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## Main Question or Discussion Point

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*C

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?

I am using Drag = 1/2*A*C

_{d}*v^{2}*ρ; A - cross-sectional area, C_{d}- drag coefficient, v^{2}- 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?