1. The second stage of a two-stage rocket weighs 2000 lb (empty) and is launched from the first stage with a velocity of 3000 mi> h. The fuel in the second stage weighs 1000 lb. If it is consumed at the rate of 50 lb> s and ejected with a relative velocity of 8000 ft> s, determine the acceleration of the second stage just after the engine is fired. What is the rocket's acceleration just before all the fuel is consumed? Neglect the effect of gravitation.
2. The missile weighs 40 000 lb. The constant thrust provided by the turbojet engine is T = 15 000 lb. Additional thrust is provided by two rocket boosters B. The propellant in each booster is burned at a constant rate of 150 lb >s, with a relative exhaust velocity of 3000 ft>s. If the mass of the propellant lost by the turbojet engine can be neglected, determine the velocity of the missile after the 4-s burn time of the boosters. The initial velocity of the missile is 300 mi>h.