Bead on a string, find y(x) if horizontal velocity is const.

[Phantoful]

Homework Statement

Homework Equations

K = (1/2)mv²
U = mgh
W=Fd
Integration/Calculus

The Attempt at a Solution

I'm not sure what I should be doing for this question, if height changes how is it possible that velocity stays the same, according to the conservation of energy (frictionless wire)? If horizontal velocity stays the same, then I would assume that some sort of slope would equal 0 of this equation; however the line would be still at y=0, and it says there's an answer besides that. I'm not sure of any other weird functions that could do this, except maybe a circle (but I doubt that's the answer because it's a wire). How should I be solving this?

 

[kuruman]

Note that the problem specifies that the horizontal velocity is constant at v₀. There is no such constraint on the vertical velocity or the speed.

 

[Orodruin]

Also, given #2, how would you get the total velocity at any given point along the wire? How can you relate that to the initial velocity using some physics principle?