Chapter 2, Problem 90RE

Solution

(a)

To find: The graph of function s

The graph is given

Given information Length of beam is 250ft.The height of the p[iling from the ground is 50ft.

  $S=\left(8.5\times {10}^{-7}\right)d^2\left(255-d\right)$

The graph of the function given below:

  

(b)

To find: The dimensions of viewing window.

The dimensions of viewing window are $s$ lies in $\left(0,50\right)$ and d lies in $\left(0,255\right)$

Given information Length of beam is 250ft.The height of the piling from the ground is 50ft.

  $S=\left(8.5\times {10}^{-7}\right)d^2\left(255-d\right)$

  $s$ lies in $\left(0,50\right)$ and d lies in $\left(0,255\right)$ .

(c)

To find: The greatest amount of vertical deflection s and where does it occurs..

The greatest amount of vertical deflection s is 2.0880 and it occurs at d=170 ft.

Given information Length of beam is 250ft.The height of the piling from the ground is 50ft.

  $S=\left(8.5\times {10}^{-7}\right)d^2\left(255-d\right)$

To find the greatest value of $s$ find $s\text{'}(d)$

  $\begin{array}{l}s\text{'}(d)=2d\times 8.5\times 255\times {10}^{-7}-3d^2\times 8.5\times \times {10}^{-7}\\ s\text{'}(d)=4.355\times {10}^{-4}d-d^{2}17.5\times {10}^{-7}=0\\ d=170\end{array}$

Now find $s\text{'}\text{'}(d)$

  $s\text{'}\text{'}(d)=-35d\times {10}^{-7}<0$

Hence s is greatest at d=247.71

  $\begin{array}{l}S=\left(8.5\times {10}^{-7}\right){\left(170\right)}^2\left(255-170\right)\\ S=2.088\end{array}$

(d)

To find: The solution part c does not occur half way.

The solution part c does not occur half way because d-170 which is not half of 255.

Given information Length of beam is 250ft.The height of the piling from the ground is 50ft.

  $S=\left(8.5\times {10}^{-7}\right)d^2\left(255-d\right)$

The solution part c does not occur half way because d-170 which is not half of 255.and the weight is placed at d so it bend maximum there.