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[iceball3]

New physics question.  Probably less vague than the last one.  The hint I'll give you is be really, really careful about units.

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Erm, I think it's D?
Not much basis other than just brute forcing the cluster of ideas through my head.

[Darvi]

Nah, then v would have constant acceleration, and m*v^2 wouldn't have a constant incline.

[G-Flex]

(I'm assuming "total energy" is the horizontal line on top)

Well, gravitational potential energy varies linearly with height. Therefore, C can be ruled out immediately.



Now, we also know it can't be B, because if it were falling at constant velocity, then kinetic energy would not be increasing (nor would total energy remain constant).

Same with A, in its own sense: If there's friction slowing it down, it would be losing energy.


So, we know that all gravitational potential energy is converted to kinetic energy (not lost to any form of friction), implying that the object is falling, and falling freely, therefore D is correct.

Nah, then v would have constant acceleration, and m*v^2 wouldn't have a constant incline.

The horizontal axis isn't measuring time, though, it's measuring distance.

Gravitation potential energy = mass * height * gravitational constant. In other words, for every inch lost in height, you're gaining the same amount of kinetic energy and losing the same amount of gravitational potential energy. In other words, it is linear, not with respect to time, but with respect to distance dropped.

It's trivial to show that there is no friction involved at all, as friction implies energy is leaving the system, yet "total energy" (also visualized as gravitational potential energy + kinetic energy) remains constant.

[Darvi]

Right, friction takes away energy. That would also mean B is wrong, since that one implies there's friction or something similar.

Still...

Wait, we don't know how the axes are scaled. They could be bogus for all we know.

The horizontal axis isn't measuring time, though, it's measuring distance.

Head ->desk

[Leafsnail]

G-Flex has it.  And the point is that it doesn't matter in the slightest how the axes are scaled as long as they're consistent.

[G-Flex]

I think it's just too easy to assume that the independent variable involved is time when looking at a graph like this.

[Darvi]

Ya, force of habit.

I will for now restrain myself from posting in this thread after 8 PM, since that's pretty much the time I'm incapable of using my brain beyond the usual stuff.

[Erkki]

"What's in my pocket?" 

[Il Palazzo]

I'll drop a quick explanation of the lightening bolt question, as the ones we've had here were not clear enough, I think:
As Vector stated, it's got something to do with the difference in speed of light and sound, but this is not an exhaustive explanation. The second part of the problem is the spatial extent of the phenomenon.
Since the lightening bolt is stretched along a significant distance, not all points alongside it's length are equidistant from the observer. While in the case of light, the difference is not large enough for our brains to notice the arrival of the signal from the farther end of the bolt and from the closer parts, it is noticeable when the signal in question is a sound wave.
Seeing how the bolts are very irregularly shaped, we hear "cracks" arriving from different parts of them at different times. The longer the bolt from our perspective(closer to being parallel with our line of sight), the longer lasting is the sound. The more perpendicular to the line of sight it is, the shorter the sound(but louder, even if equally distant).

Of course, we could imagine a situation where the lightening bolt is shaped in such a way, that all it's points are at the same distance from the observer(an arc-like bolt). Then we'd hear just one short(and loud) crack, comparable in duration to the flash it would produce.

Then there's the rumbling, which as Solifuge said, is caused by the sound waves being deflected by the landscape. Since there's diffraction involved, the sound is lower than the original crack.


Here's another one:
When you're travelling by train, as I assume all of us did at some point, you hear the sound it makes, which is quite bearable, even with a window open. But when another train passess you by, the noise is suddenly overwhelming - a lot louder than just twice what you've been hearing before.
Why is that?

[Darvi]

"What's in my pocket?" 

Air and some fluff :3

[Jreengus]

A rather sadistic prison warden gathers together 20 prisoners and tells them that in half an hour he will take them out to the yard and line them up all facing in the same direction so that they can see everyone in front of them but no-one behind them. He'll then randomly place either a blue or red hat on each prisoners head and starting at the back of line ask each prisoner what colour their hat is. If they answer correctly they are free to go, if they answer wrongly they are shot on the spot. Since the only way they can communicate once they're wearing the hats is by saying a colour when asked what tactic can they use to ensure the maximum number survive and how many will be guaranteed to live?

[Darvi]

They all live. They know the ones in front of them, they hear the ones behind them. Easy deducting if you're not stupid.

...oh wait. it's not evenly distributed is it?

[Jreengus]

To clarify he has 20 red hats and 20 blue ones so they don't know how many of each hat has been handed out.

Also while I'm the subject they can't cheat by communicating in they way they say the word. for example: "They say their colour in a Russian accent if the person in front has a blue hat." Would be invalid.

[Darvi]

well red=20-blu.

Damn I know that one, so why don't I know the anwser? xP

...well having the last one saying the color which the most people are wearing, and having  the other ones parroting him guarantees that at least 10 people get to live. So that's a minimum.

[Leafsnail]

The obvious (and probably wrong) answer is that every odd-numbered prisoner says the colour of the hat in front of them (giving them a 50-50 chance of survival) and every even numbered prisoner repeats that (guarenteeing their survival).  This would allow a guarenteed 50% survival rate.

Or... no.  Actually, code it so that you say your answer in a high pitched voice if the person in front of you has a red hat, and a low pitched voice if the person in front of you has a blue hat.  That way everyone except the first person is guarenteed to survive.