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        riddles >> easy >> Moving Lines
        
(Message started by: FiBsTeR on Dec 6^th, 2007, 2:26pm)

Title: Moving Lines
Post by FiBsTeR on Dec 6^th, 2007, 2:26pm

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)?

Title: Re: Moving Lines
Post by Noke Lieu on Dec 6^th, 2007, 2:56pm

[hide]
walk to the end of the conveyor belt
::)
pick the correct end or it'll[/hide] get messy!

Title: Re: Moving Lines
Post by towr on Dec 6^th, 2007, 3:05pm

[hide]Turn the paper a quarter turn, put down you pencil and keep it still[/hide]

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.

Title: Re: Moving Lines
Post by JiNbOtAk on Dec 6^th, 2007, 4:32pm

Draw the line as usual; [hide]just make sure you're moving at the same velocity as the conveyor belt.[/hide] ;D

The intended answer, in my opinion ( not so mathmetically inclined to prove it ) is [hide]to draw a line with m=1[/hide].

Title: Re: Moving Lines
Post by FiBsTeR on Dec 6^th, 2007, 5:11pm

Hehe, nice solutions above, but obviously not any intended ones. ::)

on 12/06/07 at 16:32:49, JiNbOtAk wrote:

The intended answer, in my opinion ( not so math[ema]tically inclined to prove it ) is [hide]to draw a line with m=1[/hide].

EDIT: original post deleted

I don't think this is correct, but I'm not mathematically inclined either so maybe I'm wrong. :P

Hint towards the (perhaps incorrect?) answer: [hide]I'll be surprised if anyone posts a correct answer with the string "m=" in their post...[/hide] "I wonder what that's all about?"

Title: Re: Moving Lines
Post by towr on Dec 7^th, 2007, 12:16am

[hide]Let's say m=1, then the drawing speed is v=m=http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(v_x²+v_y²) therefore v_x²+v_y² = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/pm.gifm
Now to remove the effect of the conveyor, it's speed and v_x have to cancel each other out, so |v_x|=m as well, which leaves 0 for v_y

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.[/hide]

:P

Title: Re: Moving Lines
Post by Grimbal on Dec 7^th, 2007, 12:21am

~~Stand~~ sit on the conveyor belt.

Title: Re: Moving Lines
Post by JiNbOtAk on Dec 7^th, 2007, 12:26am

on 12/07/07 at 00:21:27, Grimbal wrote:

Stand on the conveyor belt.

Wouldn't that require you use a really long pencil ? :P

Title: Re: Moving Lines
Post by towr on Dec 7^th, 2007, 12:32am

on 12/07/07 at 00:26:00, JiNbOtAk wrote:

Wouldn't that require you use a really long pencil ? :P

Fine, squat on the conveyor belt. ;)

Title: Re: Moving Lines
Post by FiBsTeR on Dec 7^th, 2007, 4:27am

on 12/07/07 at 00:16:31, 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.

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!