Given: A 100 story building. Each floor is 10 meters apart. The acceleration due to gravity is 10 meters per second per second. Each floor has an equal mass (doesn't matter what it is, only the relation among the various floors). Each floor has exactly zero support and it just hangs magically until the floors above fall on it AND when these floors fall on each other they don't crack, chip or fade. Thus momentum will be exactly preserved. We ignore air resistance.
We drop a pinball (if he had any, we could have used one of Dickless' balls) at the exact moment the 100th floor lets go. The pinball will hit the ground 14.1 seconds later.
Dickless thought it was a calculus problem. It's not. There's nothing to integrate here. It's a set of discrete events and the correct solution is an iteration. For each iteration (the floors above fall onto the next one down) I'll use 't' for time (seconds), Vo for the initial velocity (meters per second) of the mass and Vf for the final velocity of the mass and 'd' is the distance (meters) the structure has fallen so far.
100-99: d=10, Vo=0, t=1.41, Vf=14.1 99-98: d=20, Vo=7.01 (14.1 x 1/2), t=.87, Vf=15.8 98-97: d=30, Vo=10.5 (15.8x2/3), t=.71, Vf=17.6 97-96: d=40, Vo=13.2 (17.6x3/4... you see the pattern by now), t=.61, Vf=19.4 96-95: d=50, Vo=15.5, t=.55, Vf=21.0 ... (I'm too lazy to type them all) 91-90: d=100, Vo=23.9, t=.39, Vf=27.8
OK, so our building has fallen 100 meters so far and it took 6.35 seconds to do it. It is currently traveling, just before it hits the 90th floor, at 27.8 meters per second.
Where is the ball we dropped at the beginning? Well, in 6.35 seconds it has traveled over twice as far (201.8 meters) and is going over twice as fast (63.5 m/s).
See you later, accelerator.
Even if we now drink Osama's Magic 9/11 Kool-Aid now and the other 90 floors just vanish, the ball hits 3.2 seconds ahead of our travelling building.