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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?