While this thread is now old, I wanted to note that I just came
across another derivation of the formula for the launch angle and
maximum range of a projectile launched from a height. What's neat
about this derivation is that it uses no calculus, only geometry! The
trick is to use the hodograph. See AJP 71:261 (2003). The key insight
is that the initial and final velocity vectors will be orthogonal
when you launch for maximum range. This is true for a
surface-to-surface projectile which is launched at +45 and lands at
-45 degrees. But it is also true if you launch off a platform or out
of a hole. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/
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