A projectile is fired vertically upward from the surface of earth with a velocity `Kupsilon_e` where `upsilon_e` is the escape velocity and K `lt` 1. Neglecting air resistance, show that the maximum height to which it will rise measured from the centre of earth is `R/(1-K^2)` where R is the radius of the earth.

Explanation

If a body is projected from the surface of earth with a velocity `upsilon` and reaches a height h, by conservation of energy
`-(GMm)/R+1/2mv^2 =-(GMm)/(R+h) therefore h=R/(1-K^2)`