A projectile is projected with velocity kve in vertically upward direction from the ground into the space. ( ve is escape velocity and k < 1) . If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
Kinetic energy = Potential energy
Height of Projectile from the earth's surface = h
Height from the centre
By solving .