On the 4th of January 2010 Google used in place of its logo an animation depicting an apple that falls off a tree and bounces on the ground, in order to celebrate the 366th birthday of Sir Isaac Newton. Below, we analyze the algorithm used and display two relevant plots.
The algorithm of the falling apple goes like this:
A plot of vertical position and vertical speed by time is the following:
A figure of all the discrete positions occupied by the apple during its fall is the following: