will it take off?

[daTeacha]

You're right on the aqueduct, Pat. The problem says "comes along". When the guy jumps ship, he exerts a force on the boat, but the boat is going to temporarily displace more water during the time of his departure. If the aqueduct is working ideally, the displaced water will be instantaneously moved from the vicinity, but realistically, the act of jumping will transmit some degree of hydrostatic shock through the system to walls and floor of the aqueduct, possibly causing a catastrophic failure and drowning all the residents of the village below as the thing empties itself.

I have a tendency to skim through these things since I'm basically stealing minutes at school for a lot of them. I'm at lunch right now, prep time actually. I look at this diversion as mentally preparing me to deal with a couple crews of incredibly untalented freshmen. I spent about 20 minutes day before yesterday trying to get them to see that the change in temperature could be expressed as |T1 - T2| rather than as a known quantity. At home my internet connection is faster than dial-up, but it has a tendency to break down at random intervals, so prolonged internet time is not really available.

 

[SPYDERLK]

Quote What about a glass of ice water filled to brim and a little more (aided by surface tension) such that a single drop more and it will spill over. The ice cubes are floating well above the rim of the glass. How much water will spill over when the ice melts and adds its water to the glass?

- -The amt of water that will spill is the amount equal in weight to the air displaced by the ice cube volume that is above the water surface.- -
Larry

 

[SPYDERLK]

Simple one for some, not for others.

You are at a county fair. There is a vendor of homemade ice cream running his ice cream machines with a hit and miss engine. You stop to watch the engine run and begin conversing with the vendor. He offers you a free ice cream if you can tell him what the temperature of the ice cream is and how you know the answer. Since you really want some ice cream and have no money, what do you say? You do not have a thermometer available.

Id say I would have to taste it to tell. Then Id say it was freezing because if it wasnt it would have been running, but that now it is 98.6. - -Its impossible to know its original temperature.
Larry

 

[patrick_g]

Larry, Very good! This may in fact be less than the ONE DROP (depending on your drop size) with no run over but your theory is on target AND drop size was not stated.

Now then daTeacha, before we become aquaduct half empty pessimists, mentally inundating and drowning the innocents below in mid orgy we need to allow for the entire spectrum of jump magnitudes. I suggest there is a gentle jump possible that would not be the straw that broke the aquaducts back. Until getting into jumps so small as to envoke quantitization of quantum mech there is essentially a continuum of jump magnitudes and similar to Zeno's paradox however arbitrarily close to failing you construe the aquaduct to be the jumper should be able to jump at a magnitude of shock just below destruction threshold.

Pat

 

[SPYDERLK]

Quote Adding the cream immediately lowers the delta T between the coffee and the ambient temp. The delta T is the big driver in heat transfer in this situation. Once the cream is added there is an immediate reduction of temp and the exponential rate of the coffee's approach to the asymptote (room temp) continues but the area under the curve (heat loss) is minimized. None of the other strategies are as effective. The main driver is delta T and the non-linear heat loss. Reducing the delta up front is THE TICKET.

I agree. this is the major part of any solution of these parameters. A major one that has been neglected is evaporation. Adding the cream will benefit this as well. In order to optimize tho, I would do the following:
1) Add MOST of the cream and stir with a straw or plastic spoon,
2) Allow solution to quiet,
3) Add the small remainder of cream,
4) Drape a paper napkin over the cup,
5) Keep the cup still.

Larry

 

[patrick_g]

Larry, You may note that I mentioned TWO uses for napkins! 1. cover with napkin
2. start a fire with napkins.

Patrick

 

[daTeacha]

If indeed the ship jumper actually jumps rather than gingerly steps off the boat as it parallels the side of the aqueduct, he will impart an acceleration to the boat and thence to the water. Perhaps he could grab an overhead beam of some sort and lift himself from the boat also, but any jumping action on his part could overload the aqueduct.

About the billiard balls -- it will not work if you put 6 on each side to start.

 

[daTeacha]

Larry, You may note that I mentioned TWO uses for napkins! 1. cover with napkin
2. start a fire with napkins.

Patrick

I believe starting a fire from napkins might be considered causing an undue disturbance for the waitress, management, and other patrons of the restaurant. Since you are wanting to keep your coffee warm without causing any problems at all, this approach would have to be discounted. Why not say you move to a window and you use your glasses to focus solar energy into the cup. This only works if you're farsighted, though.

 

[patrick_g]

daTeacha, Again you assume too much. You assume JUMP WITH SUFFICIENT FORCE SO AS TO CAUSE THE AQUADUCT TO FAIL when the problem said jump. As previously stated there is a continuum of jump magnitudes. Any arbitrarily weak aquaduct could be jumped into with an arbitrarily smaller jump than the destructive threshold.

Familiar with the argument of the beard? Good, well it doesn't apply hear.. na na na naaaaa nah!

Pat

 

[patrick_g]

I believe starting a fire from napkins might be considered causing an undue disturbance for the waitress, management, and other patrons of the restaurant. Since you are wanting to keep your coffee warm without causing any problems at all, this approach would have to be discounted. Why not say you move to a window and you use your glasses to focus solar energy into the cup. This only works if you're farsighted, though.

Again you assume too much or stated another way over limit the possibilities (truly stiffling.)

You assume the skill in building a fire is so poor as to emit lots of attention drawing smoke or that the fire builder wouldn't shield a direct view of the flames with a couple menus is to lack imagination. To stay "in character" as you alluded, one would have to be stealthy with the fire.

Pat

 

[daTeacha]

Actually, I haven't heard the beard thing. Please continue to enlighten.

The argument about jumps and overloads getting smaller and smaller doesn't wash, if you'll pardon the reference to getting things wet. A certain minimum amount of force is needed to accelerate the jumpee from the boat. The problem states that the aqueduct cannot take even one additional pound of weight. I hold that any person outside the womb would need an accelerative force of a magnitude greater than one pound to be able to leave the boat unless they grabbed an overhanging branch or bridge member and simply lifted themselves from the boat. Correct that -- they might be able to carefully step onto the side of the aqueduct if the boat is moving slowly enough.

 

[Egon]

Pat, lighting matches in airplanes can make for emergency landings!

DaTeacha:
Egon does not like numbers the exceed the fingers on one hand but Egon does like numbers that equal the fingers on one hand.

 

[daTeacha]

Egon -- That's good. You can only use the balance 3 times.

Yes, you CAN know the temperature of freshly made homemade ice cream. Fahrenheit did.

 

[rback33]

Pool balls, 12 of them; that is two more than Egon likes but Egon does like the number four!

Has everyone noticed that all these numbers have disillusioned Egon so much that he is referring to himself in the third person now?... He and Bob Dole could get together...

 

[daTeacha]

Yeah, I noticed that. Kind of like Igor used to do.

 

[jimmysisson]

Larry, Very good! This may in fact be less than the ONE DROP (depending on your drop size) with no run over but your theory is on target AND drop size was not stated.

Now then daTeacha, before we become aquaduct half empty pessimists, mentally inundating and drowning the innocents below in mid orgy we need to allow for the entire spectrum of jump magnitudes. I suggest there is a gentle jump possible that would not be the straw that broke the aquaducts back. Until getting into jumps so small as to envoke quantitization of quantum mech there is essentially a continuum of jump magnitudes and similar to Zeno's paradox however arbitrarily close to failing you construe the aquaduct to be the jumper should be able to jump at a magnitude of shock just below destruction threshold.

Pat

envoke quantitization????
whazzat?
Jim

 

[SPYDERLK]

Egon -- That's good. You can only use the balance 3 times.

Yes, you CAN know the temperature of freshly made homemade ice cream. Fahrenheit did.

Dont see how. It would be colder than 32F due to solutes. Temp to vary with constituents.
Larry

 

[daTeacha]

Homemade ice cream -- What is making it cold? Fahrenheit knew how cold it gets.

I guess we should actually be phrasing this one in language that reflects the fact that cold is not really quantifiable, but we're talking temperature here, not heat.

 

[Egon]

Home made ice cream is cooled by using ice and salt around the canister. The temperature would be at whatever temp the combination melts. If you use just straight ice it should be at 32degrees F. You might even get some moisture condensing on the ice but some of the ice may turn to vapour.

Egon is talking in third person because he likes numbers divisible by twelve. After post one in third person everyone should have understood he knew the pool ball solution. And no, not the jump and double bank to the side pocket!

Once you have the privilege of licking the the thingy that stirs the ice cream you will know what Heaven is all about and care less about what the temperature is.
The Paddle it is Ehh.
​

 

[patrick_g]

Envoking quantitization. Anything looked at closely enough reveals a quantized, i.e. granular nature. What we assume to be analog or continuous in nature is at best characterized by fine granularity and is quantized. Consider the digital music on a CD or an MP3, there are only a finite number of levels of volume or differences in frequency depending on the number of bits used to represent the sound and the rate at which the digital "words" or frames are recorded and played back.

da Teacha, In common usage "jump" as in jump from a bridge or building is often more like stepping off a high place and not a very vigorous action. Since a sufficiently vigorous jump can destroy the aquaduct how about a slightly less vigorous jump? What about a slightly less vigorous jump than the previous one? At some point before not quite making it over the gunwhale of the vessel the "jumper" will have "jumped" with sufficient lack of force and vigor so as to not cause the devestation.

Argument of the beard: If I have one long hair on my chin is it a beard? Most would say not. OK, how about 2 long hairs, or three, or 4, or... At some point most everyone will agree that I have a beard. It is an argument through incrementalization and although you may not get uniform agreement about where (what number of long hairs) makes me have a beard at some point you will get general agreement that I have one. This is the antithesis of the either-or all or nothing argument. It is generally accepted that you can't be a little bit pregnant,either you are or you aren't. That is an example where the argument of the beard is not useful.

Similar and in reverse a jumper exiting the vessel could exit with sufficient delicacy so as to not overstress the aquaduct. Envision a jumper with grotesquely large feet (no insult intended, Egon) with proper technique he could almost walk on water so exiting the vessel and letting his large feet act as hydraulic dampers to his downward motion he would spread and difuse the force distributing it in its temporal extent such that peak loads would stay below the threshold. He could also violently move his hands, oversized and grotesque, in a downward motion so the reactionary force would temporarily reduce his vertical downard component (temporary weight reduction) so as to ease his entry into the water. If he had untucked his shirt and flapped it along with his downward hand movement he could generate a pulse of aerodynemaic lift to further reduce the vigor of his aqueous entry. Perhaps this individual has extraordinary lung power and forcefully exhales in a downward direction in time with his "jump."

No one said anything about his companion(s) not helping to ease his transition by direct manual means.

Being a true "waterman" and would be pirate, he may have been able to get some assistance from his pet parot which was perched on his shoulder. The Nowegian Blue is known for the powerful thrust of its wingbeats. Ahh, beautiful plumage, the Norwegian Blue!

There are innumerable additional possibilities for assistance in gaining the "jumper" a smooth non-destructive entry into the water but those will be left as an exercise for the student (or da Teacha.) None of these were specifically elliminated by the problem statement which left an open field for certain categories of assumptions. There are, of course many assumptions that could be made that doom the jumper to disaster but listing them was not my intent. I chose to weigh in on the side of NOT destroying the aquaduct.

Oh, by the way... virtually everyone agrees that I DO have a beard!

Pat >