Daredevil motorcycle max height

[Leid_X09]

Homework Statement

A daredevil on a motorcycle leaves the end of a ramp with a speed of 39.5 m/s as in Figure P5.23. If his speed is 38.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.

Homework Equations

Eo = mgy

Ek = 1/2mv^2

The Attempt at a Solution

I don't even know where to begin. I need someone to cue me on what equation i should be using because frankly I can't even fathom. I thought perhaps Eo=Ek, but I'm not sure if this is it.

 

[Epsillon]

Alright so in the beginning the motocycle has Ek only; however, when it reaches the top it gains some Ep therefore some Ek is transformed into Ep due to conservation of energy.

So

E_kinitial=E_kfinal+E_p

Ep = mgy

Ek = 1/2mv^2

so

1/2m(39.5)^2 = 1/2m(38)^2 + m(9.8)y

Now u can cross out the ms by factoring m from both sides and deviding boths sides by m.
1/2(39.5)^2 = 1/2(38)^2 + (9.8)y

y=0.1102556674m