### Classical Juggleometry Theory Is Not Sound For Modern Jugglers

ACTIONWORK IN PROGRESS - we may wish to rewrite JUG:007 making it:

JUG:007A       MODERN JUGGLEOMETRY

Just starting to sustain a four ball pattern and you notice that the height of some of your tosses (black graph) reach 36 inches while the width is 12 inches, another toss (red graph) has the same height but only 6 inches wide and yet another (light green graph) is 25 inches high and 10 inches wide.

We may find the equations for these curves using the fact that they are curves represented by parabolas and the above information.

1. Show that the black graph is given by the function y = - x ² + 36.

Using a computer game port and some wire gloves we found the time of flight for the ball represented by the black curve to be 0.863972788 seconds.

2. Show that the horizontal motion is represented by x = 13.88932634 t inches for t in seconds assuming this motion is linear with respect to time.

3. Find an equation for y, vertical position, with respect to time.

4. Find the corresponding functions for the red graph and the light blue graph.

Hint on part of 4: Time of flight for the red ball was the same as the green but what is the time of flight for the light blue ball based on the above information. Remember that Galileo found free fall acceleration was constant and independent of the small differences above the earth's surface in this problem.

5. Does 0.719977323 seconds seem right for the blue graph? Why?

6. Other tosses to work on: (a) Height = 32 Width = 8 inches or (b) Height = 27 Width = 6 inches or (c) Height = 18 Width = 6 inches or ...

7. Pick out one of these parabolas and make a real graph (not scaled down) in inches showing the points plotted in terms of (x,y) and t in seconds labels.

The Talk Outline