Calvin Of The Jungle
Last summer, I went zip lining through the Ozark Mountains. There are two platforms, and you can see the higher platform in the top left of the image, while the cameraman is standing on the lower platform. There is a rope tied between these two platforms, and I hanged from a pulley suspended on the cable. In this way, I was propelled by gravity towards the lower platform.
The horizontal distance between the platforms was 100 feet, and the vertical distance between the platforms was 15 feet. The rope joining the platforms was 102 feet long, and remained taut throughout my journey (rope from me to either platform was a straight line). As I swung through the jungle, what kind of curve did I trace out?
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Since the rope is taut throughout the sum of the distance between you and the first platform, and the distance between you and the second platform, adds up to the length of the rope, a constant. This is the definition of an ellipse.