Panic escape. The figure here shows a general situation in which a stream of peo

Question

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 = 3.450 m/s, are each d = 0.280 m in depth, and are separated by L = 1.650 m. The arrangement in the figure occurs at time t = 0. In time, people become stacked up at the door (a) at what average rate does the layer of people at the door increase? (b) At what time does the layer's depth reach 5.30 m? (The answers reveal how quickly such a situation becomes dangerous.)

Explanation / Answer

time taken by the first person is t1 = distance/speed = (1.65+0.28)/3.45 = 0.559 s

Second person will take 2*0.559 = 1.12 s

third person will take 0.559*3 = 1.677 s

A) in 0.559 s the layer increases by 0.28 m

the rate of increase of the layer is 0.28/0.559 =0.5 m/s

B) to increase the depth upto 5.3m the no.of persons required is 5.3/0.28 = 18.9 = 19 persons

So the time taken is 19*0.559 = 10.62 S

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