Hi,(adsbygoogle = window.adsbygoogle || []).push({});

it is probably a simple question, but it bothers me for quite some time.

How can I calculate time that ball needs for certain path/courve, where path equation is given?

I could use

[tex]t=\int_{T_1}^{T_2}\frac{ds}{v}[/tex]

where [tex]v[/tex] is velocity and [tex]ds^2=dx^2+dy^2[/tex].

Because of

[tex]\frac{1}{2}m\,v^2=m\,g\,y[/tex]

we get

[tex]v=\sqrt{2g\,y}[/tex]

and new "formula" for time is

[tex]t_{12}=\int_{T_1}^{T_2} \frac{\sqrt{1+{y'}^2}}{\sqrt{2g\,y}}dx, \quad y'=\frac{dy}{dx}[/tex]

If we have a curve in parametric form (e.g. cycloide), how can I calculate this equasion numericaly?

Any guidance/hint/web link is appreciated.

Many thanks!

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# Time ball needs for a certain path/courve

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