A body is projected vertically from earth's surface with ( 1 3 )^ rd of escape velocity. The maximum height reached by the body is ( R = radius of earth)

Step-by-step solution

Given that the escape velocity from Earth's surface is v_e = 2GM R , with G the gravitational constant, M the Earth's mass, and R its radius, the body is projected upward with velocity v = 1 3 v_e . Using conservation of mechanical energy, the initial energy at the surface equals the final energy at maximum height h where velocity is zero: 1 2 mv^2 - GMm R = - GMm R+h Substituting v = 1 3 2GM R : 1 2 m ( 1 9 2GM R ) - GMm R = - GMm R+h After simplification, this reduces to: GMm 9R - GMm R = - GMm R+h Dividing throu