## Related questions with answers

Deflections of diving boards A diver stands at the very end of a diving board before beginning a dive. The deflection $d$ of the board at a position $s$ feet from the stationary end is given by $d=c s^2(3 L-s)$ for $0 \leq s \leq L$, where $L$ is the length of the board and $c$ 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 $10$ feet long.

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

Solution

VerifiedThe given is

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

where:

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

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