(solved) Rotating ball flies certain height in the air

1. Jan 26, 2013

nhmllr

1. The problem statement, all variables and given/known data

(answer is h * 5 /7)

2. Relevant equations
gravitational potential energy = mgh
kinetic energy = 1/2 mv2
rotational kinetic energy of sphere = 2/5 mv2

3. The attempt at a solution
The gravitation potential energy at the beginning at the top is the same as the kinetic energy and rotational energy at the bottom

mghi = 1/2 mv2 + 2/5 mv2 = 9/10 mv2

We also know that the rotational kinetic energy at the apex of it's final height, plus the potential energy it achieves there, is equal to the initial potential energy

mghi = mgh + 2/5 mv2
h = hi - (2/5 v2)/g

and from our first equation, we know
mghi = 9/10 mv2
4/9 ghi = 2/5 v2

So combining those...
h = hi - (4/9 ghi)/g
h = 5/9 hi

But that is not the answer.... So where did I go wrong?
Thanks

EDIT: The rotational kinetic energy is actually 1/5 mv2. Sorry, it makes sense