As an appendix to the previous tutorial, and in honor of my first programming language TI BASIC, here's a similar physics simulation but for the TI-83 Plus or TI-84 Plus graphing calculator. I wrote this calculator program almost five years ago after learning about dot products, so you might say the html5 tutorial I wrote recently is kind of *puts sunglasses on* derivative.
PROGRAM:DERIBALL : ClrDraw : Input : Pt-On(X,Y) : X->O:Y->P : Input : O-X->V:P-Y->W : Xmin->A : Xmax-Xmin->B : Ymin->C : Ymax-Ymin->D : : -D/700->G : 0.9->F:0.8->E : : While 1 : If (Y1(X)≥Y)≠(Y1(X+V)>(Y+W)) : Then : nDeriv(Y1,X,X)->J : (V+WJ)/(1+J^2)->K : (F+E)K-EV->V : (F+E)KJ-EW->W : End : X+V->X : Y+W->Y : Pt-On(X,Y) : W+G->W : End
To use the program (after having entered the code into your calculator as a new program), edit
Y1 under the
Y= menu to be any function you like. Try
Y1=X^2, for example. Now plot your preferred function and set the window any way you prefer. I've set Xmin and Xmax to -4 and 4, respectively, and Ymin and Ymax to 0 and 10, respectively.
Now run DERIBALL under the PRGM menu. This will show a moveable crosshair next to your plot; select the position for the hypothetical slingshot from which the ball will launch and press ENTER. Then select the point from which you'll release the ball from the slingshot. Voila! You'll now see the ball move around with gravity and bounce against the curve with friction.