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OER Materials

Modeling Scenario

4-039-FallingDarts-ModelingScenario

Author(s): Jacob Duncan

Keywords: optimization resistance terminal velocity muzzle velocity drag coefficient free fall air drag

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Abstract

Resource Image we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined coefficients.

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Article Context

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

Description

Using the solution, students derive an expression for the terminal velocity of the object as well as a prediction of the maximum height of the object (assuming is is fired directly upwards).

The model is then parameterized for a Nerf dart by an experiment performed by students.

The terminal velocity and muzzle velocity of the dart is measured using video frames of the dart's motion.

Finally, the model is validated by an experiment wherein students fire their darts upward and measure the assent time for comparisons with their predictions.

Article Files

Authors

Author(s): Jacob Duncan

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