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A difficult math problem...[SOLVED] (pg. 2)
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| 3xx3r7 |
| Sounds like an induction problem to me. |
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| whitesmoke |
| here is what many of you are missing....the entire rubber band is stretched by 1 m each second and not simply the portion past the ant. The stretched portion inclues the distance behind the ant. so after one second when the rubber band doubles in length (1m to 2m) so do does the distance the ant walked. then when the rubber band goes from 2m to 3 m, the band has increased 1.5 times so the distance the ant walked also has to be multiplied by this. this hapnes over and over. you have to take this into account when solving. i just woke up so that is all the thinking i am going to do now. hope this helps you guys. |
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| Floorfiller |
well i don't know all of this zeno's theorem stuff, but i was just trying to think about it logically. tell me if this is kinda the way to approach it. i might be completely off hehehe...i didn't get that far in the sciences since my major doesn't require it...
the ant starts out with this .01 meters per second speed and the rubber band at its 1 meter per sec speed.
as time approaches "n", the distance the ant travels will also be absorbing some of this stretch of 1 meter per second. therefore as the ant travels a greater and greater distance...the effect the 1 meter per second becomes smaller and smaller as the distance ratios become closer together.
like i said...i don't know how to do the math, but is that reasoning somewhat right? :conf:
i love trying to solve problems hehehe...good thread :D |
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| physe |
Yeah, that's how I approached it, but remember that 1mm = 0.001m. This might make a difference in the answer. I was too lazy to find a proof so I just modelled it in excel and iterated the process a number of times. I found that the distance that the ant loses due to the stretching of the rubber band converges so the ant will continue to lose distance due to stretching no matter how long you wait. If ant did indeed move 1cm, it would... (let me check)... still converge to a number (slightly smaller in magnitude than in the first case) that would not allow the ant to cross the band. This assumes that I have modelled the movement properly. This answers the question, but by no means proves it.
EDIT: So if I have done it right, I'm interested in knowing the minimum amount the ant has to move each second to reach the end of the band?
I wish I could prove it, but I'm an engineering/physics major so I lack the training in mathematics to prove this question. I would expect that either a math or computing science major would be able to prove this.
EDIT #2: I should also point out that I modelled the band as being stationary in the center, and growing by 0.5m on both ends each time. Another way to model it would be to have one of the ends stationary and the other move by 1m every time. This should have no effect on the answer though. |
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| Floorfiller |
| quote: | Originally posted by physe
Yeah, that's how I approached it, but remember that 1mm = 0.001m. This might make a difference in the answer. I was too lazy to find a proof so I just modelled it in excel and iterated the process a number of times. I found that the distance that the ant loses due to the stretching of the rubber band converges so the ant will continue to lose distance due to stretching no matter how long you wait. If ant did indeed move 1cm, it would... (let me check)... still converge to a number (slightly smaller in magnitude than in the first case) that would not allow the ant to cross the band. This assumes that I have modelled the movement properly. This answers the question, but by no means proves it. |
oh yeah...of course... .001:D |
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| Massive84 |
hey man you can be a president of a country without knowing english and uber math..
look at france!. |
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| Lephaid |
The rubber band increases linearly with time, not exponentially...(as if it mattered anyway in this case, though)
t is time (minutes)
The ant moves at .001*t
The rubber band expands at t+1
The point at which the functions intersect is where the ant would reach the end
Both are linear functions...graph them and there's obviously no way they can intersect (unless there's negative time).
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| physe |
| Yes, but the ant also moves when the band stretches. |
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| Floorfiller |
| quote: | Originally posted by Lephaid
The rubber band increases linearly with time, not exponentially...(as if it mattered anyway in this case, though)
t is time (minutes)
The ant moves at .001*t
The rubber band expands at t+1
The point at which the functions intersect is where the ant would reach the end
Both are linear functions...graph them and there's obviously no way they can intersect (unless there's negative time).
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i'm sorry but this can't be right. the distance the the ant has travelled does not stay at a linear rate. because the rubberband stretches uniformly, the rate at which that distance increases will cause it to become an exponential function... |
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| TranceGiant |
| Noisician to the rescue.... |
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| Floorfiller |
| quote: | Originally posted by TranceGiant
Noisician to the rescue.... |
i second that heheheh.... |
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| Lephaid |
| quote: | Originally posted by physe
Yes, but the ant also moves when the band stretches. |
Point taken, but even then, it still shouldn't reach the end because the expansion of the band is far quicker than the ant could move...but I can't think of a way to prove that now, so...:conf:
Noisician, save us! |
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