Velocity Equal Along Curved Paths?

[batballbat]

Lets say a body is falling vertically . Another body is falling along a curved surface maybe like a combination of helix and inclined plane. taking any two corresponding points of the paths, such that the points are at same height from the surface of earth. Or in other words the line joining the points is parallel to horizontal surface. Will the velocity acquired at the two points be equal. Prove it.

Ps. The acceleration of the body in such a curved path won't be uniform. Also neglect friction

 

[Stonebridge]

If you neglect friction (both air and with the curved surface) then you can apply energy considerations. At the same vertical height both bodies will have lost the same amount of potential energy.
What does this tell you about their kinetic energy?

(I'm assuming the curved surface you refer to is smooth and the object makes contact with it at only one point)