[UPSC CSE 1993] Conservation Laws (Q54, 20M)

A rocket of mass 1000\text{ kg} is ready for a vertical take off. The exhaust velocity of its fuel is 4.5\text{ km/s}. Deduce (i) the minimum rate of fuel ejection so that the rocket weight be just balance, (ii) the velocity acquired in 8\text{ s} if the fuel ejection rate is 2.50\text{ kg/s}. (You may neglect the effect of changing mass of the rocket in the given conditions.)