Let be the change in the mass of the rocket during a small time interval . So, is the mass of the exhaust released from the rocket during the time interval . Let be the velocity of the rocket before the mass is released, be the velocity of the rocket after the mass is released, and be the velocity of the mass after it is released. Conservation of momentum tells us that
Ignoring the second order term gives
is the speed of the exhaust relative to the rocket, so answer (E) is correct.