A Simple One-dimensional Model of Collapse of Some Tall Buildings

We develop one-dimensional model of an avalanche to examine the destruction of World Trade Center (WTC) 2 on September 11, 2001, after the building was hit by an airplane. Its main ingredient is the way the building opposes the progress of the avalanche, which is expressed in terms of a reaction force ${\cal R}$ at the location of the collapse front (a moving interface between the building and the avalanche). We consider realistic expressions for ${\cal R}$ in terms of two scaled parameters, {\em reaction} $r$ and {\em safety} $s$, and find when the total collapse times are equal to that of WTC 2, $T_c = 11$ sec. A comparison with the minimal values of parameters $r$ and $s$ that building must have in order to be standing indicate that the collapse of the building is most likely inconsequential to the damage sustained in the collision with the airplane