Calculus – deriving the equations for simple projectile motion

We have worked several examples of simple projectile motion – meaning that the acceleration of gravity was constant and vertical, and there was no acceleration in the horizontal direction. (In particular, there is no air resistance.)

I simply handed us four equations and used them in a firstsecond… and third post. I said I would show how to derive them.

It was junior year in high school that I learned the equations for position and speed as a function of a constant acceleration. I didn’t take calculus until I was a college freshman… and at some point I decided that I knew enough calculus to derive the equations I had been told to memorize two years before.

This is about as elementary as it gets in calculus, but when it was all new to me, it was a thrill to see what it could do for me in physics. I will actually derive them in two slightly different ways.

Here we go.
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