The forum discussion centers on the physics riddle involving the Brachistochrone problem, which examines the fastest path between two points under the influence of gravity. Participants analyze various paths, including straight lines and curves, and discuss how factors like initial velocity and path shape affect travel time. Key equations are presented, including time calculations for different trajectories, emphasizing that the Brachistochrone curve is always the fastest path. Ultimately, the conclusion is that while some paths below the horizontal can be faster, not all are guaranteed to outperform a flat trajectory.
PREREQUISITESPhysics students, educators, and enthusiasts interested in classical mechanics and optimization problems involving motion under gravity.
But it isn't one. The more on kinetic energy gained downwards is lost again upwards. (But I haven't done the math, maybe it doesn't cancel out, however I think it does. I desperately try to remember the analogous experiment in a math museum I once visited, I thought they were equally fast at the finish ...)Borek said:Then how come brachistochrone exists, if time on all curves is identical?
fresh_42 said:But it isn't one. The more on kinetic energy gained downwards is lost again upwards. (But I haven't done the math, maybe it doesn't cancel out, however I think it does.)