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Description:

This simulation shows a ball launched by a spring-gun in a building with a very high ceiling. The student's task is to calculate an initial velocity so that the ball barely touches the 80-foot ceiling. Students can test their answers by setting the initial velocity on the simulation, then watch the ball's path. Graphs of position vs. time or velocity vs. time may be turned on to view the ball's motion as a function of time. Editor's Note: This model is especially helpful for visualizing the relationship between the one-dimensional motion of this example and its graph, as it displays the ball continuously bouncing at constant velocity in a straight line from floor to ceiling. There is no horizontal displacement. For students who need help determining time of flight and peak height, SEE ANNOTATIONS for an editor-recommended tutorial. This item was created with Easy Java Simulations (EJS), a modeling tool that allows users without formal programming experience to generate computer models and simulations. To run the simulation, simply click the Java Archive file below. To modify or customize the model, See Related Materialsfor detailed instructions on installing and running the EJS Modeling and Authoring Tool.

Subjects:

• Mathematics > General

English

Access Privileges:

Public - Available to anyone

Creative Commons Attribution Non-Commercial Share Alike

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Update Standards?

CCSS.Math.Practice.MP4: Common Core State Standards for Mathematics

Model with mathematics.

CCSS.Math.Content.HSA-CED.A: Common Core State Standards for Mathematics

Create equations that describe numbers or relationships

CCSS.Math.Content.HSA-CED.A.2: Common Core State Standards for Mathematics

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

CCSS.Math.Content.HSA-CED.A.4: Common Core State Standards for Mathematics

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

CCSS.Math.Content.HSF-IF.B: Common Core State Standards for Mathematics

Interpret functions that arise in applications in terms of the context

CCSS.Math.Content.HSF-IF.B.5: Common Core State Standards for Mathematics

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?

CCSS.Math.Content.HSF-BF.B: Common Core State Standards for Mathematics

Build new functions from existing functions

CCSS.Math.Content.HSF-BF.B.3: Common Core State Standards for Mathematics

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.

CCSS.Math.Content.HSF-LE.A: Common Core State Standards for Mathematics

Construct and compare linear, quadratic, and exponential models and solve problems

CCSS.Math.Content.HSF-LE.A.1: Common Core State Standards for Mathematics

Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSS.Math.Content.HSF-LE.A.1b: Common Core State Standards for Mathematics

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
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