Ball rolling down a segment then up a parabolic segment

[talaroue]

Homework Statement

A 181 g ball is released from rest H=5.19 m above the bottom of the track shown in Figure. It rolls down a straight 21° segment, then back up a parabolic segment whose shape is given by y=x2/4, where x and y are in m. How high will the ball go on the right before reversing direction and rolling back down?

Homework Equations

Ki+Ui=Kf+Uf
K=mv^2/2

The Attempt at a Solution

I am not sure how to start this because everytime i go to one direction i hit a dead end.
At the beginning it has both Ki=0 and Ui=0 correct?
Then at the final it has Kf and Uf right?

 

[talaroue]

Here is my work but I don't even think I am on the right track...

This is for rolling down incline

This is for rolling up the parabola

EDIT: I put the wrong dominator in for the very last part when calculating Y it should be 4, but that anwser did not work either

 

[talaroue]

WOOOOOOW I am so sorry for wasting everyones times the parabola made me over think this equation since Ki+Ui=Kf+Kf...energy would force the ball up the same height as it began.

 

[Cyosis]

The question gave you additional information to deceive you. Realizing this in the end only makes you understand energy conservation better. It's hardly wasting anyone's time.

 

[talaroue]

Yeah, I see what you mean but I didn't need to make a thread after.