"...the top half should have become top heavy and simply slide off the tower."
Sorry to shoot holes in that statement, but gravity pulls objects down, straight towards the center of the earth. The planes hit with incredible force spreading fuel around the structure. Watch the collapse, it happeneded accordian style with the top levels compressing the steel until it, in its weakened state, failed. What ensued was a domino effect with the air being forced out the weak points in the collapse, ie: the windows, resulting in the so-called lower level explosions.
"They all fell at free fall speed..."
Free fall speed on earth is 9.81 m/s^2. Use this figure and another simple equation d=1/2at^2 and you can calculate the acceleration rate of the towers collapse. I'm not bored enough to do this but, give it a try. You need the exact height of the structure, the exact duration of collapse and then simply solve for "a". If you don't get an acceleration of at 9.5 m/s^2 than it could in no , I repeat, no way have been free fall speed.
Even attaining a similar number only illustrates the acceleration, which by definition should be reasonably close to "free fall spped" once the collapse began in ernest since it was then being sped by gravity. Breaking it down into 10 chuncks would give you multiple data points which could graphed resulting in more accurate data in regards the buildings' collapse at any one given time.
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EDIT
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The figures and equations I gave above are for acceleration and yes that is how to calulate collapse speed. Nothing has to be tweaked simply do what I suggested. The final speed will be far more than 9.81 m/s, since after 10 seconds of such an acceleration rate the speed of the object would be 98.1 m/s. Get it now?