written by
Wolfgang Christian
supported by
the National Science Foundation

The EJS Ceiling Bounce Model shows a ball launched by a spring-gun in a building with a very high ceiling and a graph of the ball's position or velocity as a function of time. Students are asked set the ball's inital velocity so that it barely touches the ceiling. This simple model is a designed to teach both physics and EJS modeling.

Please note that this resource requires
at least version 1.5 of
Java.

Ceiling Bounce Model source code
The source code zip archive contains an XML representation of the Ceiling Bounce Model. Unzip this archive in your EJS workspace to compile and run this… more... download 10kb .zip
Last Modified: December 16, 2008

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

11. Common Themes

11B. Models

6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.

9-12: 11B/H3. The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that other models would not work equally well or better.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.^{?}

Building Functions (9-12)

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

W. Christian, Computer Program CEILING BOUNCE MODEL, Version 1.0 (2008), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926).

W. Christian, Computer Program CEILING BOUNCE MODEL, Version 1.0 (2008), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926>.

Christian, W. (2008). Ceiling Bounce Model (Version 1.0) [Computer software]. Retrieved April 24, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926

%A Wolfgang Christian %T Ceiling Bounce Model %D December 16, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926 %O 1.0 %O application/java

%0 Computer Program %A Christian, Wolfgang %D December 16, 2008 %T Ceiling Bounce Model %7 1.0 %8 December 16, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926

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