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 would think the problem depends on the nature of the dip.  There is a curved path which would get the ball to the end faster than any other (I am not remembering any details) so if the dip is close to this shape this ball would be first.

I can think of a couple of cases where the ball encountering the dip would be slower than:
\
  \
    \
      \
        \
compared to this dip:
|
|
|
|____
         \
where the ball gets no forward momentum.

Posted by Jer on 2009-11-04 16:56:11