Project-Based Learning with ODEs: Modeling Straw Rocket Motion with Air Resistance

This paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and drag coefficient. These parameters are then used to predict the outcomes of angled launches, highlighting asymmetries in flight time and range caused by drag. The activity connects theoretical modeling with experimentation and provides students with hands-on experience in testing assumptions, fitting parameters, and validating models.