Sisyphus

I assume you're talking about an object in the room that is hot but then cools off. In that case, I believe it's because the heat is transferred from object to room by the collision of the molecules of object and air. If the object is hotter, its molecules are moving more quickly on average. The bigger the difference in temperature, the bigger the difference in speed, which means the bigger the difference in energy. So say the average air molecule has 1 unit of energy, and the average object molecule has 10 units. When they collide, the total energy is conserved, but some is exchanged. And so, on average, the air is going to gain energy and the object is going to lose some, causing the object to cool and the air to warm. Later, let's say the average air energy is 5 and the average object energy is 6. You can see that, on average, the object is going to lose less energy per collision, and so the temperature change slows down.

The big slingshot is a good idea, but why through the air? Wrap it up in a ball, then sling it along the floor so it rolls and has less chance of breaking. Or just bowl it! Is that cheating?

No electricity. But maybe you could just have a small wheeled cart, and start it on a ramp. 50m is a long way, though. Is it specified whether or not its a smooth surface?

Er, yes... I was a tad mixed up there. The ratio is NOT total distance:man's distance::pole height:man's height but RATHER total distance:total distance - man's distance::pole height:man's height So: The ratio of the shadow to the whole is 2 to 5 (simplified from 6 to 15). Therefore the ratio of the man's distance to the whole is 3 to 5. The speed is constant, so the ratio of the man's speed to the shadow's speed is also 3 to 5. The man's speed is 5ft/s. Therefore, the shadow's speed is 25/3. I put the blame entirely on you.

Rocket sled.

And it's not exactly equal. It's just close. By "perfect" do you mean complete? Because that would still happen if the moon was bigger or the sun was smaller. Anyway, I don't think a few minutes of unscheduled darkness every hundred years (or however long the time is between eclipses at a given location) would make any difference in anything.

I don't think one generally buys money in stores. I'm pretty sure the "300" and such are not actually 300 of something. More like 3 of something. Like 3 digits. Like for house numbers. Like I said...

Is he buying house numbers?

You've got some similar triangles. Therefore: length of shadow:man's height::distance from end of shadow to pole:pole's height Since both the man and the pole have constant heights with a constant ratio of 6:15, so too will the ratio of man's distance to shadow's distance be constant, with the same ratio. So if the man is walking at 5ft/s, the shadow is moving at (15/6)(5ft/s)=12.5ft/s. EDIT: Since this is in the calculus forum, I guess you want a calculus solution. You can write the total length (y) as a function of the man's distance from the pole (x) with y=f(x)=15x/6=5x/2. Also, you can write the man's distance as a function of time: x=g(t)=5t. Combine for f(g(t)) to get total distance as a function of time, y=(15/6)(5t)=75t/6=12.5t. Then you just take its derivative at t=8 to find the ft/s there, which in this case will always just be 12.5.

I wasn't sure whether to put this here or in politics. (I guess that in itself is revealing of the sad state of things.) Anyway, this was an editorial in the Saturday Washington Post. It made me smile. Here it is: IF YOU LIVE BY politics, you can die by politics, too. That's the lesson of the school board vote on Tuesday in Dover, Pa. All eight of the board's Republican incumbents were defeated. And all of the defeated incumbents had supported a policy -- the first in the country -- requiring the teaching of "intelligent design" as an alternative to evolution in ninth-grade biology classes. The board had been sued by a group of parents who argued that intelligent-design theory is a thinly veiled cover for creationism and that it is therefore unconstitutional to force teachers to teach it in public school classrooms. A federal judge is still pondering the case, but in the meantime eight Democrats campaigning against the intelligent-design policy have thrown out the school board. That vote is a fitting end to the Pennsylvania chapter of this saga. Because advocates of intelligent design have never been able to convince scientists that their theory has scientific merit, they've relied on political methods to get it into school curriculums. They've marketed their ideas to politicians using Web sites, news releases and free textbooks. Although the more nuanced proponents of intelligent design, such as the Discovery Institute in Seattle, frequently claim that their intent is not to promote a literal interpretation of the Bible, many of the politicians they win over are in fact creationists and do in fact deny that evolution took place. That certainly appears to have been the case in Dover. Now the limitations of promoting a theory through politics are clearly visible: The voters can vote the undercover creationists out. Soon there may be an opportunity to do it again. This week the Kansas Board of Education voted 6 to 4 to force teachers to include intelligent design's critique of evolution in their curriculum. The constitutionality of that decision will certainly be challenged in the courts and possibly at the ballot box as well: Three candidates who oppose the teaching of intelligent design theory have already announced that they will be running for seats on the Kansas Board of Education. It's a strange way to resolve a scientific controversy, but once that controversy has been politicized, it's hard to see how it can be resolved any other way.

Not only that, but THIS!

Well, the sun is one, as well as 99% of the matter in the universe, but I'm guessing he means something more like this: http://www.egglescliffe.org.uk/physics/fun/plasma/plasma.html

I don't see how he's equating randomness with free will, nor do I see how predetermination precludes free will. If you are able to make a choice, that is an exercise in will. Whether or not that choice is entirely determined by prior history doesn't seem at all relevant. Random=free? I guess you can define it that way, but what possible significance could that have?

Over the short term, pure oxygen isn't harmful to animals. It can even be helpful, since breathing it means the lungs don't have to work nearly as hard, which is why they give it to smoke inhalation victims, and why people with emphysema have oxygen tanks to help them sometimes. For a prolonged period of time, however, it can cause something called oxygen toxicity, which can damage brain tissue, among other things. That wouldn't have time to happen, though, since if the atmosphere were pure oxygen, everything on earth would become incredibly flammible, and the whole planet would go up in flames pretty much immediately.

The fact that cells only copy themselves a certain number of times is why we age, and its why death is inevitable with time, since sooner or later something vital is going to stop functioning and not be repaired. What actually defines death, though, is (I believe) just the destruction of the brain, which is caused in almost every case by lack of oxygen. For example, the weakened heart stops, blood stops circulating, the brain stops getting oxygen, and it dies within a few minutes.

Tea has a lot of them, too... Now why can't we live indefinitely? Why will it always be that way? Obviously we can never get rid of everything that can kill us, but surely its not fundamentally impossible to combat those aspects of aging that lead inevitably to death, is it? Sure we're nowhere near that now, but never? Or is the objection philosophical/practical rather than medical?

Do you want to know how to do it, or where the actual numbers are? If it's the latter, how does that help you?

I too used to think I was telepathic. That I could see the future and read minds, but only unreliably. Then I realized that the subconscious combined with simple coincidence would likely produce that same impression in just about anyone, regardless of any "powers" they had. For example, all the time the brain takes in information that we are not consciously aware of. And so you know things without remembering why you know them, which you think has something to do with psychic powers, but really is just your brain automatically putting things together that you don't even remember experiencing. And, of course, there's coincidence. Something occurs to you, and then, by chance, it happens. This sticks out in your mind for obvious reasons, but you're ignoring all of the times it doesn't happen, which of course is far, far more often. So of course sometimes what you think is going to happen really does - it would be strange if it didn't. And of course sometimes you think you can read minds, and it turns out the person really is thinking what you thought - if you have any idea how a person thinks, you know what external cues will push their thoughts in a given direction, and you can be pretty good at guessing at their internal thoughts. It's not telepathy, it's just basic awareness and luck. The better you know someone, the more often this happens. When my girlfriend and I talk, often others have no idea what we're talking about, just because so much is left unsaid, because each knows what the other is thinking. Are we telepathic? No. Sorry, but if it were real, it would most definitely be demonstrable.

The reason it approaches zero but doesn't actually reach it is because infinity is not actually a quantity that can be manipulated as if it were finite. "4/infinity" is just as nonsensical as "4/happiness." You can, however, take the limit of 4/x as x approaches infinity, since you aren't saying that x is infinitely large, only indefinitely large, meaning it is larger than any given finite value.

http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.html So that question is settled with a definitive "sort of."

Oops. You shouldn't have said anything, though. If he didn't know it was wrong, he could have learned a valuable lesson about accepting magical equations from nowhere without seeing where they come from.

I realize that. I was being facetious to begin with. I assumed teachers wouldn't assign students to violate fundamental laws of physics, which was my point. Although if I were a teacher, it would be funny to assign and see what they come up with.

Ok, so it has a name. But still nobody has any idea what it actually is or what causes it. Wonderful.

It is the law of cosines. Namely, c^2 = a^2 + b^2 + 2ab cosC, where a and b are the fixed sides, C is the increasing angle, and c is the increasing side. You know what a and b are, and so it becomes: c^2 = 12^2 + 15^2 + 2(12)(15) cosC simplified to c^2 = 369 + 360cosC or c = sqrt(369 + 360cosC) That can be rewritten as a function, with C as the independent variable and c as the dependent. Then you just take its derivative at C=60 to get the rate of change (increase in meters of c per degree of C). Since there is an increase of 2 degrees C per minute of time, just divide by two to get change in meters per minute.

I mean... he is.