Reply #102: Sorry, momentum and energy are related.

[longship]

The energy lost is directly related to the loss of velocity. This change in energy is exactly the amount of "work" done by the collision.

An arrow is a different type of collision. It's a classic inelastic collision where the projectile and the target become one object at the outcome. This means that the arrow is able to transfer 100% of its momentum to the target.

A bullet that penetrates all the way through a target and subsequently hits another target is not acting like an inelastic collision so that physics is entirely different. You cannot use the inelastic model to solve it. The momentum is *not* dissipated by the collision (which is clear by the fact that the bullet exits and causes further damage). Therefore, any reaction by the target cannot be from the momentum of the bullet.

Here's a site with a full analysis of the head lurch:
http://www.kenrahn.com/JFK/Scientific_topics/Physics_of_head_shot/8-Plausibility.html
Warning, this site contains some pretty graphic descriptions of the physics of a head shot.