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?.

I take back my contention re Newton at my comment below .

I remembered something I think I read in one of Martin Gardner's books about the shortest time for a body to traverse a distance from A to B via a vertically curved path.

I found this comment from a Google search:

The cycloid curve is "brachistochrone", i.e. a curve of least time: given two points A, B in a vertical plane, a heavy point will take the least time to travel from A to B if it is displaced along an arc of a cycloid.

While the "dip" may not have this profile I think we can infer that a vertically curved path will be quicker than one that is horizontal.

Posted by brianjn on 2009-11-05 20:01:35