The velocity with which an object should be projected from the surface of the earth such that it reaches a maximum height equal to “n” time the radius of earth “R” is : (M = Mass of the earth)

[(n*G*M)/(n+1)R]^1/2

Total initial energy = Total final energy

1/2(m x v²) – (G*M*m)/R = -(G*M*m)/(n+1)R

Simplifying the above equation, we get ;

v = [(n*G*M)/(n+1)R]^1/2.