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 think we must assume that the table top is level as well as flat, and that the dip starts at the surface level, goes monotonically lower to some point, and then rises monotonically from that point to the surface level and pointed on a path parallel to that taken by the ball which remains on the same plane throughout and never touches the sides of the dip (introducing drag)... I'm not sure what affect it would have if the dip were a "cork-screw" path, as long as the depression is entered and exited on the plane and never rises above it. Since this is categorized as "science" I suppose we need Newton's Laws, the conservation of linear momentum, and the like. School bells a-ringing.
Assumptions
