The Great Grade 11 Bouncing Ball Experiment So Far, all of our work on graphs has been directed...

The GreatGrade 11

Bouncing Ball Experiment

So Far, all of our work on graphs has been directed towards linear

and quadratic relationships.

These relationships represent only a small (but important) part of the overall topic of

modeling.

There are numerous other models that are used in

mathematics

The Quadratic

E = mc2

The Cubic

Periodic Functions

Cardioid Four Leaf

Lemicon

Mobius Transformation

A bouncing ball provides and excellent illustration of an Exponential relationship.

Copy and complete the chart below:

Trial 1

Trial 2

Trial 3

Average trials

Height (cm) (no decimals)

Initial Height NA NA NAHeight after 1 bounceHeight after 2 bouncesHeight after 3 bouncesHeight after 4 bouncesHeight after 5 bouncesHeight after 6 bounces

173 171 178 174300

154 151 160 155

Decay

Factor

H1/iH

H2/H1

H3/H2

Etc…

Draw the graph

Average Height VS Number of Bounces

Average

Height

Number of bounces0 1 2 3 4 5 6

300 cmDon’t forget to plot the initial height

1. Write the exponential model that describes the decay of the basketball you used.

Hf=Hi(X)n

2. Does it make sense that the reflection height decays at the same rate every bounce? Explain.

3. The moon has about 80% less gravity than Earth. How do you think your data would change if you repeated the experiment on the lunar surface?

Each person, hand in the completed graph, table, and answered questions once you finish.

Responses will vary but should be close to a 0.67 rebound factor!