Projectile Motion: Pushing the Envelope

Think everything that's publishable for say an old classical topic like projectile motions has already been published? Turns out the old 'lob the projectile at a constant velocity in a constant gravitational field' problem is still producing. Check out this paper from J. L. Fernandez-Chapou, A. L. Salas-Brito, and C. A. Vargas published in 2004. It eventually made its way into the American Journal of Physics. In the paper, the authors show that if you write down the trajectory of a projectile in terms of its launch angle and then solve for the x and y position when the projectile has reached it's maximum height, the solutions will trace out a nice little ellipse like the figure below excerpted from the arxiv version.

References:
1. Elliptic envelope of parabolic trajectories paper
http://arxiv.org/abs/physics/0402020v1

1.a. AJP version of the paper
http://scitation.aip.org/content/aapt/journal/ajp/72/8/10.1119/1.1688786

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Copasetic Flow

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