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Re: Reach of a projectile



Quoting "Fakhruddin, Hasanbhai" <hfakhrud@BSU.EDU>:

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?

1) The question is self-inconsistent. If (r,theta) is the polar
coordinate of a point along the trajectory, then we must not
re-use the symbol theta to represent the angle of the launcher.
Let the latter be called alpha from now on.

2) Note that the derivation involves:
a) for each x
b) find the alpha (launch angle, not polar coordinate)
that maximizes y
c) record the corresponding maximal y (as a function of x).

Note the importance of ingredient (a).

3) You could do the same thing in polar coordinates:
a) for each theta
b) find the alpha that maximizes r
c) record the corresponding maximal r (as a function of theta).

... but this seems like a less-convenient method.