Question

A rocket of initial mass m (including fuel) ejects mass at a constant rate of 25 kg/s with a speed 60 m/s relative to the rocket. If the acceleration of the rocket 3.5 minutes after the firing is 2 $m/s^2$, find the initial mass of the rocket? [Neglect gravity] If your answer is in the form of n x ${10}^3$kg. Fill n.

Answer 1

Acceleration of rocket after 3.5 minutes, $a=2m/s^2$

Let the mass of rocket at that instant be $M$.

Thrust force $F_t=\frac{dm}{dt}{V}_{rel}=25\times 60=1500N$

So, $Ma=F_t$

Or $M\times 2=1500$

$⟹M=750kg$

Mass of the rocket after $3.5$ minutes $M=m-25\times 3.5\times 60=5250$

or $750=m-5250$

$⟹m=6000Kg$

We get $n=6$