Quin Bouncing

https://www.desmos.com/calculator/htnvtxkpx9

Meet Quin, the quintessential human traveler. She begins life centred at the origin.

Quin travels up and down the y-axis, bouncing, at the top, off the line y = 5 and, at the bottom, off the parabola

Your task is to build the animation and a key part of that is to identify the exact point at which Quin hits the parabola and bounces back up. This is an interesting problem and there are number of ways to solve it.

One of these uses calculus and is great for grade 12.

The solution we discuss here examines the descending circle keeping track of the number of intersections between the circle and the parabola. This goes from 0, to 2, to 4, and we want that transitional point where there are exactly 2. One on each side.