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

Question

Panic escape. The figure below shows a general situationin which a stream of people attempt to escape through an exit doorthat turns to be locked. The people move toward the door at speedvs = 3.8 m/s,are each d = 0.20 m in depth, andare separated by L = 1.75 m. The arrangement in the figureoccuurs at time t = 0. (a) At what average rate the layer of people atthe door increase?
1 m/s

(b) At what time does the layer's depth reach 5.4 m? (The answer reveals how quickly such asituation becomes dangerous.)
2 s (a) At what average rate the layer of people atthe door increase?
1 m/s

(b) At what time does the layer's depth reach 5.4 m? (The answer reveals how quickly such asituation becomes dangerous.)
2 s

Explanation / Answer

   People's speed vs = 3.8m/s depth d = 0.20m 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     = (0.20m) (3.8 m/s) / ( 1.75 m)    =  0.43 m/s
B) The amount of time is given by        D = 5.4 m
t = D/R = ------ s Solve it People's speed vs = 3.8m/s depth d = 0.20m 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     = (0.20m) (3.8 m/s) / ( 1.75 m)    =  0.43 m/s
B) The amount of time is given by        D = 5.4 m
t = D/R = ------ s Solve it

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