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Deflections of diving boards A diver stands at the very end of a diving board before beginning a dive. The deflection dd of the board at a position ss feet from the stationary end is given by d=cs2(3Ls)d=c s^2(3 L-s) for 0sL0 \leq s \leq L, where LL is the length of the board and cc is a positive constant that depends on the weight of the diver and on the physical properties of the board (see the figure). Suppose the board is 1010 feet long.

If the deflection at the end of the board is 1foot1 \mathrm{foot}, find cc.

Solution

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Answered 2 years ago
Answered 2 years ago
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The given is

d=cs2(3Ls)0sLd=cs^2(3L-s) \hspace*{30pt} 0\leq s \leq L

where:

L:=Length of the boards:=position of the of the diver from the stationary endd:=deflectionc:=positive constant; depends on the weight of the diver\begin{align*} L&:= \texttt{Length of the board}\\ s&:= \texttt{position of the of the diver from the stationary end}\\ d&:= \texttt{deflection}\\ c&:= \texttt{positive constant; depends on the weight of the diver}\\ \end{align*}

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