Problem 3

## Up And Down The Mountain

One day at noon, Annie runs to the top of a mountain. She sits and ponders the meaning of life until the next day at noon at which time she runs down the mountain along the same trail that she ran up. Was she necessarily at some point on the mountain trail at the same time on both days? Prove your answer — Mr. Simmons

Well, that depends. Did she get to the top of the mountain at noon? or did she start running up at noon?

-Ryan D.

Also, theoretically, going down a mountain should be faster than going up, so i dont think she ever was on the same point at the same time on both days.

-Ryan D.

well, i don't think that thinking about the meaning of life would take ONE DAY.
and besides no food/drinks?
anyway.
she isn't necessarily on the same exact spot.
because of the force of gravity, you tend to move much faster downward. (agreeing with ryan)
also, trip, fall, slide down mountain might be a possibility. (ouch)

-Peter F.

Yeah, I agree with Ryan and Peter.
(aww man, i'm not first.)
Anyway, she won't necessarily be going the same speed, even if she was in a vacuum or something.

-Michelle L.

Wait, at first i didn't get how this applied to math…
but now i get it!
It's like a parabola right?
When you're going up, you're at a certain height (and you'll be at that height twice, but only the peak, where Annie is, will only be one time) and so obviously, both lengths are different distances from the bottom (the starting point) to the top (where Annie is coming down from) so you won't be the same.
As for the middle point, where the exact same length from the top and the bottom, well, i think this is where gravity plays a role. Also, steepness is not necessarily the same.
But if she decides to sprint up the mountain and walk slowly down, i suppose it's a possibility.. though not likely.

-Michelle L.

why me??? I mean the name… but whatever…

~Ann

Well, lets say she ran up the mountain the same speed she ran down the mountain. then, she would be at the middle of the mountain the same time each day. i think.

-Ryan D.

That's supposing that she goes up and down the same speed.
so technically it would be right.

-Peter F.

page revision: 64, last edited: 19 May 2009 02:08