3 ms·
Yes. Assuming a relatively consistent body density, mass will be proportional to the cube of the linear dimension (say height of person falling) and cross-secti
by todd8 10y ago
Yes. Assuming a relatively consistent body density, mass will be proportional to the cube of the linear dimension (say height of person falling) and cross-sectional area will be proportional to the square of the linear dimension. This is why an ant can make it to the ground without a parachute.
F_drag = K_1 * velocity^2 * Size^2
F_gravity = K_2 * Size^3
Acceleration will be zero when the forces balance so terminal velocity is:
v_term = sqrt((K_2 * Size^3)/(K_1 * Size^2)) = K*sqrt(Size)
So if an ant is say 10mm long and a human is 2m long (200 * the length of the ant) the human falls 14 times faster.
Furthermore, the forces on our bones at impact will be likely be proportional to the cube of our size while their strength will be proportional to their cross section, related to the square of our size. This give the ant a big advantage at impact as well.
Finally, I would probably die of fright on the way down, the ant wouldn't know any better.