Question 184399
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To start with, your height function is incorrect.  You have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ h=s-16t^s]


Whereas it should be:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ h=s-16t^2]


Having settled that, you need to solve for <i>t</i> when <i>h</i> = 5.  The only problem is the exact value of <i>s</i> to use.  Was the window washer standing on a scaffold that was positioned between the 2nd and 3rd floor (at 24 feet) and he pushed the bottle off of the scaffold with his foot?  Was he holding it above waist level with his feet on the scaffold at (maybe) 24 feet, so the bottle dropped from 28 feet?  Or maybe the scaffold was half-way up the 3rd floor at 30 feet and he either kicked the bottle off the scaffold (s = 30) or dropped it from just above waist height (s = 34).  It is highly unlikely that he dropped it from the full 36 feet if he was cleaning windows that extend from 24 to 36 feet.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ s-16t^2 = 5]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ -16t^2 = -s + 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ t^2 = \frac{s - 5}{16}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ t = sqrt{\frac{s - 5}{16}} = \frac{sqrt{s-5}}{4}]


You can try some different values for <i>s</i> and see what you get.


John
*[tex \Large e^{i\pi} + 1 = 0]
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