A projectile is fired vertically upward from the surface of earth with a velocity K v_(e) where v_(e) is the escape velocity and K lt 1. Neglecting air resistance, show that the maximum height to which it will rise measured from te 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 K v_(e) where v_(e) is the escape velocity and K lt 1. Neglecting air resistance, show that the maximum height to which it will rise measured from te 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 v and reaches a height h, by conservation of energy `-(GMm)/(R) + (1)/(2) mv^(2) = -(GMm)/(R+h) therefore h = (R)/(1-K^(2))`