Vernier Software and Technology
Vernier Software & Technology

That's the Way the Ball Bounces - Height and Time for a Bouncing Ball

Figure from experiment 11 from Real-World Math Made Easy

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

y = a{x^2} + bx + c

where y represents the ball’s height at any given time x. Another form of a quadratic equation is

y = {a{(x - h)^2} + k}

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 experiment features the following Vernier sensors and equipment.

Option 1

Option 2

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Standards Correlations

See all standards correlations for Real-World Math Made Easy »

Real-World Math Made Easy

See other experiments from the lab book.

1Walk the Line - Straight Line Distance Graphs
2Making Cents of Math: Linear Relationship between Weight and Quantity
3Pool Plunge - Linear Relationship between Water Depth and Pressure
4Funnel Volumes - Volume and Weight
5Keep It Bottled Up - Rates of Pressure Increase
6Graph It in Pieces: Piecewise Defined Functions
7Mix It Up - Mixing Liquids of Different Temperatures
8Spring Thing - Newton's Second Law
9Stretch It to the Limit - The Linear Force Relation for a Rubber Band
10What Goes Up - Position and Time for a Cart on a Ramp
11That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
12Walk This Way - Definition of Rate
13Velocity Test - Interpreting Graphs
14From Here to There - Applications of the Distance Formula
15Under Pressure - The Inverse Relationship between Pressure and Volume
16Light at A Distance - Distance and Intensity
17Chill Out: How Hot Objects Cool
18Charging Up, Charging Down - Charging a Capacitor
19Bounce Back - The Pattern of Rebound Heights
20Sour Chemistry - The Exponential pH Change
21Stepping to the Greatest Integer: The Greatest Integer Function
22Swinging Ellipses - Plotting an Ellipse
23Crawling Around: Parametric Plots
24Lights Out! - Periodic Phenomena
25Tic, Toc: Pendulum Motion
26Stay Tuned: Sound Waveform Models
27Up And Down: Damped Harmonic Motion
28How Tall? Describing Data with Statistical Plots
29And Now, the Weather - Describing Data with Statistics
30Meet You at the Intersection: Solving a System of Linear Equations
31Titration Curves: An Application of the Logistic Function

Experiment 11 from Real-World Math Made Easy Lab Book

<i>Real-World Math Made Easy</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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