This is a follow on question from Physics SE Question "Can a Skydiver Land On a Large Slide and Survive?".
User Steeven gives this answer here.
User Dargscisyhp asks:
What is it exactly that kills you. I've never understood this. Is the maximum amount of force in this kind of impact?
So what is it that injures someone in an impact such as that at the bottom of a fall? Is it maximum force, acceleration, or what?
It is not that simple. Injury arises from a variation of acceleration with position over parts of the body. In the case of a fall, when the first part of you hits the ground (say your feet) and stops suddenly, there is nothing decelerating the rest of your body aside from the force that the feet can transmit to it. So this situation gives rise to compressive stresses that the body's tissue simply cannot support and the latter is thus crushed.
I have sketched a system below whose mathematical description will give you full insight into the problem, if you care to write down and solve the equations of motion for the discrete masses. Here we model the body as an array of masses $m_j$ separated by springs (connective tissue) with spring constants $k_j$, and the masses are all moving towards the ground at the same velocity $\vec{v}$ when the first spring is brought to an abrupt halt at its lower edge. You will find, amongst other things a maximum force (proportional to connective tissue stress) for each spring, that the lowest springs undergo the greatest peak stress (corresponding to the everyday observation that you bruise at the surface of an impact and the injury diminishes with depth i.e. distance from the bruise) and that the peak stress in each spring can be "engineered" considerably by using a varying spring constant profile. Thus you can also play with the spring constants and, for example, design a crumple zone for a car: choose the spring constants so the first few feel the higher stress (the "sacrificial" zone) whilst those furthest from the impact feel much less and there are definite optimum spring constant profiles for this kind of thing.
Contrast all this with the case where you imagine all the body to be electrically charged with charge density exactly in proportion to the mass density. Then you accelerate the body with a whopping electric field. In this case, all parts of the body are always accelerated at exactly the same rate and there is no stress between any two parts of the body. You could accelerate arbitrarily fast with this setup and feel nothing unusual. I've read somewhere (or more likely been told by my daughter) that Emperor Palpatine's personal ship could accelerate at $1 600\,g$. With an electrostatic drive like the one above, human occupants could brook this, no problem! (aside from that now we need to find an Imperial electrostatic force drive engineer....)
A Community Wiki Answer to capture another User James Large's most excellent summary made in the comment:
Two key words to take away from the answers below are stress and strain. Good words to search for if you want to learn more. And remember, "It's not the fall that kills you, it's the sudden internal strain at the end."
This is an excellent way of putting it, and of summarizing my answer. Particularly the focus on strain. Fundamentally, we test for a kinematical consideration: if every point undergoes the same motion, no matter what the jerk, acceleration or whatever, no strain can ever result because the set of points making up the body undergoes an isometry.
Sharp deviations from this condition lead to large strains within the body, and these are calculated as sketched in my non Wiki Answer.
If I may explain by means of a few "detours". I am structural engineer (not a doctor), but I do have a good sense of forces and energy dissipation through a structure. In this case the structure being the human body.
Your question does not only apply to skydivers who get fatally injured, but every injury relating to an impact. The only difference is the vector at which the "victim" was moving prior to coming to as sudden stop. Whether a person travels at 1 m/s horizontally (usually walking), 17 m/s driving (+- driving a car in town) or 54m/s (+- terminal velocity when skydiving) and comes to a sudden stop (dt being very small), the human body ends up having to absorb, transfer and even dissipate the kinetic energy.
Assuming that the pedestrian, passenger in a vehicle and skydiver are identical tripplets who have the same physiology, we can cancel Mass, friction resistance (environmental and physiological (in the victims bodies) out. Thus we are left with an relative magnitutes of energy of 1 vs 17 vs 54. If they all collide with huge, solid masses which don't absorb energy, they all have to accomodate increasing amounts of energy somehow.
Assuming that the pedestrian walks into the corner of a huge desk, the tissue of his quadricep will bear the brunt of the event and thus will have to absorb some of the energy in the form of a point load on his quad. This occurs by deformation of the tissue, possibly rupturing some muscle tissue and in the process causing a small haematoma. The energy which is not absorbed by the deformation would then be transferred to the femur, which would bend slightly under load and then transfer the energy into the knee, and hip. The pedestrian will buckle over at the hip, falling forward slightly, ... etc. I could go into more detail here, but I think you get the point. The only casualty in this 1m/s to 0m/s event is the quadricep which has a bruise.
Scaling this up to the person in the vehicle travelling at 17m/s will show a different picture. Assuming it is a modern car with sufficient safety features (crumple zone, airbag and seatbelt) usually a 17m/s to 0m/s event will result in the car absorbing the brunt of the kinetic energy to reduce the velocity of car+passenger increasing the the time taken to decelerate from 17m/s to 0m/s and thus the person in the car will effectively have to accomodate less of an impact force. Let's assume that the energy dissipated due to safety features is proportional to the velocity and we assume that it has effectively reduced the energy the body of the passenger has to absorb. This leaves the body moving at (let's say) 10m/s before the airbag deploys and the seatbelts tension. When they do, the body moves against the seatbelts and airbag. The seatbelt spreads the load against chest and clavicle, causing bruising. Effectively the pre-tensioned seatbelt has while the airbag reduces travel of the head, reducing strain on the neck of the passenger. Nonetheless, the brain of the passenger still moves at 10m/s and pushes against the skull from the inside at t=0 and thus gets slightly deformed and possibly bruised causing a concussion.
Now to our skydiver who moves at 54m/s and has no means to increase dt. His body has to accommodate the entire energy in a very short time. Assuming that he is experienced, he will attempt to use his leg muscles to act as springs and thus extend dt and partly absorb some of the energy. It is unlikely that the human skeleton quadriceps and gluts are strong enough to absorb this much for though, and therefore he will not land on his feet. Most likely he will land on his buttocks, which will be compressed before the (reaction) force is transferred through the muscle tissue into the pelvic bones, into the SI joint, up the spine. Thus his back will experience excessive compression on the discs and bones. The internal organs (soft tissue) would still be moving at a higher velocity in comparison with other more rigid organs. Also they deform easily, allowing other soft tissues more distance to travel. In essence, you have soft tissues in the chest cavity and abdominal areas moving at different velocities in relation to each other, causing strain and possibly tears in between them. In a nut shell, the bone and muscle structure is stressed to the limit of its capabilities, and can thus can not protect the soft tissue (intestines and brain). These are subjected to immense forces which they were never intended to accommodate and rupture. Internal hemorrhaging is the result and the person bleeds to death internally. Of course secondary damage to bone fragments piercing organs, etc. can (and do) also occur.
I hope this answers your question in a trivial way.
