Brachistochrone Problem · BPhO 2007 #6

Physics · mechanics

Problem

A small mass, M, is given an initial velocity v0v_0, and it slides from A to B via two possible paths; either down the shallow dip X or over the hump Y, both of which are the same shape but inverted. Friction is to be ignored. Along which path does the mass take the shortest time to slide from A to B? [Figure: Two paths shown - path X goes through a shallow dip, path Y goes over a hump, both connecting points A and B at the same height] A. Via X B. Via Y C. You cannot say D. Same time taken

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