A projectile is fired vertically upwards from the surface of earth with a velocity Kupsilon_(e)where upsilon_eis the escape velocity and K lt 1Neglecting 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 upwards from the surface of earth wit

1.	A projectile is fired vertically upwards from the surface of earth with a velocity Kupsilon_(e)where upsilon_eis the escape velocity and K lt 1Neglecting 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` REACHES a height h , by conservation of ENERGY `-(GMm)/R+1/2mv^(2)=-(GMm)/(R+h):. h=R/(1-K^(2)`