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Topic: Moving Lines (Read 461 times) |
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FiBsTeR
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Moving Lines
« on: Dec 6th, 2007, 2:26pm » |
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I want to draw a vertical line on a piece of paper, so, of course, I take my pencil and draw a vertical line. Suppose that I can draw a line at a rate of 1 cm/s.
Say, however, that the paper is on a conveyor belt, and is moving horizontally to the left at a rate of 1 cm/s. If I try to draw vertically (ignore friction and whatnot), I find that the resulting line on the paper is not vertical; it has a slope of -1.
With the same drawing speed, how should I draw the line, relative to me, so that the resulting line on the paper is vertical (i.e. what is the slope of the line relative to me)?
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| « Last Edit: Dec 7th, 2007, 4:28am by FiBsTeR » |
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Noke Lieu
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Re: Moving Lines
« Reply #1 on: Dec 6th, 2007, 2:56pm » |
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walk to the end of the conveyor belt
pick the correct end or it'll get messy!
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towr
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Re: Moving Lines
« Reply #2 on: Dec 6th, 2007, 3:05pm » |
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Turn the paper a quarter turn, put down you pencil and keep it still
Yes, I know, the real solution is simple enough, but I'm going to postpone even that small calculation until I've gotten some sleep.
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JiNbOtAk
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Re: Moving Lines
« Reply #3 on: Dec 6th, 2007, 4:32pm » |
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Draw the line as usual; just make sure you're moving at the same velocity as the conveyor belt. 
The intended answer, in my opinion ( not so mathmetically inclined to prove it ) is to draw a line with m=1.
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| « Last Edit: Dec 6th, 2007, 4:35pm by JiNbOtAk » |
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FiBsTeR
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Re: Moving Lines
« Reply #4 on: Dec 6th, 2007, 5:11pm » |
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Hehe, nice solutions above, but obviously not any intended ones.
on Dec 6th, 2007, 4:32pm, JiNbOtAk wrote:| The intended answer, in my opinion ( not so math[ema]tically inclined to prove it ) is to draw a line with m=1. |
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EDIT: original post deleted
I don't think this is correct, but I'm not mathematically inclined either so maybe I'm wrong. 
Hint towards the (perhaps incorrect?) answer: I'll be surprised if anyone posts a correct answer with the string "m=" in their post... "I wonder what that's all about?"
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| « Last Edit: Dec 6th, 2007, 5:16pm by FiBsTeR » |
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towr
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Re: Moving Lines
« Reply #5 on: Dec 7th, 2007, 12:16am » |
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Let's say m=1, then the drawing speed is v=m= (vx2+vy2) therefore vx2+vy2 =  m
Now to remove the effect of the conveyor, it's speed and vx have to cancel each other out, so |vx|=m as well, which leaves 0 for vy
So the answer to "How should I draw the line, relative to me, so that the resulting line on the paper is vertical " should at the very least include "faster".
Otherwise it can't be done.
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| « Last Edit: Dec 7th, 2007, 12:18am by towr » |
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Grimbal
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Re: Moving Lines
« Reply #6 on: Dec 7th, 2007, 12:21am » |
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Stand sit on the conveyor belt.
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| « Last Edit: Dec 7th, 2007, 4:03am by Grimbal » |
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JiNbOtAk
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Re: Moving Lines
« Reply #7 on: Dec 7th, 2007, 12:26am » |
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on Dec 7th, 2007, 12:21am, Grimbal wrote:| Stand on the conveyor belt. |
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Wouldn't that require you use a really long pencil ?
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towr
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Re: Moving Lines
« Reply #8 on: Dec 7th, 2007, 12:32am » |
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on Dec 7th, 2007, 12:26am, JiNbOtAk wrote:| Wouldn't that require you use a really long pencil ? |
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Fine, squat on the conveyor belt. 
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FiBsTeR
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Re: Moving Lines
« Reply #9 on: Dec 7th, 2007, 4:27am » |
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on Dec 7th, 2007, 12:16am, towr wrote:So the answer to "How should I draw the line, relative to me, so that the resulting line on the paper is vertical " should at the very least include "faster".
Otherwise it can't be done. |
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That was my thought as well, though I intended the problem to imply that you draw at the same speed in each case. Thanks for the verification!
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