A rocket moving in space, far from all other objects, has a speed of 2.5 103 m/s relative to the Earth. Its engines are turned on, and fuel is ejected in a direction opposite the rocket's motion at a speed of 7.5 103 m/s relative to the rocket.
(A) What is the speed of the rocket relative to the Earth once the rocket's mass is reduced to half its mass before ignition?
(B) What is the thrust on the rocket if it burns fuel at the rate of 56.5 kg/s?
What if we need to slow down the rocket now? By reversing the engine's direction, now fuel is ejected in the same direction as the rocket's motion at the same speed as before. To slow down to a speed of 4.5 103 m/s (relative to Earth), what will be the final mass when the rocket is slowed to this speed? Given that the initial mass of the rocket (when it was still at 2.5 103 m/s) is Mi = 6400 kg. And for consistency, use the final velocity as found in the example as the "initial" velocity here.