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Panic escape. The figure here shows a general situation in which a stream of people attempt to escape through an exit door that turns out to be locked. The people move toward the door at speed vs = 3.350 m/s, are each d = 0.270 m in depth, and are separated by L = 1.600 m. The arrangement in the figure occurs at time t = 0. In time, people become stacked up at the door at what average rate does the layer of people at the door increase? At what time does the layer's depth reach 4.63 m? (The answers reveal how quickly such a situation becomes dangerous.)

Explanation / Answer

a) 1person t = L/v

2person t = 2L/v

n person t = nL/v

average person rate = n/nL/v = v/L = 3.63/1.6=2.26875 = 2 persons per second

b)depth = 4.63/0.27 = 17 person

so t = 17*1.6/3.63 3.08 s

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