(a) Use the substitution v dydt to solve (13) for v in terms of y. Assuming that the

Chapter 5, Problem 14

(choose chapter or problem)

(a) Use the substitution v dydt to solve (13) for v in terms of y. Assuming that the velocity of the rocket at burnout is v v0 and y R at that instant, show that the approximate value of the constant c of integration is . (b) Use the solution for v in part (a) to show that the escape velocity of the rocket is given by . [Hint: Take 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 ft/s2 and R 4000 mi to show that the escape velocity from the Earth is (approximately) v0 25,000 mi/h. (d) Find the escape velocity from the Moon if the acceleration of gravity is 0.165g and R 1080 mi. Vari