A rider in a roller coaster lets go of a particle such as a small marble. How far does the marble travel horizontally from the point of release before hitting the ground, assuming the speed of the roller coaster is determined by conservation of mechanical energy starting from the highest hill up which it was pulled. Where should the marble be released along the track if one wishes to maximize the range of the marble. These questions constitute interesting variations on conventional problems in two-dimensional kinematics, appropriate for an undergraduate course in classical mechanics. Exploration of various shapes of tracks could form interesting student projects for numerical or experimental investigation.
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