1APSC 254 MEASUREMENT, MODELING AND UNCERTAINTY OBJECTIVESTeach students the role of modeling in experimental science and the examination of experimental uncertainties. THEORYModeling of experimental results can be conducted in two ways. The most comprehensive method is when the model is developed from “first principles” i.e. from the fundamental physical, chemical, or biological properties of a system. With this type of a model, the mathematical basis for the model is developed, predictions are made from this, and these are tested experimentally. The second method of model development is to perform experiments and then develop a model that can be used to describe the data. It is incumbent on the experimenter to then refer the components of any equation that is used as a “curve fit” back to fundamental system properties thus creating a model. The difference between a curve fit (a mathematical equation that can be used to describe a trend in data) and a model is the understanding of the basis for the variables in the model. In this exercise, we are examining projectile motion. The fundamental principles describing projectile motion are well understood. The two basic parameters are the velocity and the angle of the launch. The horizontal range, Δx, for a projectile can be found using the following equation: tvxx=Δ(1) where vxis the horizontal velocity and tis the time of flight. To find the time of flight, t, the following kinematic equation is needed: tvgtyy0221+=Δ(2) where Δyis the height,gis the acceleration due to gravity and vy0is the vertical component of the initial velocity. When a projectile is fired horizontally (from a height), the time of flight can be found from rearranging Equation 2. Since the initial velocity is zero, the last term drops out of the equation yielding:
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