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.

A projectile is fired vertically upward from the surface of earth with

1.	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.
Answer» Solution :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)`