Chapter 12.7, Problem 4P

To determine

To calculate: How far captain can see if he is 10 m above the water .Given if his ship is 4m above the water he can see about 30m across the ocean. also given the height of a person is above the water is directly proportional to the square of the distance .

Answer to Problem 4P

The distance of ship $d\simeq 117.2km$

Explanation of Solution

Given information:

The height of a person is above the water is directly proportional to the square of the distance.

Let, distance = d

height = h .

So $d\prec h^2$

Let k be a constant

  $d=k\cdot h^2$ ...... $\left(1\right)$

Also given, if his ship is 4m above the water and he can see about 30m across the ocean.

If he is 4m above the water and he can see about 30m across the ocean

Put the value of distance and height to get value of k .

  $d=k\cdot h^2$

  $d=$$30\times 1000$$=k\cdot 16m^2$

Solve further to get k .

  $\begin{array}{l}k=\frac{30000}{256}\\ k=117.1875\end{array}$

Now, put the value of h and k equation 1 to get the value of d .

  $\begin{array}{l}d=k\cdot h^2\\ d=\mathrm{117.1875.}{\left(10\right)}^{2}m\end{array}$

Solve further to get d .

  $\begin{array}{l}d=117.1875\cdot 100m\\ d=11718.75m\\ d=117.18km\end{array}$

Changing it to nearest tenth.

  $d=117.2km$