You MUST Try This Classical Mechanics Problem

A Challenging Math Puzzle From High School

I remember getting taught this problem by my mechanics teacher, Tristan S. It was a lesson on collisions and the coefficients of restitution. To this day it’s still one of my favorite classical mechanics problems.

A ball is dropped from height h to the ground, and the coefficient of restitution of the ground and the ball is E. As the ball keeps bouncing, it eventually comes to a stop. What is the total distance the ball has travelled as it bounces?

Of course the ball will lose a bit of energy from each bounce, and in fact the ball will bounce an infinite number of times before coming to a stop. Except those infinitely many distances eventually converge to zero.

Now really do grab your pen and paper for this one, as you can’t really just do it in your head.

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When you are ready, let’s dive in.