Panic escape. The figure below shows a general situation in which a stream of pe

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 = 2.9 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?

(b) At what time does the layer's depth reach 4.7 m? (The answer reveals how quickly such a situation becomes dangerous.)

Explanation / Answer

A person covers the 1.75 m to the next person (stopped) in about 1.75 m/2.9 m/s = .603 seconds
so the stopping rate = 1/.603 = 1.66 people stop per second
that means the pile grows by
1.66*.2 = .332 m/second

then .332 m/s * t = 4.7 m
t = 14.16 seconds

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