experimentX
Find a shape of inclined plane(not necessarily plane) that takes shortest time to reach from top to bottom. Assume the ball is sliding without any friction.
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experimentX
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|dw:1347894497129:dw|
estudier
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geowotsit?
experimentX
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assume both h and w are not zero.
experimentX
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|dw:1347894819011:dw|
experimentX
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could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.
experimentX
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it's a pretty famous problem ...
experimentX
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yep ... this is brachistochrome problem.
estudier
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I was thinking geodesic at first, shortest distance....
experimentX
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i did this with calculus of variation. haven't done this with purely calculus.
sauravshakya
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What about when h=w and h and approaches infinity
sauravshakya
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h and w*
experimentX
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take a circle with zero radius, you will get a straight line.
experimentX
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* if w = 0 ...
experimentX
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|dw:1347895370580:dw|
sauravshakya
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I got that cycloid part........
sauravshakya
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What if h and w approaches infinity.....
estudier
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It will never get to the bottom and you will never know..:-)
sauravshakya
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Then I think this should work:|dw:1347895555863:dw|
experimentX
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yep ... this is a physics problem actually.
sauravshakya
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Oh ya @estudier ........ But what if h and w are very large.... but some finite number
sauravshakya
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Will it still be that cycloid
experimentX
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yep .. it should be cycloid ... make by a huge circle.
sauravshakya
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OMG! This math stuff is out my level
sauravshakya
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Didnt get why cycloid........ I just know we need to maximise the accleration
estudier
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Maybe at infinity, you have to go to some other mathematical model, maybe conformal, to analyze that (in conformal everything is a circle, point is circle with zero radius, line is infinite circle etc)
estudier
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or sphere, perhaps..
sauravshakya
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I mean why cycloid is the answer to @experimentX question
sauravshakya
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It will only increase the length
experimentX
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well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.
estudier
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When you solve the problem, that's what comes out, a deeper meaning, you mean?
sauravshakya
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oh
experimentX
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trust me ... things aren't that intuitive.
sauravshakya
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Ok..... I trust u. @experimentX
sauravshakya
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When did u learnt these stuff. @experimentX
experimentX
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i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.
sauravshakya
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At university
sauravshakya
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I will think on this problem.... see If I can get to the solution
experimentX
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told you i'm old guy