1. The problem statement, all variables and given/known data A particle is projected vertically upward from the earth's surface with initial speed Vo. Prove that the maximun height H reached above the earth's surface is H= Vo^2R/(2gR-Vo^2) 3. The attempt at a solution R is the earth's radius. If the gravitational attraction at the earth's surface is mg, then the attraction at some height r above the surface will be mgR^2/(R+r)^2. The attraction can be integrated from r = 0 to r = H to get the total work involved, which must equal the kinetic energy mVo^2/2. HOWever, when we integral from r=0 to r=H of mgR^2/(R+r)^2 and set it equal to mVo^2/2, H= does not give the value Vo^2R/(2gR-Vo^2) ??