Comment: Re:terrible article (Score 4, Informative) 395
You are right. This article is awful, conveying no sense of the nature of the problem or its complexity, and giving no idea of the solution at all.
The only equations I'm aware of for a falling particle subject to air resistance take the form
m v' = -mg -a*v-b*v^2
which is a constant coefficient Riccati differential equation for the velocity v. I'm reasonably sure this would have an analytic solution.
Maybe complications arise in the 2D motion case, or perhaps the problem includes a particle which is also spinning. Maybe the drag terms take more complicated forms. I don't know. The article is pretty dreadful to be honest.