Question

A rocket has a mass M and velocity v at a
time t. if U(rel)-> is the velocity of the
exhaust with respect to the rocket show that
V-> -V0->=U(rel)->ln(m/m0)- g->t where g-> is the acceleration due to gravity.
Here V0->and M0 are the respective initial values of the velocity and mass. Would this
equation have been valid if g-> had simply been written as g? Explain your answer.