Gravitational Illusions -- Two balls rolling down differently-shaped ramps

[Jurgen M]

Without this test,using only math, would you prove that left ball will comes first?

 

[anorlunda]

Why make us do all the work? You'll never learn unless you do the problems yourself.

Write your own mathematical solution and post it here. We'll comment on it.

 

[A.T.]

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