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[iceball3]

Yes. I like this new thread.

[Leafsnail]

Via X of course. How would I know that the ball would have the initial velocity to overcome the hump in the first place?

Not a trick question.  The mass can overcome the slight hump.

EDIT: Uh, by the way, the main thing is to read the last sentence of the question carefully.  Make sure you know what you're answering.

[Strife26]

I think that it's X

Explanation:

Spoiler (click to show/hide)

Friction is being ignored, but gravity is in play. That means that the ball is going to accelerate going down the hill equal and inverse to what it loses going up.

This means that if it's a hump, not a dip, the ball is going to go Start speed-decelerate as it goes up the hump-accelerate back to start speed on the way down.

If it's a dip though, it's going to go Start speed-accelerate on the way down, THEN decelerate on the way up, back to start speed.

In the second case, the elevation change is going to mean that it's going to have an average velocity faster than the start seed, while the first one will be less than start.


I think that the actual math would be something with Integrals, but hell if I know it for sure. 

[woose1]

Well, let's assume that going up a hill is V-1, and going down a hill is V+1. If the two humps are exactly equal in size but simply in inverse, then both balls would reach the end in the same amount of time. That is; if friction was still in play.

Since it's not, the ball from Y has increased velocity for a longer duration of time, so ball Y reaches the end first. I think. I really haven't taken physics yet so I don't know the mechanics of what would actually happen in a frictionless environment, but there's my rough stab at it, at least.

[Leafsnail]

Strife's answer is completely correct.  They both end at the same speed, but since X had a faster bit in the middle (while Y had a slower bit in the middle) X finishes earlier.

I don't think introduction of friction would change things much (except making it a bit more complicated).

[Sowelu]

I am very sure it's faster via X.

It will travel the same speed before and after the valley/hump no matter which path it takes.  But in X, its velocity will rise above its original velocity then slow back to normal, and in Y, its velocity will drop below its original velocity then raise back to normal.  Therefore it will cross the valley in less time than it will cross the hump.

...Wow, very ninja'd.  Also I'm slow while at work.

[woose1]

I am very sure it's faster via X.

It will travel the same speed before and after the valley/hump no matter which path it takes.  But in X, its velocity will rise above its original velocity then slow back to normal, and in Y, its velocity will drop below its original velocity then raise back to normal.  Therefore it will cross the valley in less time than it will cross the hump.

...Wow, very ninja'd.  Also I'm slow while at work.

I didn't think of the accumulated drag from the initial rise. Turned out I was right initially, but for the wrong reasons. 

[Strife26]

We need some more questions!

Here's my super number riddle all in one spot.

Spoiler (click to show/hide)

The answer's a number, but it's more than that. It has length. It has the original spark for half of my name. It's where cloaks and 16 tomes of magic spells came into my closet. Elegantly bound books. It's where I got more than Fire, Earth, Water, and Air. It's a game, it's a song, it's a movie . . .

What is it?

It's neither 13 nor 7. But one of them is somewhat correct. Of course, the other is closer and further.

Suppose you go back in time and muck with history a bit. One thing leads to another and you eventually become your own parent. Weird, true, but the Guide tells us that it's a survivable thing in a relationship. How does your DNA work?



I could go get some Diabolic Cheesecake riddles from C&A if we want more . . .

[Zrk2]

Y! Because the extra momentum from coming down rthe other side makes it travel faster for longer to travel the distance to B! I think.

[Strife26]

Y! Because the extra momentum from coming down rthe other side makes it travel faster for longer to travel the distance to B! I think.

In a frictionless environment, the momentum gained from going down the far side of the hill is exactly equal to what is lost on the near side.

[G-Flex]

Y! Because the extra momentum from coming down rthe other side makes it travel faster for longer to travel the distance to B! I think.

In a frictionless environment, the momentum gained from going down the far side of the hill is exactly equal to what is lost on the near side.

It's D. Simple thermodynamics: In order to go up a certain elevation, you lose an amount of energy equal to the amount of energy you'd gain going down that same elevation. Unless some is being lost to friction or some other thing, which it isn't.

In one case, it goes up h centimeters and loses k joules of kinetic energy, then goes down h centimeters and gains that same amount k of kinetic energy. In the other case, the opposite thing happens, but in either case, after the hump/dip it has velocity v₀ as there is no net gain or less in kinetic energy whatsoever.

[Urist Imiknorris]

Actually, the kinetic energy of the mass is being converted to gravitational potential energy and vice-versa. The energy's not going anywhere, because nothing's doing work on it.

[Zrk2]

Shhh! I thought I was right! Then theoretically, they both take the same amount of time.

[G-Flex]

Actually, the kinetic energy of the mass is being converted to gravitational potential energy and vice-versa. It's not going anywhere, because nothing's doing work on it.

Correct. When I refer to it "losing" kinetic energy, obviously that energy is going somewhere, and it's going into gravitational potential energy of the object (relative to whatever gravitational potential energy it already has).

[Urist Imiknorris]

Going through path X, the mass gains speed as it enters the dip, until it reaches the bottom. With Y, it loses speed. Then, both accelerations are reversed until the mass reaches its initial speed. There's no denying that the mass goes faster through X.