Yes, but also no. Firstly, there is nothing special about shotguns here, any gun follows the same basic principle, when fired a bullet is pushed forward, and the gun is pushed back with equal force. However guns don’t actually have that much total force behind them, bullets only move so fast because they are so light, so you aren’t gonna get much push. For example an AK-47 generates about 6 newtons of force per bullet fired. It takes about 10 newtons of force to lift a 1kg object.
xkcd that gives a better answer to a slightly different question (Is it possible to build a jetpack using downward firing machine guns?), and goes over the math better linked below.
[https://what-if.xkcd.com/21/](https://what-if.xkcd.com/21/)
In theory yes. The case in point would be the A-10 warthog’s gun. If it fired too long of a burst, the aircraft risks stalling due to the immense recoil of the massive gun coupled with the extremely high rate of fire.
So in theory, if you took a 10 gauge shotgun and made it feed from an electrically driven motor and 10 rotating barrels at 10k rounds per min, and you strapped a 6 lbs baby to it, my assumption is that baby would go sailing.
Guns aren’t too dissimilar from thrusters you expell some mass in one direction and momentum is conserved which kicks you in the opposite direction.
An AK-47 bullet 7.62×39mm has a muzzle velocity of 710 m/s and a mass of 8g (according to Google) which gives us a momentum of 710 m/s × 0.008 kg = 5.68 kgm/s.
Say a human with 80 kg mass sliding at v velocity on a frictionless table would fire a bullet in the sliding direction, at what v would they stop? So p_0 = m_h × v.
p_0 = p_1 + p_b
p_1 = m_h × 0 as they stopped
p_b = 5.68 kgm/s
5.68/80 m/s = v = 7.1 cm/s = 0.2556 km/h
So of course there is knockback but you can see hoe its not that much.
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