Panic escape. The figure below shows a general situation in which a stream of pe
ID: 1950388 • Letter: P
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 = 3.0 m/s, are each d = 0.30 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 4.5 m? (The answer reveals how quickly such a situation becomes dangerous.)
Explanation / Answer
Given : People's speed vs = 3.0m/s depth d = 0.30m Speration between them L = 1.75m Initial time = 0s The amount of time it takes one person to move a distance L withspeed vs is ?t = L/vs A)The rate of increase of people is R = d/?t = d/(L/vs) = dvs/L = (0.30m) (3.0 m/s) / ( 1.75 m) = 0.514 m/s B) The amount of time is given by D = 4.5 m t = D/R = 4.5m / 0.514m/s = 8.75s
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