That’s the Way the Ball Bounces Name_____________________________

Name_____________________________

Think of a basketball being bounced up and down. Sketch a reasonable graph of the distance the ball is from the floor as it is being bounced for a few seconds.

A motion detector (CBR) unit will collect data of the distance the ball is from the device over a period of time (a few seconds). It would damage the CBR if it was placed on the floor and the ball would then be bounced on it. Therefore, a program called Ball Bounce will be used so the CBR can be held above the bouncing ball and the graph will automatically be inverted so it matches your sketch above.

For this experiment, you will need the following equipment:

CBR unit

TI-83 plus (If using a TI-82, download the ranger program from the CBR by pressing the button that shows the type of calculator you are using.)

Ball (Basketball works the best)

Part I Experiment Setup:

Connect the CBR to your calculator. On your calculator, press APPS, CBL/CBR, Ranger. Press enter when it says to. Choose APPLICATIONS, then FEET, and then BALL BOUNCE. Collect the data by following the instructions on the screens to follow. When satisfied with the data collections, hit enter and choose PLOT TOOLS, then SELECT DOMAIN. For this experiment, we will need the data from only one bounce of the ball. Pick a lower bound and upper bound for the best bounce of the ball. Exit the program. The program has transferred the data into lists. L1: time, L2: distance, L3: velocity L4: acceleration.

Part II Analysis of Data

Using STAT PLOT, make a scatter plot of distance vs. time using a ZOOMSTAT window. Make a sketch of the graph and show the window used. Label the axes. Do not connect the dots.

Use the scatter plot to verbally describe how the object fell.

Since a quadratic function would best model this data, find a quadratic equation of best fit by the trace feature on your calculator to approximate the vertex and another point. Use these two points and vertex form: y = a(x-h)²+k to solve for a. Write the equation of the quadratic in vertex form and then expand into y = ax² + bx +c form.

Vertex form: __________________________________________________________________________

Standard form: ________________________________________________________________________

Compare this last equation to the one the calculator computes by using the QuadReg found under the STAT key. Use the following commands in order for the calculator to compute and place the equation into Y1:

Using a ZoomStat window, show the graph of the quadratic regression on the scatter plot above. Write the equation of the quadratic regression: How well did it match the equation you wrote in standard form?