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

Step-by-step solution

aligned & K_f+P_f=K_i+P_i & O - G M m R+h = 1 2 m ( V_e 2 )^2- G M m R & - G M m 1 [- 1 R + 1 R+h ]= 1 8 m V_e^2 aligned aligned & -G M m [ -h R(R+h) ]= 1 8 m V_e^2 & -G M [- R(R h) ]=- ( 2 R . G M ) & h R^2+R h = 1 4 R 4 R h=R^2+R h & R^2=3 R h & h=R / 3 aligned