Answer Happy

Some notorious Space Pirates are gearing up for a
training exercise that will take place in a deep space desert, far
away from any gravitational influences. You will be joining them
and you're about to start their boot camp to learn the
ropes. Fun times! Space
Pirates use three types of weapons and each new recruit must learn
how to handle them properly. As a new recruit, you must securely
affix a personal THRUSTER to your space suit while tightly gripping
your WEAPON. Immediately after your weapon fires its test
projectile (aka "AMMO"), your personal thruster fires so that you
can chase after your ammo. The thruster continues to
accelerate, more than compensating for your weapon's recoil,
and allows you to pursue and eventually recover your test ammo and
use it again. (Ammo's expensive, so they only give
you one bullet, or lead ball or whatever for your entire training
course. Reduce, Reuse, Recycle and all
that.)
Note: Your total Space Pirate mass is the sum of your
actual body mass, your thruster mass, your weapon mass plus 130kg
of space suit.
Note: Your mission is to calculate the
duration of your thruster burn to the nearest second,
so resist the temptation to perform any rounding until the final
step of your calculation.
Big Question: How long does your thruster need to fire
in order for you to reach the same speed as the
ammo that you're chasing?Please declare your answer in minutes and
seconds (mm:ss).
Answer in Claim, evidence, reasoning format. In your
CLAIM, please explicitly state your WEAPON and THRUSTER models as
well as your body mass.
You have been issued with a weapon, its one piece of ammo, one thruster as well as a 130kg space suit. Mass WEAPON AMMO Mass (kg) Muzzle Velocity (m/s) (kg) Pistol 3.4 0.077 760 Blunderbuss 7.8 0.25 274 Cannon 118.8 6.6 1070 THRUSTER Mass (kg) Thrust (N) Alpha 45.9 123 Epsilon 77.7 234 Omega 113.1 345