The rocket seen in the figure is

initially at rest and contains

pressurized air at $20C$ and $20$ bars

$($kept constant$).$ Rocket and the

pressurized air inside weigh M$1$ and

$M2$ respectively. At $t=0$ nozzle

opens and the air jets out

adiabatically and invicidly from the

nozzle. Drive an expression for the

time dependent velocity of the

rocket as function of $d,M1$ and M$2.$

Assume no air drag due to rocket

motion.

HINT:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{ax+b}dx=\frac{x}{a}-\frac{b}{x}ln|ax+b|$