Two identical balls roll across the top of a table on parallel paths. One of the balls has to roll down into and up out of a dip in the table. The other ball rolls on the flat all the time. Which ball gets to the far side of the table first, and why?.
Don't we need the Second Law here? Do we need to assume that the dip is entirely along a straight route from start to finish for the second ball (otherwise the horizontal distances will be different) ? Does the phrase "on parallel paths" include that inference for the dip? Even if so, we are not told that the descent and ascent in the dip are horizontally equal (covering the same distances as if on the flat). Speed will accelerate on the way down and decelerate on the way up. This is probably a straight-forward problem for a physicist, not a puzzle. My last physics course was over 50 years ago, and in all this time since I can recall no need to apply such rules. Any authority? (Google on this produces various interpretations: the most extensive discussion I found was at www.educatedguessswork.org
-- the last post in that thread, by a Vladimir Vysotsky, seems to argue that the ball in the dip will have less (or perhaps equal) travel time, so would arrive first.)