Falling Object with Air Resistance

Not formally a part of my physics book (which I am posting here chapter by chapter, completely for free as it is being written), but following the same trend, I decided to write up the solution to an interesting problem: that of deriving the solutions to the differential equations for an object falling in a gravitational field  through an atmosphere.  It is useful to know how to solve this problem, because the same method can be generally applied to any situation where there is both a variable force and a constant force that work together to cause an acceleration, or perhaps even eliminate acceleration, as in the case of terminal velocity, when the positive constant force and the negative variable force find their equilibrium. I will assume a relatively high mathematical literacy, but if you do have any questions, leave a comment and I’ll get back to you as soon as I can.

Here is the PDF.

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