Modeling Scenario


Author(s): Jacob Duncan

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

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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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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.

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Author(s): Jacob Duncan



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