Let’s Bounce
Overview
In this activity you will be using a motion detector to explore some of the mathematics
involved in the bouncing of balls. You will be comparing the bounce height of different
balls, exploring their elasticity, or their “bounciness,” by examining their decreasing
bounce heights.
Getting Started
You will need to choose two balls for this experiment. Your options include:
 comparing different sized basketballs
 comparing different sized four-square balls
 comparing a new tennis ball with an old one
 comparing different super balls
The Set Up
You will need to drop the balls from the same height each time. In order to ensure this,
mark a “drop height” of five feet with masking tape on the wall.
Connect your motion detector, the Calculator Based Ranger (CBR), to the calculator.
Using the CBR
1. Press [PRGM] in the 3rd row and 3rd column on the calculator and select the
“Ranger” program by pressing [Enter].
2. Arrow down to [3: APPLICATIONS] and press [Enter].
3. Arrow down to [2: FEET] and press [Enter], as that is what we are measuring
today.
4. Arrow down to [3: BALL BOUNCE] and press [Enter].
Collecting the Data
Note: The CBR needs to be held 1.5 feet above the drop height of the ball.
1. When you are ready to drop each ball, make sure hands, toes and other things that
might cause movement within the range of the CBR are out of the way or very
still. The CBR measures the distance from itself to an object within its range, five
times every second. You will hear clicking while the CBR is measuring. (In the
“Ball Bounce” mode, it actually measures between the ball and the floor.) Then
press “Trigger” on the CBR to start gathering data .
2. Follow the directions on the calculator screen (press enter) to view results.
3. You should repeat the data collection until an accurate graph is obtained.
4. Using the Trace feature move the cursor to find the maximum height for each
bounce, recording your data on “Let’s Bounce: Results.”
 Repeat steps 1 – 5 above for your second ball.
Analyzing Your Data
1. Find the ratio of consecutive bounces by dividing the height of the first bounce
(Bounce 1) by the Drop Height, then divide height of Bounce 2 by height of
Bounce 1, etc. Fill in this information on your “Results” sheet.
2. Find the mean of your ratios. This will be the decay (how much the bounce
height decreases on each successive bounce) of the bounce for the ball.
3. Repeat this for the second set of data.
4. Answer the questions on the Going Further sheet.
Exploring Velocity vs. Time Graphs
Discuss how the velocity of the ball changes as it is bouncing. Recall velocity keeps
track of direction and speed. In your group, try to draw a graph of the velocity vs. time
(with velocity on the vertical axis and time on the horizontal axis) as the ball is bouncing.
To check your graph, you can create a velocity vs. time graph with the CBR.
The Set Up
1. Repeat the same data collection procedures in “Using the CBR” and steps 1-3 of
“Collecting the Data” above.
2. Press [Enter] to get to the Menu.
3. Arrow down to [2: VEL – TIME], and press [Enter].