A body is projected vertically from earth's surface of radius R with velocity equal to half the escape velocity. The maximum height reached by the body is

Step-by-step solution

Escape velocity from the surface of the earth is given by v_e = 2GM R Initial velocity of the body is v = v_e 2 = GM 2R Applying conservation of mechanical energy at the surface of the earth and at maximum height h : K_i + U_i = K_f + U_f 1 2 mv^2 - GMm R = 0 - GMm R+h Substituting the value of v^2 : 1 2 m ( GM 2R ) - GMm R = - GMm R+h GMm 4R - GMm R = - GMm R+h - 3GMm 4R = - GMm R+h 3 4R = 1 R+h 3R + 3h = 4R 3h = R h = R 3 Answer: R 3