This is a quadratic equation of the form y = ax2 + bx with the coefficients a and b as shown in the equation.
Even though the equation graphs as a parabola, projectile motion is considered to be a linear system (not to be confused with the equation of a straight line, y = mx + b).
It’s linear because a small change in the input(s) initial velocity and/or launch angle, produces a small change in the output, that is, the point where the projectile lands.
Deterministic chaos is the study of nonlinear systems. That is, systems where a small change in input can cause a huge change in output. In chaos theory, that is the basis for the Butterfly Effect (see the Lorenz Attractor in Scratch project).
The purpose of this project is to demonstrate the ‘small change in input’ creates a ‘small change in output’ characteristic of linear systems. Watch this short video to see how the Scratch program helps you understand a linear system.
A free pdf file, Projectile Motion in Scratch, explains how the equation of motion is derived and also explains how the Scratch program was coded to make understanding the code as simple as possible.
To obtain a free copy of this file, send an email request to firstname.lastname@example.org.
A free download of the project can be had at http://scratch.mit.edu/projects/popswilson/3083963