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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.