Its very hard to predict exactly what will happen. First, it's an inelastic collision so the momentum of the system is conserved, but the kinetic energy of the system is not (part of it is lost to deform the steel and bullet). Second, we can't really predict how many pieces the projectile will split into upon collision, or their respective masses. Third we would need to calculate how much momentum is transferred to the plate. Fourth, we'd have to figure out trajectories for the fragments...
Basically you need a physics degree and lots of precise measuring equipment to get a straight answer, and every shot will behave differently.
10% of the energy of a 9mm is still 35-40ftlbs, which is basically on par with a 29gr 22short w/800 fps muzzle velocity - and I'm not about to volunteer to step infront of that...
Maybe I am misunderstanding you, but I think you have momentum and kinetic energy mixed up. Prior to collision the plate is not moving and the bullet is moving very quickly both with forward motion and rotation around its axis of forward travel. After Collision the plate will move, maybe a little, maybe a lot, the bullet will slow considerably or completely drop, and all rotational motion is lost immediately. Virtually all of the momentum factors in the collision system are changed, and not by a trivial amount. At the same time asides from a little bit of friction, all of the KE is still there.
It is not momentum that is transferred to the plate, but KE.
You would not need a degree in physics or anything else to come up with a reasonable approximation of where the fragments would go, the number of fragments, their masses or the distribution of mass among those fragments. You can develop a good reasonable guess either through a very expensive bit of Finite Effects Analysis software, or by firing a hundred rounds under identical circumstances and precisely measuring outcomes. After a hundred shots you should have a pretty good set of data to extrapolate what happened before into what is likely to happen the next time. FEA requires just as much information about what is going on inside the bullet and target material in terms of composition, consistency Modulus and Elastic Limit, as it does on the outside with Energy and Velocity etc.
In either case we would need to know a lot more about the question in order to give an answer.
As for the 9mm, a 124 gr bullet that retained 95% of its mass (worst case after an impact), and had 40 ft lbs of energy would be travelling at approximately 390 FPS, give or take. If fired directly without striking a target this would be comparable to being hit with a direct shot from a range of 1350m +/-. However, as I previously mentioned, the energy in a bullet is not organized the same way before and after an impact. A bullet still rotating on its axis from the rifling is far far more dangerous than a bullet that is tumbling randomly, even with the same mass and speed. A direct hit from a 9 mm at 1300m or a .22 short at PBR are obviously going to cause significant injury. I wouldn't be volunteering to step in front of either one either, but I'd love to see what that tumbling 9 mm round with only 40 ft lbs would do. I suspect it would give you a real good welt, maybe crack a bone, but otherwise would not be life threatening. The effect that the introduction of rifling had on both external and terminal ballistic had was significant.
For the record, a 9 mm round coming off a plate that retained 95% of its mass and is traveling at almost 400 FPS is more what you would expect for a round that just winged a plate and carried on down range, not one what came back up towards the shooter after a bounce. After searching over a hundred you tube videos and blog posts for stories of range ricochets from steel, it seems even with the worst possible set ups and range practice, the only way blood gets drawn is from small cuts from jacket fragments and not the penetration of more substantial lead bullet fragments.
Sureshot gave an example of a small fragment embedding in his neck. I Would love to know more about that fragment, and how it was produced. The odds of such a fragment being produced is already pretty slim. The odds of it coming back towards a shooter even slimmer, at least when you follow basic principles of safe use. I suspect the probability of injury in such events would be measured in the 1 in millions, if not billions.