Best Answer Anza Power, 07 December 2012 - 06:38 PM

Spoiler for

the answer is yes. Andy the ant is placed on the elastic band at the point of 1/100 an hour, or after 36 seconds.

as noted by rainman, (though i don't agree with his result) if the ant stands still the relative distance to the truck will remain the same.

so, after the next 36 seconds, the elastic band will double, and andy will be at slightly more than 1/10000 of the way. after the next 36 seconds, the elastic band will be 3/2 larger, putting andy at roughly 3/20000 +1/10000 = 5/20000. after the next 36 seconds, the elastic band will be 4/3 more, putting andy at roughly 20/60000 +1/10000 = 26/60000.

more precisely, we have... e^(0.01*x) -1 = 100; or that andy will reach the truck after 461.5 hours roughly.

I think your first sentence is wrong

Spoiler for

If the ant was to stand still, let's say exactly in the middle of the band, it will always be in the middle of the band, if it stood at 1 quarter of the length of the band, it will always be at one quarter of the length of the band and so on...

You can imagine splitting the band to N points and marking them, now if the ant stood between any two points when the band stretches it will always be between those two points

You can imagine splitting the band to N points and marking them, now if the ant stood between any two points when the band stretches it will always be between those two points

But you can put it another way:

Spoiler for

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get a marker and mark N points on the band at equal distances, the band grows linearly, it's length at time t would be

So if we take an N that is big enough so that v

**L(t) = L**, you can see that the distance between every two points would be exactly_{0}+ v_{0}t**1/N * L(t)**, take the dirivative and you'll see that the growth rate of that piece is**v**._{0}/NSo if we take an N that is big enough so that v

_{0}/N is less than the ant's walking speed then the ant could get from mark k to mark k+1 in finite time, and since there is a finite number of points it will get to the last point in finite time as well,,,