OK, sorry I'm so late into this thread. I would let it die, but I think I can shed some light on the subject (I am a mechanical/strength engineer, or at least I used to be).

The problem with this discussion is the word "damage" and some confusion about the nature of "inelastic" collisions. These things are related. "Inelastic" means that the cars don't bounce off of one another. It means that all of the energy of the impact is *absorbed* by the bodies rather than remaining kinetic energy.

In an elastic situation (as if the cars were billiard balls), the two cars bounce off of one another and sustain *no* damage. Their speeds change is all. Like billiard balls. I can't remember the relative speeds used in the example, but in a perfectly elastic situation, the kinetic energy is conserved and the slower vehicle speeds up and the faster one slows down.

The inelastic situation is different. When we speak of inelastic collisions, we are entering into the realm of "deformable body mechanics". That means the bodies in question "deform" or go beyond the elastic region of the material and "bend" or "break". As they do so, they absorb the energy of the collision. [Technical folks will remember that the total energy absorbed is the area of the hysteresis in the stress/strain curve.] This is why cars are designed to "crumple". By designing a car to crumple, the energy of an impact is dissipated by the crumpling, if you will. If you're clever about how you design the vehicle to crumple, you can lengthen the duration of the energy transfer quite significantly so that the forces are significantly smaller.

So, you can see the relationship between the inelasticity and "damage". Damage is what happens when the kinetic energy of the impact is absorbed by the bodies and the materials deform or fracture.

You can see that "damage" is a function of design. *If* the vehicles are of identical design (which the won't be, because the front of one car is hitting the rear of another) and the impact is totally symmetrical, then they should sustain nearly identical damage. This is never the case, obviously.

The speed that the vehicles are travelling relative to the road is irrelevant. As mentioned above, it is their speed relative to each other that matters.

The high school physics teacher is correct that the faster car has more kinetic energy, but what matters is the relative speed and the energy that must be absorbed to bring the cars to the same speed. All things being equal (which they never are), the cars will share the impact energy and sustain the same damage.

To answer the question about the baseball bats: it is because the systems are not of identical design, as mentioned above. Swing two bats at each other and see what happens.

Hope this helps,

Jim