November 11, 2016

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.

- Mathematics > General

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Model with mathematics.

Create equations that describe numbers or relationships

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

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

Interpret functions that arise in applications in terms of the context

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

Build new functions from existing functions

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.

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

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

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