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.

- experimentX

- chestercat

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- experimentX

|dw:1347894497129:dw|

- anonymous

geowotsit?

- experimentX

assume both h and w are not zero.

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## More answers

- experimentX

|dw:1347894819011:dw|

- experimentX

could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.

- experimentX

it's a pretty famous problem ...

- anonymous

http://en.wikipedia.org/wiki/Brachistochrone_curve

- experimentX

yep ... this is brachistochrome problem.

- experimentX

cycloid is a shape made my rolling circle.
http://en.wikipedia.org/wiki/Cycloid

- anonymous

I was thinking geodesic at first, shortest distance....

- experimentX

i did this with calculus of variation. haven't done this with purely calculus.

- anonymous

What about when h=w and h and approaches infinity

- anonymous

h and w*

- experimentX

take a circle with zero radius, you will get a straight line.

- experimentX

* if w = 0 ...

- 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

|dw:1347895370580:dw|

- anonymous

I got that cycloid part........

- anonymous

What if h and w approaches infinity.....

- anonymous

It will never get to the bottom and you will never know..:-)

- anonymous

Then I think this should work:|dw:1347895555863:dw|

- experimentX

yep ... this is a physics problem actually.

- anonymous

Oh ya @estudier ........ But what if h and w are very large.... but some finite number

- anonymous

Will it still be that cycloid

- experimentX

yep .. it should be cycloid ... make by a huge circle.

- anonymous

OMG! This math stuff is out my level

- anonymous

Didnt get why cycloid........ I just know we need to maximise the accleration

- 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

or sphere, perhaps..

- anonymous

I mean why cycloid is the answer to @experimentX question

- anonymous

It will only increase the length

- 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

When you solve the problem, that's what comes out, a deeper meaning, you mean?

- anonymous

oh

- experimentX

trust me ... things aren't that intuitive.

- anonymous

Ok..... I trust u. @experimentX

- anonymous

When did u learnt these stuff. @experimentX

- experimentX

i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.

- anonymous

At university

- anonymous

I will think on this problem.... see If I can get to the solution

- experimentX

told you i'm old guy

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