Originally Posted by
Schmaven
Good guess, I thought the same at first, but our intuition is off in this case. I looked up the terminal velocity of a human (the coefficient of drag is difficult to determine, as it is in the drag crisis region for our free-fall conditions), and it is around 53 - 56 m/s depending on whether your arms are outstretched or not (not that big of a difference in speed)
The mass to weight ratio of a mouse, is about 11 kg/m^2, and for a human, it is about 120 kg/m^2, probably due to our longer, heavier limbs, compared to the mouse's small little feet. While the mass to area ratio to a degree determines the terminal velocity an object has, the coefficient of drag also plays an important role, and is completely dependent on the shape, and size of the object, as well as the speed it is falling, and the fluid it is falling through. The coefficient of drag does not depend on the mass of the falling object at all, which throws a wrench into the gears of intuition in some ways.
Assuming a mouse with a mass of 0.035 kg, and a projected area of about 0.0032 meters^2, falling in air, it would reach a terminal velocity of approximately 12.6 m/s. This is much slower than our terminal velocity. The coefficient of drag for a mouse is approximately 1.1, and is about a factor of 10 away from the drag crisis region (the area on the Reynolds number vs Drag Coefficient plot that gets all screwy and isn't a straight line, resulting in pain in the ass iterative calculations)
At the moment of impact, the mouse would have a kinetic energy of 2.78 Joules, whereas a human with a mass of 72 kg (about 160 pounds), would have a kinetic energy of 112,900 Joules.
But the real damage comes from the momentum of the collision over the time in which the collision occurs. Assuming that the collision occurs over a 0.1 second interval, from the moment your feet hit, to the moment you come to a rest, a person would experience 40.3 Kilo-Joules of force (38.1 kJ if you're falling with your arms out). A mouse, being much smaller, could be assumed to take 0.01 seconds for the impact to occur, this would result in only 44 Joules of force, (note 40.3 Kilo-Joules is 40,300 Joules), which is a much smaller impact force, and thus, a lot more survivable.
Having your arms spread out, would decrease the energy of your impact with the ground by 2200 Joules. I say it's worth the effort, as that's only less energy your bones have to absorb. That being said, 38.1 KJ is still a dangerously high amount of physical energy. If you were to belly flop into the ground, instead of landing feet first, your collision time would be reduced dramatically, resulting in much greater forces.