Activity Overview
In this adventure , students will make a Height-Time plot of a bouncing ball using the CBR 2™. They graph height as a function of time. They identify and understand the vertex form of a quadratic equation that is generated to describe the ball's motion.
Before the Activity
Connect CBR 2 to the calculator.
Launch the CBL /CBR 2™ App
Start the Ranger program and select the Ball Bounce application
Transfer files to the student calculators using the TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity
Print pages 78 - 79 from the attached PDF file for your class
During the Activity
Distribute the pages to your class.
Follow the Adventure procedures:
Collect Data:
Set up the CBR 2 at shoulder height with a ball 0.5 meters directly below it
Release the ball and collect ball bounce height data
Plot time versus distance data
Examine any one bounce, the plot has a parabolic shape
Explore the quadratic equation that describes this motion is quadratic:y = A(x - H)2 + K where A affects the width of the parabola and (H, K) is the vertex of the parabola. In this activity, the control variable, x, represents time and y represents height.
Identify the vertex (H, K) of the first complete bounce and substitute the values in the equation
Use different values of A in the equation and view the graph formed
Find the value of A that best fits bounce data and write the equation of a parabolic ball bounce
Find the equation for the second bounce
Explore how as values of A increases, the parabola gets narrower and as A decreases, the parabola gets wider
Value of A for a quadratic equation of a bouncing ball is constant
TI-Navigator activity:
Load the Arch.act activity settings file
Have students submit quadratic equations that best fit the arch
After the Activity
Students analyze the results and answer the questions in the worksheet
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary