Modeling Free Fall Data

A free falling ball is an excellent model for the effects of gravity on objects. Once data is collected, the problem is that teachers are too quick to have students model the position function using regression. The best way is to have students try to find a function by trial and refinement. This gives them a much better feel for the influence of the parameters on the graph.

Collect the data:

Hook a CBR up to a TI-83 Plus.

Run Ranger through the CBL/CBR application under the APPS key.

From the Main Menu choose Applications and then Ball Bounce.

Collect motion for three or four seconds using meters or feet as the unit of measurement.

Display the Distance graph.

Hold the CBR steadily at least 1.5 feet above a ball (a basketball usually provides good data)

Drop the ball and start the motion detector simultaneously.

The Ball Bounce program will adjust the data so the graph is from the perspective of the CBR being on the ground.

A typical graph looks like the one below.

Modeling the data:

Have the students type an equation into y1 to try to fit a quadratic function to one parabolic arc.

The vertex location can be found by tracing on the Stat Plot.

The value of the leading coefficient is entered by trial and revision until there is a good visual fit of the function to the plot.