The first two models are based respectively on the common simplifying assumptions of no air resistance and linear air resistance, and the third is based on the correct physical form of air resistance (which students are asked to identify). Data is provided both for parameter estimation and for model verification, and the verification data is used to compare results of the models. While most calculations associated with the first two models can be carried out by hand, technology is essential for analysis of the physical model.
Ballistics is the science of projectile motion and impact, phenomena well described by Newtonian mechanics. The number of applications of this type of analysis is staggering, ranging from such mundane issues as automobile accident simulations and optimal golfing to the critical studies of missile defense and space exploration. Somewhat less dramatically, in this project we will use Newtonian mechanics to describe the flight of a sponge dart (a Nerf dart or an off-brand), light enough so that air resistance will play a critical role.
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