it seems like the first thing an artilleryman ought to know
Yeah, but most of them just memorized the final formulas. Actually working them out on the spot would've been a bit much to expect, especially in the midst of battle. For extra fun, throw in centrifugal forces, Coriolis forces, and air resistance.
The fact that the period of a simple pendulum is unaffected by its length
Originally posted by Jon Pincott:
The nasty looking trig you get when you eliminate t can be turned into a quadratic in tan theta using:
1) sin / cos = tan
2) 1 / cos^2 = 1 + tan^2
You can then just calculate your coefficients and plug into the normal quadratic formula to get two values for tan theta.