You are oversimplifying things and only considering the body as a whole. You forget that factors internal to the body can, and do, affect the motion of the individual components of that body.
Take my example of the figure skater doing a spin. When the arms are extended the rotation velocity of the skater as a whole is low. Pull in the arms, rotational velocity goes up in order to conserve the total momentum of the system. No external forces are acting upon the skater and yet the rotational speed increases.
No it's not nonsensical and your next statement correctly indicates why:
Which is exactly the point we're trying to make. The instantaneous velocity of an individual component of a rotating object - such as the head of a tumbling skier - can be moving much faster than the object as a whole.
We don't have video of the fall. We don't know how he fell. The speed he was travelling before the impact is only one factor in a very complex equation that determines how fast his head was moving when it hit the rock. It's actually entirely possible that the head was moving slower than the rest of his body relative to the rock at the moment of impact. It's also entirely possible that it was moving much faster.
All we can definitively say is that the initial speed down the slope does not give us anywhere near enough information to figure out how much force his head took at impact.
Cheers,
Luke.
*sigh*
If a skier is travelling fast enough for a fall to result in either a) end-over-end catapulting into the air, or b) tumbling at a significant rate of angular momentum........ then the skier must, by definition, have been travelling fast (probably over 25-30mph) in the first place.
Otherwise an accident would a) not throw the skier airborne in any significant manner, or b) not cause the skier to do any more than fall to the slope and perhaps roll and skid for a short while before coming to a rest.
Look: I totally agree that a tumbling skier can have a temporary head velocity that is significantly higher than his CoG velocity (and, as you say, posibly also slower). BUT: if a skier is tumbling that violently, then it means that the CoG velocity is/was high anyhow. QED.
So here's the thing. Let's for one moment assume that the helmet damage indicates that it hit the rock at 50mph (and that might not even be correct, but for the moment let's assume it is). A head impact of 50mph either implies that the whole body was moving towards the rock at around that velocity, or that the body was tumbling/somersaulting such that the head was moving at 50mph while the CoG was perhaps moving at a slower velocity.
But if it's the latter, then one has to explain how the body came to be tumbling or somersaulting such that there was significant angular momentum generated. And that would require the body to have been moving at a significant velocity prior to the first impact anyhow.
So, as I see it, the probability - either way one chooses to look at it - is that Schumacher was travelling at significant downhill speed at the time of the accident. Again, that's not a criticism or a denouncement. Schumacher was free to ski in whichever manner he liked, just as some people choose to ride motorbikes fast on quite country roads (and some of them lose control, hit trees and die or end up paralysed....).
I also note with interest that the apparent leak from the investigation explicitly referred to the likely downhill speed at the moment of the accident. It did not refer to the likely speed at which the helmet hit the rock. I would reiterate that I tend to believe that people who investigate these sorts of accidents are pretty experienced in divining skiing speed from impact damage and injuries. I tend to think that they understand probably better than anyone else how to account for factors such as somersaulting or tumbling (and that they understand that those factors are in themselves indicative of high speeds). And since speed at the moment of accident is often significant from an investigative standpoint (e.g. was the behaviour reckless or inappropriate for the conditions), I would tend to think that they are generally quite good at making estimates of pre-impact ski speed.
Who would?