Panic escape. The figure below shows a general situation in which a stream of people attempt to escape through an exit door that turns to be locked. The people move toward the door at speed vs = 3.7 m/s, are each d = 0.20 m in depth, and are separated by L = 1.75 m. The arrangement in the figure occuurs at time t = 0.

Question

Panic escape. The figure below shows a general situation in which a stream of people attempt to escape through an exit door that turns to be locked. The people move toward the door at speed vs = 3.7 m/s, are each d = 0.20 m in depth, and are separated by L = 1.75 m. The arrangement in the figure occuurs at time t = 0. 
(a) At what average rate the layer of people at the door increase?
 m/s

(b) At what time does the layer's depth reach 5.9 m? (The answer reveals how quickly such a situation becomes dangerous.)
 s

Damon · Accepted Answer

A person covers the 1.75 m to the next person (stopped) in about 1.75 m/3.7 m/s = .473 seconds
so the stopping rate = 1/.473 = 2.11 people stop per second
that means the pile grows by
2.11*.2 = .423 m/second

then .423 m/s * t = 5.9 m
t = 13.9 seconds