This is a
quadratic equation of the form y = ax

^{2}+ bx with the coefficients*a*and*b*as shown in the equation.*linear*system (not to be confused with the equation of a straight line, y = mx + b).

*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

*project).*

**Lorenz Attractor in Scratch**
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 grandadscience@gmail.com.

A free download of the project can be had at http://scratch.mit.edu/projects/popswilson/3083963