well, yeah, i said its a crappy approximation, i know about the units, also i know that a function usually is not proportional to its derivative, but its at least some kind of dependency and could pose as a placeholder for the real calculations. i dont know how much time toady already invested in this kind of thing since linear momentum is exactly what youre talking about when you dont want to bother about what happens inside the bolt/armour/bodypart.
even when the bolt gets stuck in the target afterwards, its about what kind of forces he applies to the materials involved. its true that the energy to apply the force is just the kinetic energy, but when checking, whether the bolt is piercing the plate or not, its about the forces, their absolute values and directions inside the material and its structure. there can be force applied to a wall too. also, while hitting the target, the bolt is decelerated and the target is being deformed, which is where you see movement even when the bolt gets stuck. if someone wants to know more about forces inside of materials, which can get quite complicated, they best start reading around a little on stress and and all the material values. there is a magmawiki-page on "material science" to get started and find the vocabulary one needs to look things up more thoroughly.
edit: seriously, i need to start thinking about what im doing before hitting enter, or at least read it once myself...
heres the link