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John,
I am able to derive the equation y = A - Bx^2 that you mentioned.
However, I still have a question: How can we be sure that maximizing
y wrt theta will span all the points covered by the projectile?
What if I maximize r wrt theta where (r,theta) is
the polar coordinate of a trajectory?
Hasan Fakhruddin
I've seen this written up somewhere in the past almost certainly
TPT I would imagine.
First you find
y = x*tan(theta) - g*x^2/(2*v0^2*(cos(theta))^2)
then maximize y wrt theta and plug the answer back into this equation
.
The result is the upper envelope of all points that can be reached by
the projectile and the answer is the parabola
y = A - B*x^2
where A = v0^2/(2*g) and B = g/(2*v0^2).
--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm