There are two slides at the park between which you are deciding. both start at the height of 6 meter. one is short and steve while the other is long and shallow. if both sides are frictionless, which one should you choose if you want to be moving as fast as possible at the bottom? a. short and steep. b. long and shallow. c. it doesn't matter.

It doesn't matter.  If the slides are truly frictionless, then
your kinetic energy at the bottom will be equal to the
potential energy you had at the top, no matter what kind
of route you took getting down.


The only way I can think of that it would make a difference
would be if the shallow slide were REALLY REALLY long,
and you didn't have anything to eat all the way down. 
Then you might lose some weight while you're on the slide,
and your mass might be less at the bottom than it was at the
top.  Then, in order to have the same kinetic energy at the
bottom, you'd need to be going a little bit faster.

But if it takes less than, say, two or three days, to go down the
long, shallow slide, then this effect would probably be too small
to make any difference.

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