YourGuideToFreedom/WorldTradeCenter/ProgressiveCollapseMaxSpeed

The "collapse of the towers" with near free-fall speed is quite stunning. More than that, it can easily be proven that it is physically IMPOSSIBLE for a progressive collapse to happen with a speed clearly seen on the videos.

Why ? Because of "conservation of impulse". This is the most basic theory in physics.

If m1 mass moving at v1 speed sweeps a body with m2 mass, than the resulting speed of the m1+m2 cannot be higher than v12 = (m1*v1) / (m1 + m2)

This allows a simple model to prove that it is absolutely impossible for a 110 storey pencake collapes (as it happened in the USA government official conspiracy theory) to take less than 14 seconds (starting at floor 90) or 13.2 second (starting at floor 78). Elementary school physics - with laborsome calculation or some help from your PC - allows anyone to prove the official government conclusion - the result of a 16+ million USD investigation - a nonsense. DO NOT BE FOOLED. THINK ABOUT IT YOURSELF. PHYSICS is stronger than the government. What is the USA government trying to hide ?

#!/usr/bin/perl -w

$total_height=402;
$floor_count=110;
$start_floor=78;

# using metric units for simpler calculations (no magic constants)
# 400 thousand tons :
$total_floor_weight=400000000;
$floor_weight = $total_floor_weight / $floor_count;
$floor_height = $total_height / $floor_count;

$cap_floors = $floor_count - $collapse_start_floor;
$cap_mass = $cap_floors *  $floor_weight;
$cap_height = $cap_floors * $floor_height;

# gravity constant: 
$g = 9.81;      # m/(s*s)

# This function is not used, but easier to understand the inverse function (below).
# After t time, if started with v0 speed, the travelled total height is:
sub height_t_v0 {
       my ($t, $v0) = @_;
       # speed at the end is v0 + t * g
       my $average_speed= $v0 + ($t * $g/2);
       return $t * $average_speed;
}

# inverse of height_t_v0, using quadratic formula
# g/2 * t^2 + v0 * t - height = 0 
sub t_height_v0{
       my ($height, $v0)= @_;
       my $a= $g/2;
       my $b= $v0;
       my $c = - $height ;
       return (-$b + sqrt( $b * $b - 4* $a * $c)) / (2 * $a);
}

# floor-after floor we pencake the building, assuming absolutely no resistance from
# the floors structure below - other than the (inevitable) floors' mass.
sub pencake{
       my $floor;
       my $t=0; # starting time = 0
       my $v=0; # starting speed = 0

       my $collapse_start_floor = $start_floor;

       my $falling_floors = $cap_floors;
       for( $floor = $start_floor; $floor >= 0; $floor--){
               my $t_floor_collapse = t_height_v0( $floor_height, $v );
               $t += $t_floor_collapse;
               $v += $t_floor_collapse * $g;   # gravitational acceleration
               print "collapse $floor: \t $t_floor_collapse sec\t; v=$v m/s\n";

               # because of the floor's mass, the falling mass loses some speed (conservation of impulse):
               $v = $v * $falling_floors / ($falling_floors + 1);
               $falling_floors ++;
       }

       # finally, let the cap collapse:
       my $t_cap_collapse = t_height_v0( $cap_height, $v );
       $t += $t_cap_collapse;

       print "collapse cap = $t_cap_collapse sec\n";
       print "Pencake collapse time= $t \n";
}

pencake();

Note than in reality weldings and bolts transfer some impulse (via the still standing parts of the building below) down to the bedrock. So in reality the time needed for a realistic fall is much much higher than the model that only allows slowing by the inevitable mass of the floors.