Walker, Halliday & Resnick — Motion Along a Straight Line: Problem 8

8 Panic escape. Figure 2-16 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 \(v_s = 3.50\text{ m/s}\), are each \(d = 0.25\text{ m}\) in depth, and are separated by \(L = 1.75\text{ m}\). The arrangement in Fig. 2-16 occurs at time \(t = 0\). (a) At what average rate does the layer of people at the door increase? (b) At what time does the layer's depth reach \(5.0\text{ m}\)? (The answers reveal how quickly such a situation becomes dangerous.)