Maximum height reached by a rocket fired with a speed equal to 50 % of the escape speed from the surface of the earth is ( R - Radius of the earth)

Step-by-step solution

v _ i = 1 2 v _ e = 1 2 2 GM R , U _ f =0 Applying conservation of mechanical energy, K_i+V_i=K_f+U_f aligned & 1 2 mv _ i ^2+ - GM _ m R =0+ - GM _ m R + h & 1 2 ~m ( 1 2 2 GM _ m R )- GM _ m R =- GM _ m R + h & 3 4 R = 1 R + h & h = R 3 aligned