even simplifying to just bv^2 seems to be too much for me. Is this the best way to do it? Is there a numerical way to do it? (I've never done integrals numerically on a computer or anything)

In general, I don't really know how to tackle these kinds of messy integrals. Are there any resources I could learn from?

Thanks.

 

[Simon Bridge]

mdv/dt = av+bv^2 - mg

so:$$\int \frac{mdv}{av+bv^2-mg} = \int dt$$... then find the constant of integration from the fact that v(0)=u.

http://www.jstor.org/pss/2372332