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3-011-EulerBallThrowing-ModelingScenario

Author(s): Chris McCarthy

BMCC City University of New York, New York NY USA

Keywords: coding dragon Vectors Euler's method ball

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Abstract

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
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

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.

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Authors

Author(s): Chris McCarthy

BMCC City University of New York, New York NY USA

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