Chapter 3, Problem 45RE

To determine

Height $h$ of the arch $2ft$ from shore.

Answer to Problem 45RE

Height $h$ of the arch $2ft$ from shore is $3.6ft$ .

Explanation of Solution

Given information:

  

Calculation:

Consider the above figure,

In the below of diagram shape of parabola is,

  

For finding out the coordinates of the point $P$ , let the equation of parabola the $x=a{y}^2$ .

On getting the above graph it is clear that the point $A$ lies on the parabola and coordination $A$ is $\left(10,10\right)$ .

So, substitute the value $x=10$ and $y=10$ in equation $x=a{y}^2$ so we get,

  $\begin{array}{l}x=a{y}^2\\ 10=a{10}^2\\ 10=a100\\ a=\frac{10}{100}\\ =0.1\end{array}$

Therefore, equation become $x=0.1y^2$ .

Let the coordinates of the point $p\left(x,.1\right)$

Since the point $P$ lies on parabola so it satisfies the equation $x=0.1y^2$ .

Substitute $x=x$ and $y=8$ in equation $x=0.1y^2$ we get,

  $\begin{array}{l}x=0.1y^2\\ =0.1\times 8^2\\ =0.1\times 64\end{array}$

Hence, the coordinates of $P$ is $\left(6.4,5\right)$ .

Therefore, the height $h$ of arch is,

  $\begin{array}{l}h=10-6.4\\ =3.6ft\end{array}$