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RE: Should he jump? - On cartoon mechanics
I think that the air resistence has a greater influence on the end result since the air resistence increases quadratically with the velocity.
It even might be the case that he by himself can generate more air resistence then the piece of rock.
It also might be the case that lying down on the rock will reduce the damage since the impact will be more equally distributed.
Air resistance is definitely something to consider on free falling objects, specially because it's that drag what determines the terminal velocity of the object and consequentially the maximum amount of kinetic energy the body can achieve before impact.
The case in which the person generates more drag than the rock doesn't really convince me. It's possible, but drag depends on fluid density, drag coefficient, area and the square of the velocity as you mentioned and since the fluid and the velocity are the same for both bodies, what makes the drag force different for each bodies are the Cd and the area. As much as both drag coefficients may vary (and I'm inclined to think it would be higher for the rock than for the human) the area contribution tends to be bigger because of the order of magnitude since one of the considerations is that the rock is much more massive than the human. Hence, drag would be bigger for the rock than the human, I think.
As for the lying down, it made me think. It would make for a better distribution of the forces on the body indeed (since the stress is proportional to the force but inversely proportional to the area) but the human body is somewhat 'designed' to sustain charges vertically coming upwards. The bones on the legs and hip are sturdier than those on other parts of the body. The meniscus on the vertebral column as well as those in the lower articulations contribute to the absorption of the forces and of course the muscles on the legs which work (a little) like springs and dampeners, dissipating the forces as well. My opinion is that attempting to bend the knees to absorb the hit with the muscles would make for a better reduce on damages; it would protect most major organs too that would be crushed if the subject was lying down.
I hope all that doesn't sound as tongue tied as it did in my mid! Thanks for your comment and observations :)