Panic escape. The figure shows a general situation in which a stream of people attempt to escape

Panic escape. Figure 2-24 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 m/s, are each d = 0.25 m in depth, and are separated by L = 1.75 m. The arrangement in Fig. 2-24 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 m? (The answers reveal how quickly such a situation becomes dangerous.)

If there is another problem from this textbook or problem set that you would like me to explain, please send me a request. My e-mail is given in the channel description, and I've included other contact links below.

If my videos have helped you, and you would like me to keep making more, please *consider* subscribing. Even one person helps and supports me immensely. :)

[KTBWorld]

Someone just commented and asked "why did you bring 'vs' into the numerator?", and then they deleted the comment as I was typing up a reply. Well, since they asked, I might as well post the answer for anyone else who might be wondering the same thing:

Because it was in the denominator's denominator. The ratio was d / (L / vs), which looks messy and is hard to work with. But since vs was in the "denominator" of the denominator, this is equal to vs simply being in the numerator of the entire ratio.

In other words: a / (b / c) == a*c / b.