Find a curve such that time travel is minimum

[ksuer]

Homework Statement

[PLAIN]http://vctson.com/temp/curve.jpeg
Find the curve y = f(x) so that the ball travels from A to B in minimum time?

Thanks!

 

[daveb]

What have you worked out thus far? You have to show some effort.

 

[ksuer]

I tried at some point on the curve, the gravity force goes down, then use 2nd Newton law. Thus, P = ma = my''. But, P = mg. It does not seem right and I can't find the relation y and x.

 

[ksuer]

Any hint? Thanks!

 

[Liquidxlax]

this is the brachistochrone, so what is you kinetic and potential energy?

solve in terms of v then separate for ds/dt.

ds = sqrt(dx^2 + dy^2)