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The Free Fall Air Resistance model allows the user to examine the motion of an object in free fall, and motion under the effect of air resistance. This is simply one-dimensional motion (vertical motion) under the influence of gravity. The blue ball moves under the influence of gravity alone. The red ball moves under the influence of gravity and air resistance - the strength of the air resistance parameter can be adjusted.

The Free Fall Air Resistance model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_bu_freefall_airresistance.jar file will run the program if Java is installed.

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

Free Fall Air Resistance Model Source Code
The source code zip archive contains an XML representation of the Free Fall Air Resistance model. Unzip this archive in your EJS workspace to compile and run this model using EJS.

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

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.

4G. Forces of Nature

3-5: 4G/E1. The earth's gravity pulls any object on or near the earth toward it without touching 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.

9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

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.

6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

Common Core State Standards for Mathematics Alignments

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

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.

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

A. Duffy, Computer Program FREE FALL AIR RESISTANCE MODEL (2010), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10002&DocID=1641).

Duffy, A. (2010). Free Fall Air Resistance Model [Computer software]. Retrieved March 2, 2015, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10002&DocID=1641

Duffy, Andrew. "Free Fall Air Resistance Model." http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10002&DocID=1641 (accessed 2 March 2015).

%A Andrew Duffy %T Free Fall Air Resistance Model %D April 16, 2010 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10002&DocID=1641 %O application/java

%0 Computer Program %A Duffy, Andrew %D April 16, 2010 %T Free Fall Air Resistance Model %8 April 16, 2010 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10002&DocID=1641

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An editor-recommended interactive tutorial that explores the influence of air resistance on free-falling objects and introduces the concept of terminal velocity.