Ratio of max height of a projectile to planet radius

[yankans]

Homework Statement

Hint:Disregard any dissipative effects of the atmosphere of the planet.
A projectile is launched from the surface of a planet (mass M, radius R)
with a launch speed equal to 60 percent of the escape speed for that planet.
The projectile will rise to a maximum height and fall back to the surface of
the planet.

What will be the ratio of its maximum height above the surface to the radius of the
planet, h/R?

Homework Equations

escape speed:
KE = E(gravity)
1/2 mv^2 = (GMm)/R
F/m = a
a(gravity) = GM/R^2

The Attempt at a Solution

1/2 mv^2 = (GMm)/R
v(escape) = (2GMm)/R
v=sqrt((2GM)/R)
vi = 0.6 sqrt((2GM)/R)

vf^2 = vi^2 - 2gh
0 = 0.72GM/R - 2(GM/R^2)h
2(GM/R^2)h = 0.72GM/R
h/R = 0.36

 

[yankans]

Sorry I reworked this problem by myself and I solved it!