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How High?! Modeling Free Fall with Air Drag

Presented by: Jacob Duncan, Winona State University, Winona MN USA https://qubeshub.org/community/groups... Abstract: Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. In this talk, I discuss a SIMIODE modeling scenario centering around the construction of a free fall model that accounts for the force of air drag. In the module, students develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students solve the model using two different methods – reduction of order and separation of variables, and method of undetermined coefficients. 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 it 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 are 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.