[UPSC CSE 2002] Conservation Laws (Q44, 20M)

Using the rocket equation and its integral find the final velocity of a single stage rocket. Given that

(i) the velocity of the escaping gas is 2500\text{ m/s},

(ii) the rate of loss of mass is. (where m_0) is the initial mass and 0.27 m_0 is the final mass).