A rocket is launched vertically from the surface of the earth of radius fi with an initial speed v. If atmospheric resistance is neglected, the maximum height h attained by the rocket is given by

The total energy on the surface of the earth is given byT= K.E. + P.E. =12mv2−(GmM/R)where m is the mass of rocket. At highest point, y =0. Thus at a distance {R+h) i.e .highest point, the energy is entirely potential. So, energy at highest point is given by P.E. =−[GMm/(R+h)]According to law of conservation of energy12mv2−GmMR=−GMm(R+h)or 12mv2=GmM1R−1R+hor v22=GMhR(R+h)or R+hR=2gRv2 ∵g=GMR2h=R2gRv2−1