|
A difficult math problem...[SOLVED]
|
View this Thread in Original format
| tribu |
A tenacious little ant is marching its way across a rubber band at a steady pace of one millimeter per second. It starts out from one end of the band and is headed towards the other end. When it starts, the rubber band is one meter long. After a second has passed, however, the band instantaneously stretches elastically so as to be elongated by an additional meter (i.e. it is now two meters long). This process repeats every second, so n seconds after the ant begins his trek, the band is n+1 meters long. The question is this:
Does the ant ever reach the other end of the rubber band? If so, how long does it take? If not, why not?
EDIT
Here are a couple givens for Floorfiller:
The rubber band increases exponentially each time.
This special rubber band will not break.
Time is infinite.
Space is infinite.
This ant will not die.
(I'll add more if i need to)
(congrats to *Noisician* who is apparently the math wizard around here, for solving this problem) |
|
|
| Floorfiller |
well...theoretically the rubberband would have a limit to elasticity so it would either eventually reach a point where the rubberband wouldn't stretch anymore and allow the ant to cross or it would snap...
*waits for nosician to answer the question with math*
no pressure hehee
also i'm sure he'll get to the end...i just don't know how to do the math perse...but i think it has something to do with the proportion of the rubberband he has already crossed in comparison to the extension of 1 meter per second...but like i said...i don't know the math behind it... |
|
|
| milanster |
| no it wont reach the end..give it sometime and the rubberband will be torn kicking the ant up high into outer space! :D |
|
|
| Floorfiller |
| is the place where the ant starts a fixed point in time and space and the rubberband is elongating in one direction or is the lengthening in both directions adding to a total increase of 1 meter per second... |
|
|
| tribu |
The rubber band increases exponentially each time, thus the length is not added to the end but to the entire rubber band.
Ive added this above as well, for people new to the thread. |
|
|
| rabbitjoker |
| Solved easily using Zeno's theorem/Zeno's Paradoxes.. |
|
|
| djdawn |
i would think you don't need a theorem for this one.
after 1 s, the band is 2 meters long, the ant has walked 1mm
after 2 s, the band is 3 meters long, the ant has walked 2mm.
so after 1000s, the band is 1001m (=1km 1m) long, the ant has walked 1m (!).
how is it supposed to reach the end? |
|
|
| tribu |
Rabbit Joker is quite correct with his idea.
| quote: | i would think you don't need a theorem for this one.
after 1 s, the band is 2 meters long, the ant has walked 1mm
after 2 s, the band is 3 meters long, the ant has walked 2mm.
|
read the givens for this problem, it may help see your error in logic. |
|
|
| rabbitjoker |
| quote: | Originally posted by tribu
Rabbit Joker is quite correct with his idea. |
 |
|
|
| rabbitjoker |
| quote: | Originally posted by djdawn
after 1 s, the band is 2 meters long, the ant has walked 1mm
after 2 s, the band is 3 meters long, the ant has walked 2mm.
so after 1000s, the band is 1001m (=1km 1m) long, the ant has walked 1m (!). |
Exponential growth mate... not linear. |
|
|
| Tranc3 |
| quote: | Originally posted by rabbitjoker
Solved easily using Zeno's theorem/Zeno's Paradoxes.. |
That's exactly what I was thinking. |
|
|
| mot10n |
ahh physics.. how i miss the days of odd mechanics questions..
HURRY UP SCHOOL !! I FEEL EMPTY WITHOUT YOU BREATHING DOWN MY NECK !! |
|
|
|
|
