experimentX
  • 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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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experimentX
  • experimentX
|dw:1347894497129:dw|
anonymous
  • anonymous
geowotsit?
experimentX
  • experimentX
assume both h and w are not zero.

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More answers

experimentX
  • experimentX
|dw:1347894819011:dw|
experimentX
  • experimentX
could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.
experimentX
  • experimentX
it's a pretty famous problem ...
anonymous
  • anonymous
http://en.wikipedia.org/wiki/Brachistochrone_curve
experimentX
  • experimentX
yep ... this is brachistochrome problem.
experimentX
  • experimentX
cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid
anonymous
  • anonymous
I was thinking geodesic at first, shortest distance....
experimentX
  • experimentX
i did this with calculus of variation. haven't done this with purely calculus.
anonymous
  • anonymous
What about when h=w and h and approaches infinity
anonymous
  • anonymous
h and w*
experimentX
  • experimentX
take a circle with zero radius, you will get a straight line.
experimentX
  • experimentX
* if w = 0 ...
anonymous
  • anonymous
http://www.cmsim.eu/papers_pdf/january_2012_papers/25_CMSIM_2012_Pokorny_1_281-298.pdf (brachistochrone as special case of geodesic)
experimentX
  • experimentX
|dw:1347895370580:dw|
anonymous
  • anonymous
I got that cycloid part........
anonymous
  • anonymous
What if h and w approaches infinity.....
anonymous
  • anonymous
It will never get to the bottom and you will never know..:-)
anonymous
  • anonymous
Then I think this should work:|dw:1347895555863:dw|
experimentX
  • experimentX
yep ... this is a physics problem actually.
anonymous
  • anonymous
Oh ya @estudier ........ But what if h and w are very large.... but some finite number
anonymous
  • anonymous
Will it still be that cycloid
experimentX
  • experimentX
yep .. it should be cycloid ... make by a huge circle.
anonymous
  • anonymous
OMG! This math stuff is out my level
anonymous
  • anonymous
Didnt get why cycloid........ I just know we need to maximise the accleration
anonymous
  • anonymous
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)
anonymous
  • anonymous
or sphere, perhaps..
anonymous
  • anonymous
I mean why cycloid is the answer to @experimentX question
anonymous
  • anonymous
It will only increase the length
experimentX
  • experimentX
well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.
anonymous
  • anonymous
When you solve the problem, that's what comes out, a deeper meaning, you mean?
anonymous
  • anonymous
oh
experimentX
  • experimentX
trust me ... things aren't that intuitive.
anonymous
  • anonymous
Ok..... I trust u. @experimentX
anonymous
  • anonymous
When did u learnt these stuff. @experimentX
experimentX
  • experimentX
i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.
anonymous
  • anonymous
At university
anonymous
  • anonymous
I will think on this problem.... see If I can get to the solution
experimentX
  • experimentX
told you i'm old guy

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