(a) Use the substitution v = dyldt to solve (13) for v in terms of y. Assume that the

Chapter 3, Problem 14

(choose chapter or problem)

(a) Use the substitution v = dyldt to solve (13) for v in terms of y. Assume that the velocity of the rocket at burnout is v = v0 and that y = R at that instant; show that the approximate value of the constant c of integration is c = -gR + !v5 (b) Use the solution for v in part (a) to show that the escape velocity of the rocket is given by v0 = \/ZiR. [Hint: Take y oo and assume v > 0 for all time t.] ( c) The result in part (b) holds for any body in the solar system. Use the values g = 32 ftls2 and R = 4000mi to show that the escape velocity from the Earth is (approximately) Vo= 25,000 mifh. (d) Find the escape velocity from the Moon if the acceleration of gravity is 0.165g and R = 1080 mi.