Finding location of turning points. Potential Energy?

[Patdon10]

Homework Statement

On the segment of roller coaster track shown in the figure, a cart of mass 233.7 kg moves from left to right and arrives at x = 0 with a speed of 16.5 m/s. Assuming that dissipation of energy due to friction is small enough to be ignored, where is the turning point of this trajectory?

x = ?
y = ?

Homework Equations

Ke_i + Pe_i = Ke_f + Pe_f

The Attempt at a Solution

This problem is really tough, and I really have no idea where to start. I know the turning point is where the derivative of the function is at a max or min. The only point in that happens which looks to be about (17m, 4m).

I don't know how to I would incorporate kinetic energy into this, but I'm pretty sure I have to. Can anyone push me in the right direction?

 

[Kurdt]

In an ideal situation the roller coaster will continue on its uphill trajectory until it loses all kinetic energy and it is converted to potential energy. This is the point where you will want to change the track so that the rollercoaster uses its potential energy and doesn't slip backwards down the track.

 

[pg05]

x= 41.39 m
y=23.89 m