In basketball, one may shoot the ball along a variety of different trajectories and still make a basket. For example, your shot may only reach a height a couple feet above the rim at its apex, or it may be a rainbow shot that well exceeds the height of the backboard. In both cases one can make the basket and score the same number of points. Nonetheless, one of the trajectories may be better than the other in the sense that it may be less sensitive to errors in aiming (left and right) or errors in how strongly one shoots the ball. This research project will seek to discover the optimum free throw shot in basketball. We will determine the answer computationally, based on physical principles, the way an engineer would solve the problem. We will compare our results to how expert basketball players (at the college and possibly professional levels) shoot free throws.
B.D. Coller (coller@ceet.niu.edu)
If you have driven on urban expressways during hush hour, you have likely experienced traffic jams: when the traffic slows dramatically or comes to a complete stop. Often this does not occur because of a traffic accident. Instead they occur simply because of the collective behavior of hundreds of motorists. In their desire to get from point A to point B in a timely manner, they create thick density waves in traffic. (See the discussion at www.amasci.com/amateur/traffic/traffic1.html for simple explanations.) There are scientists who have spent their professional lives studying traffic dynamics. Undoubtedly, though, there are aspects that are unexplored and not understood.
In this project, we will construct simple computational models of traffic flow. The computational models will consist of the dynamics of hundreds or thousands of individual cars, each with its own algorithm which determines how the car accelerates or brakes depending on the gap between it and the car ahead of it. We shall investigate how the driving algorithms for individual cars affect the overall traffic dynamics. It would be interesting to learn the degree to which one (or a few) aggressive drivers can bring all traffic to a halt.
B.D. Coller (coller@ceet.niu.edu)