A mass m is shot vertically upward from the surface of the earth with initial speed vo. The gravitational force on the mass is Fg = GMm/(r ² ) where M is the mass of the earth and r is the distance from the center of the earth. R is the radius of the earth.

(a) Show that the maximum height is r_max = R/((1 - vo ² )/(2gR))

(b) And the escape velocity is v_esc = (2gR) ^(1/2)