I am looking at the problem of a freefalling sphere and want to calculate time taken to fall a distance. I want to model drag as well as take account of the varying density in the atmosphere. I am using Drag = 1/2*A*Cd*v2*ρ; A - cross-sectional area, Cd - drag coefficient, v2 - velocity squared and ρ - air density. I have been able to form a DE and solve it for v and s (distance) but this assumes a constant density of air. I am also having trouble with the hyperbolic trig functions so think i might be taking a 'large hammer to break a small nut'. Any ideas on how to simplify this or is the DE the right way to approach?