
#1
Feb2605, 03:24 PM

P: 366

This was in a maths textbook.
An arrow approaches its mark, (where its supposed to hit) but as it approaches closer and closer, it will approach half the distance it was at some time ago away from the target, and so on and so on and so on.. So im asking: Why does the arrow ever reach the target? 



#2
Feb2605, 03:33 PM

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Ask yourself this first: why wouldn't the arrow ever reach the target?




#3
Feb2605, 03:38 PM

P: 366

I don't understand what you mean. Forgive me if i am being an idiot of somewhat flavour.. To answer your question in a ridiculous, ambiguous, and idiotic way: the distance between the arrow is somewhat infinite..? I've heard it reaches the target because it depends on dimentions..but i wasn't quite satisfied with that answer, so im asking here.. 



#4
Feb2605, 03:47 PM

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Not an exact brain teaser, but..
The arrow is one object,how do you define:"the distance between the arrow"...?
What dimensions are involved here...? Daniel. 



#5
Feb2605, 03:54 PM

P: 366





#6
Feb2605, 04:27 PM

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Well,then do some recherche on the problem and then come with a "sound" version to us...
Da 



#7
Feb2605, 04:48 PM

P: 366

Fair enough. I will try and reword the question, and put down my 'hypothesis'. 



#8
Feb2605, 04:57 PM

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I mean to be stated very clear,just like a maths problem,not to leave room for interpretations or missunderstandings.
Daniel. 



#9
Feb2605, 05:25 PM

P: 33

Space is quantized so eventually it gets to the point where it can't go halfway any more and has to "make the leap"



#10
Feb2605, 06:01 PM

P: n/a

Are you trying to tell us one of the Zeno's paradoxes?
http://mathworld.wolfram.com/ZenosParadoxes.html 



#11
Feb2605, 06:04 PM

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Yes,my guess is that is sounds very much like one of them.Anyway,let there be noted,that,up until now,the OP is not clear what he is trying to ask...
Daniel. 



#12
Feb2605, 07:11 PM

P: 366

Let me try and make the question more accurate. (although it has already been answered) Consider a archer firing his arrow to a target at a certain distance away, E. When he fires the arrow, the arrow will travel towards the target, until it reaches a distance of E/2, then E/4, then E/8 and so on. Looking at this, the arrow shouldn't hit the target at all. However, we know this is not true, as we do actually see the arrow hitting the target. So, what causes the arrow to hit the target? 



#13
Feb2605, 07:26 PM

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This is an ancient paradox, and one that was not satisfactorily resolved till the theory of limits was formalised.
Ask yourself : Can the sum of an infinite series be finite ? Under what circumstances ? What does a constant velocity of the arrow mean ? What is the relationship of the distance travelled to the time taken to travel that distance ? Hence what is the time taken to travel each smaller "division" of the distance ? What is the total time taken ? I think you can answer your own question here. 



#14
Feb2605, 07:27 PM

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It is true that you have divided the problem into an infinite number of subtasks, the distance is still finite. 



#15
Feb2605, 07:38 PM

P: 366

EDIT: 'infinite' removed. 



#16
Feb2605, 08:10 PM

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Just think of it as an infinite series problem. What conclusions can you draw ? 



#17
Feb2605, 08:23 PM

P: 2,450

You can look at this another way too. If you are marking off the milestones then why should it even ever leave the starting point? It is never halfway to anything before it leaves the starting gate.



#18
Feb2605, 09:44 PM

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