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Modeling Scenario


Author(s): Chris McCarthy

BMCC City University of New York, New York NY USA

Keywords: coding dragon Vectors Euler's method ball

101 total view(s), 17 download(s)


Resource Image If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the thrower.


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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level


This model needs to take into account air resistance (drag).

This scenario can be used to introduce students to Euler's method for higher order ordinary differential equations. To do this project students should be comfortable with the concept of second order ODE's, vectors, and F = ma from elementary physics. A little programming knowledge is a plus. But beyond that, not much is needed.

The student version contains the necessary physics background, including a brief discussion of drag, as well as a quick introduction to Euler's method for higher order ODE's. A Python script to solve the problem, if we neglect drag, is provided to the students. Their job is to modify the script to take into account drag. A full script, which solves the problem and includes drag is provided for teachers.

Article Files


Author(s): Chris McCarthy

BMCC City University of New York, New York NY USA



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