1. The problem statement, all variables and given/known data At the Earth's surface a projectile is launched straight up at a speed of 8.1 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth. 2. Relevant equations F = GMm/r2 Ug = -GM/r2 G = 6.67 e -11 whatever units it happens to be That's all I'm 'given' for this problem. 3. The attempt at a solution Well, I figured that the kinetic energy that the rocket/thing starts off with converts into gravitational energy. 1/2 mv2 = GM/x2 where x is the distance between the centers of the rocket and the earth. So that would mean x = r + h? So if we rearrange terms to solve for x, we get: x = ±2GM/v2 - r However, that doesn't seem to work, either sign for the potential energy. Am I missing something?