Activity Overview
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
Open a new TI InterActive!™ document
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.