You're right Brian I only have a Master's degree...but, I manage to hang with the propeller heads from the national laboratories....
However, let's get back to what you've said
If the beanbag has enough momentum to knockdown the person it hits, the gun has enough momentum to knockdown the person who pulled the trigger
You have obviously conflated the momentum of the object and recoil momentum of the gun with kinetic energy.
You have described the bean bag as being unable to knock someone down because its momentum is the same as the gun recoil and the shooter would have to be knocked down.
You have described only 1/2 of the force / power equation regarding a projectile.
Momentum does not equal kinetic energy = you will agree?
Momentum is the amount of energy or force used to accelerate the object.
Once at is maximum velocity the energy inherent in the object is now described as KINETIC ENERGY = agree?
The kinetic energy equation is:
KE = 1/2M x V^2 ----agree?
Then what ever theoretical energy is contained in the object when it strikes another object is described as kinetic energy. Agree?
It is NOT MOMENTUM so your original statement about the bean bags cannot be correct.
Brian - it's okay, everybody gets confused on the subject of recoil versus "knockdown power."
As I have already stated - all of the kinetic energy of a bullet cannot be transferred to power as that is work and it involves movement (displacement) of an object over time. I'm not going into it again - you can re-read my post on "knockdown power" versus work.
Just stop conflating momentum and recoil with energy contained in a moving object.
There is no way to know what part of kinetic energy will remain kinetic energy and what part will convert to heat energy, deformation, etc.
MMmmm sort of...the bullet's energy "remains kinetic" until the bullet velocity is = 0. Once the bullet starts impacting a target, the energy in converted to a number of different types of energy and forces - so the bullet is "losing kinetic energy" as it converts to other types of energy or forces including, heat, shock wave, thermal energy, etc. Meaning - the bullet is slowing down faster as the kinetic energy is converted to other types of energy.
But, all of the energy is conserved - including passing through the object and traveling down range if that's what happens until the bullet's forward velocity is equal to zero (it's resting on the ground), and the bullet has zero kinetic energy.
Momentum is always, always conserved and it is a VECTOR quantity. It is conserved in both quantity and direction.
During bullet acceleration down the barrel and resultant gun recoil - 100% correct.
After the object is at maximum speed after leaving the barrel - the energy contained in the object is described as kinetic energy - not momentum.
F(momentum) = M x V
KE = 1/2M x V^2
You do see the difference?
Beanbag not knocking someone down is not connected to not knocking down the shooter. Not knocking down the target is because the kinetic energy has been converted to other types of energy other than "power" - or "work" that includes displacement (movement) of the object.