That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
Recommended for grades 9–12.
Introduction
Picture a bouncing ball. Between impacts with the floor, the ball rises and slows, then descends and speeds up. For any particular bounce, if the ball’s height is plotted as a function of time, the resulting graph has a parabolic shape. In other words, the relationship between height and time for a single bounce of a ball is quadratic. This relationship is expressed mathematically as
where y represents the ball’s height at any given time x. Another form of a quadratic equation is
where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and a is a parameter. This way of writing a quadratic is called the vertex form.
In this activity, you will record the motion of a bouncing ball using a Motion Detector. You will then analyze the collected data and model the variations in the ball’s height as a function of time during one bounce using both the general and vertex forms of the quadratic equation.
Objectives
- Record height versus time data for a bouncing ball.
- Model a single bounce using both the general and vertex forms of the parabola.
Sensors and Equipment
This activity requires each of the following Vernier sensors and equipment (unless otherwise noted):
Additional Requirements
You may also need an interface and software for data collection. What do I need for data collection?
Download Experiment Preview
The student-version preview includes:
- Step-by-step instructions for computer-based data collection
- List of materials and equipment
Note: The experiment preview of the computer edition does not include essential teacher information, safety tips, or sample data. Instructions for Logger Pro and other software (such as LabQuest App or TI handheld software, where available) are on the CD that accompanies the book. We strongly recommend that you purchase the book before performing experiments.
Standards Correlations
See all standards correlations for Real-World Math with Vernier »
Included in the Lab Book
Vernier lab books include a CD with word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.