In this activity, students collect motion data for a bouncing ball using a motion detector. They analyze the data and attempt to find the exponential relationship between the bounce number and maximum height that the bounce reaches.

Before the Activity

Connect the computer to the CBL 2™ using the TI connectivity cable

Connect CBR 2™ to the DIG/SONIC port of the CBL 2™ unit

See the attached PDF file for detailed instructions for this activity

Print pages 41 - 46 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Hold the motion detector 1.5 to 2 meters above the floor

Hold a ball 0.5 meter below the detector and drop it

Collect distance versus time data and plot a graph

Record initial drop height as bounce zero and find the maximum heights of each successive bounce

Plot bounce number versus bounce height

Observe the graph is exponential in form and can be modeled by the equation y = ab^x

Find the value of a - the initial height

Find the ratio of maximum height of each bounce in relation to the preceding bounce

Record the ratios and find the average ratio which represents b

Enter the values of a and b in the equation to find y

Observe this equation y = ab^x is a relationship between bounce height and bounce number

Use the exponential model to find the height of the ball at the 8th bounce and also the number of bounces the ball makes before it no longer reaches a maximum height of 5 centimeters

After the Activity

Students complete the analysis and answer questions.

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

If you use TI-Navigator™, you can download the attached EDC file and use as a quiz to check understanding. If you are using the TI-73, you may need the attached PDF.