There's Something in the Air
Professor Nova built a nano aircraft which can travel around the Earth* along the equator. While giving a demo he sent two prototypes at the same time. First one he started by his feet, the second one at the height of his head, in the air.
He spent some time on the super computer, calculating the distance traveled by the first one. When he was querying again for distance of the second one, beyond the first, much to his surprise, little mathematician Alice told him the value. How?
*Aircrafts had the ability to pass through any solid or liquid substance
He spent some time on the super computer, calculating the distance traveled by the first one. When he was querying again for distance of the second one, beyond the first, much to his surprise, little mathematician Alice told him the value. How?
*Aircrafts had the ability to pass through any solid or liquid substance
Labels: mathemagic, thinktank
posted by Rajesh Lal at
9:06 AM
40 Comments:
there is definetly something in the Air today
Alice pulled out a peice of paper and drew a circle and gave it a circumfrence of the distence traveled then took the higth of the professor and drew a line straight up from the top of the circle in correct measurements to represent him standing on earth. Then she found the center of the original cirle and used a compass to draw another circle, boardering the original.
Now taking the given distence divided by the actual circumfrence of the original circle gave her X. She then found the circumfrence of the outer cirlcle and multiplied by x.
To do that she had to take miles down to a much smaller unit of measurement. She may have used mm or dm. Would be my guess. And that means x was a huge number. So if someone else wants to go through the trouble of doing the actual math compared to the average highth of a man, be my guest.
if little alice can do it it should be simpler than that
It does say Alice is a mathematician, so she could be a really smart midget or magical computing dwarf....
Couldn't you just calculate the difference based off the height of the guy...so assuming the guy is 5'7" or so (1.55 meters?) you would get an additional 134 * 3.14159... inches added onto the distance right?
or about 421 inches, 35 feet, or 10.5 meters
This is rather easy for an actual mathematician to do but it's probably wrong anyways...
I assume that since the 2 planes where sent off at the same time with the same speed. alice could have used the vt = d.
i have to agree with zyl it is easyer to just do the difference with the hieght of the guy
(His height) * pi
The diameter of a circle is 2 * Pi * radius, so if the radius is increased by the height of the guy. Therefore the additional distance travelled is ...
2 * Pi * Height
she could just use 2 x pi x r for both or pi x d and both of those equations are simple maths
you could just calculate the speed of the aircrafts and the time they took to come around.
alice gave the answer because she isn't an idiot and used a computer and the internet and google... duh
doesn't it say that it travels through solids and liquids but not gases. it would be zero nanometers.
This post has been removed by the author.
pi times twice his height is correct
diameter of earth is approx 7900 miles. there are 5280 feet in every mile. diameter of earth in feet therefore is 7900 x 5280 which equals 41712000 feet.
circumference of earth is pi x diameter. If pi is taken to be 3.142, then circumference of earth is 41712000 x 3.142 which gives 131059104 feet.
now then, assuming Professor Nova is 6 feet tall, the diameter in question would be 41712000 PLUS twice his height (6x2=12)which gives 41712012 feet. Multiply this by pi to get the new circumference. 41712012 x 3.142 is 131059141.704.
subtracting the first circumference from this new one gives 131059141.704 - 131059104 = 37.704 feet.
12 x 3.142 = 37.704
Alice would therefore have been correct in suggesting that the extra distance was merely double the professors height multiplied by pi.
they have the same time
all of your answers assume that both nanos, when drawn a line to the first plane from the ground, if extended the line would hit the second plane at the same place where it hit the first.
Or in other words, the plane at head level was always right above the plane at feet level.
Since the distance needed to be covered by the second plane is going to be longer than the first if this was to be true, then you guys assumed that the second plane had a different speed than the first. We don't know this, therefore it would be correct to surmise that we cannot assume this.
Since this piece of information was included "he sent two prototypes at the same time" and nothing else. We can only assume that they travelled at the same speed. Therefore, we can only assume that they travelled the same distance. No calculations are necessary in this case.
However, if in fact the second plane kept up with the first so that it was always above it, then yes I believe you guys would be correct although I have not done those calculations myself yet.
If they are travellin at the same speed, The second one will travel the same distance in the same amount of time regardless of the path.
Now, if we were looking for how many radians they traveled, we don't have enough info. But, we could create a fomula to calculate the answer.
Alice said "same distance dummy"
mitch is right. if they are going the same speed it would be the same distance but since the second plane is higher off the ground it has a longer flight path so it looks like it went a shorter distance. for example. if two people run around a track at the same speed then stop at the same time the runner on the inside track will be farther ahead on the track but they will have ran the same distance. this is because the second runner is farther away from the center of the turn so he must run farther to get out of the turn than the inside runner. make sense?
Both Aircraft traveled the SAME DISTANCE = 1 EARTH CIRCLE.
Here's a reasoning - If I walked all round the equator - would my head have travelled further than my feet?
I don't think so - therefore I would like to retract my earlier comment :)
your all missing the point.
1) They are both the same. so we can presume that they fly at the same speed.
2) The first was started at his feet and the second at the height of his head. IN THE AIR.
3) When he did the SUPER COMPUTER calculations. the second one was BEYOND THE FIRST.
So we know that even though the second one had 2 * Height * PI distance more to travel it was still further ahead. WHY? and Alice told him the VALUE. So what is the value?
Its simpler than all that guys--if they travel at the same speed (which we presume from being identical) then in the same time they cover the same distance, PERIOD. She told him the distance of the second because he had just said the distance of the first--they are the same. ITS TRUE that they would not perpendicularly aligned to the center of the planet--that is, that they will not be in the same location on the planet--the one at the feet will most certainly be at a location further from the scientist than the one at 6' up--but it only asked the distance travelled, and they travelled the same distance. The difference is that the one in the air has a longer trip, and therefore is making progress on it more slowly, and will come home after the first.
Sorry mitch--i didnt see you had already given the right answer--just consider the above expounding upon your answer :-)
and yes--your head does travel further than your feet, a tiny bit
2piR is my 1st guess, r is smaller from the guys feet so the circumfrance is smaller and would be by quite a bit in retrospect to the earths size
they were probably just going REALLLLLLLLLLLLLLLLLLLY SLOWLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
headcage, your head DOES travel a larger distance than your feet, that's why your body is still in one piece.
And anonymous, it's MUCH further.
Why is everyone saying they traveled the same distance? This is true, but it's not the answer to the question asked.
The question was not, "How far each traveled from the starting position." but, "The distance of the second one, beyond the first," which means the distance between the planes.
Even though they are moving at the same speed, they are on different paths, and so the distance between the two would increase as time increases.
The anser could be that the second plane never travels beyond the first, because it would be behind, not beyond. But now I'm just assuming wordplay is involved in the question.
If wordplay is not involved then I have no clue. But I believe a lot of you are also wrong in assuming it's asking for the total distance traveled.
~Cenyu
C1 =2 x r x Pi
C2= 2 x (r +Y) x Pi
c2= (2xPi x r) + (2 x Pi x Y)
C2 = C1 + (2 x Pi x Y); if Y (distance between his head and his feet, very short prof) = 1 m, then C2 = C1 + 6.28 m,
which is total distance travelled, which wasn't the question.
but
s = V/t since t is the same for both, and v is the same for both, therefore both airplanes
travelled the same distance at any given time. So she said, wouldn't the distance travelled be the same at any given time?
B.
Cenyu, I believe you're right. I mistook the "beyond the first" as just a part of the description. As in, "the second rocket which is beyond the first" as in higher up in altitude (which was a given).
It would go exactly the same distance.
The two aircraft are built identically and with the same properties. So, if they can move through any obstruction, it doesn't matter where they start. They move at exactly the same speed, so in the same time frame, they would cover the same distance.
It isn't a question of how far it moves along the equator, but the distance it has moved in total.
it would e the same cuz they would go at the same speed, and the same distance, so what would it matter?
what you guys dont get is that the super computer is telling the proffesor that the second nano aircraft is further then the first one, But the super computer is not tellling the porffesor on which way the super computer is computing this.
So in theory, the second nano aircraft is actually behind the first aicraft, BUT the super computer is telling the proffesor that it is actually ahead beacuse the second one is closest to them. So when you think about it, the second is closest to them, but the first aircraft will be the first to get back to him.
so the profesor actually had the super computer programed so that it would show him which of the two nano aircrafts would be closeset to him and the super computer obayed and showed that the second one is closest only because it is behind the first one thus when the first one reaches 1/2 point, the second one would be around the 1/4 point, still making the second aircraft still closer to the profesor then the first even if the first was further ahead.
Ok did the question say that the plane could travel through the air itself? It just said that it could go through gas and liquids, but it never said that it could fly... Just a thought.
Alright they both traveled all the way around the earth. That is the only set distance, one lap around the earth along the equator. Now if you tell me the circumference of the hole in a dognut is the same as the ouside then your strait silly. The one at his feet is the hole. The one at his head is the outside. The 2*height of proff * pi will give the differece. The one at the head went farther. Little Alice just plugged in the proffs height and walla.
i'm pretty sure she told him using her mouth.... but maybe little math magician alice is deaf, in which case i propose she used the American Sign Language method.
ANSWER = 10 meters (approx.)
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DETAILS
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Interesting thing is to calculate the difference we don't need to know the radius of the earth. we only need the height of the professor and the value of pi which little mathematician alice knew.
2 * pi * (r + h) - 2 * pi * r
= 2 * pi * h
= 2 * 3.14 * 170 cm ( ~ Average height is 5 feet and 7 inch)
= 10.67 meters
GOT RIGHT
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Zyl, bald, jonathan, B.,
What if he were to travel along a north-south line? The diameter would be different because the earth is not a perfect globe. The difference would be small but significant.
~inquiring minds.
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