Consider rocket that has mass m(t) and velocity v(t) at time t. it gains speed a by expelling propellant at constant velocity ver relative to the rocket. the amount of pro- pellant expelled between times t and t+ dt can therefore be written as -dm(t). the rocket starts with initial velocity uo and initial mass mo (including the propellant). (a) ignoring gravity, write down the equation relating the momenta of the rocket+propellant system at times t and t+dt. 5 points (b) use the result from part (a) to find the velocity of the rocket v as a function of vo, vens mo, and m. [10 points (c) redo part (a) but now assuming that the rocket is rising vertically in a uniform gravita tional field with acceleration g, and that the rate at which the rocket loses mass is a constant value k = -dm/dt. [10 points (d) use the result of part (c) to find both the velocity and height of the rocket as a function of t, o ves mo. and k.