Applying energy conservation Ki​+Ui​=Kf​+Uf​21​mu2+(−RGMm​)=21​mv2−2RGMm​v=u2−RGM​​ ...(i)By momentum conservation, we have
10m​vT​=109m​2RGM​​....(ii)& 10m​vr​=mv⇒10m​vr​=mu2−RGM​​....(iii)Kinetic energy of rocket =21​m(vT2​+vr2​)=20m​(2R81GM​+100u2−R100GM​)=20m​(100u2−2R119GM​)=5m(u2−200R119GM​)