John,
I am able to derive the equation y = A - Bx2 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
Instructor of Physics
The Indiana Academy for Science, Mathematics, and Humanities
BSU
Muncie, IN 47306
E-mail: hfakhrud@bsu.edu
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