I'm lost on terminology; i.e. free fall

[William Seger]

22. Wrong again

Actually, Bazant is one of the few analyses I've seen that DOESN'T try to calculate the impact energy from the velocity of the falling mass. Just so you know, here's what he really does:

After a drop through at least the height h of one story heated by fire (stage 3 in Fig. 2 top), the mass of the upper part of each tower has lost enormous gravitational energy, equal to m g h. Because the energy dissipation by buckling of the hot columns must have been negligible by comparison, most of this energy must have been converted into kinetic energy K = m v^2 / 2 of the upper part of tower, moving at velocity v.

In other words, since he is constructing an energy analysis, he starts by assuming that a mass m at a height of h has a gravitational potential energy of m g h which must go somewhere if that mass falls h. In terms of the energy, it doesn't matter how fast the fall is; Bazant is saying that much potential energy must be accounted for. He then says that the energy required to buckle those first columns was negligible by comparison, and seeing no other energy sink, he assumes that it was converted to kinetic energy, and you could use the formula he provided to calculate the velocity. In other words, you could say he derived the velocity from the energy, not the other way around, but it's the energy he's concerned with, anyway.

If you would like to say he is wrong, you will need to explain where the energy disappeared to.