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?.

(In reply to re: Second attempt - physics based solution by Vishal Gupta)

To your first query, the average speed is 1/2 the speed at the top of the dip + 1/2 the speed at the bottom.  The speed at the top is V0, the speed at the bottom is V0 +sqrt(v0^2 + 2*g*h).  QED.

If I understand your second point correctly, you are attempting to mix relationships.  The point is, for every unit of distance (or speed) down (or up) the "dip" as I have described it, the horizontal distance travelled (or speed) is that amount * cosine (theta).

Edited on November 17, 2009, 8:29 pm

Posted by Kenny M on 2009-11-17 20:29:03