Juggling

Sadly I didn’t bring my juggling balls to college. As a precursor to analyzing more complicated maneuvers, I decided to remember my juggling by looking at the physics behind it.

The main trick with juggling three balls is getting the timing right. You have three balls: A, B, and C. You throw A then, when A reaches its peak, you throw B. When B reaches its peak you catch A and throw C. And so on and so on. There are variations when you throw a ball higher to either do some kind of trick or just by accident. But if you were able to throw each ball with the exact same velocity, then that is how it would work. Following is an analysis (which assumes no air resistance and therefore constant acceleration due to gravity) to find where the balls will be at the exact height as a ratio of their maximum height.

 So at 3/4 the maximum height, the two balls in the air will be at the same height. Before I analyze the situation with juggling 5 balls, I want to learn how to do that. So stay tuned.