SOLUTION: Where does the -16 come from in the vertical motion formula?

Question 557922: Where does the -16 come from in the vertical motion formula?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Good question. Start with the general equation for vertical motion:

where a is the acceleration due to gravity.

This equation can be derived using integral calculus (I'll prove it next). The acceleration due to gravity can be derived from the equation

where G is the gravitation constant, m1 and m2 are the masses of some object and Earth respectively, and R is the radius of the Earth. Plugging in, we find that a is approximately -9.8 m/s^2 (about -32 ft/s^2). Half of that is -16 ft/s^2, which is where the -16 comes from.

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To derive the vertical motion formula, start with the fact that

(the v0 is our constant of integration)

Integrating again,

And we are done.

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