Chapter 7.3, Problem 8CYU

To determine

The average depth $\left(d\right)$ of the water round to nearest hundredth of a kilometer using the equation $v=356\sqrt{d}$ where $\left(v\right)$ is the speed in kilometers per hour of the tsunami which travels at the rate of 145 kilometers per hour.

Answer to Problem 8CYU

The depth of the water is 0.16km.

Explanation of Solution

Given information: The speed $\left(v\right)$ of the tsunami for the depth $\left(d\right)$ of the water is given by the equation

  $v=356\sqrt{d}\mathrm{......}\left(1\right)$

Also the speed of the tsunami is 145 kilometer per hour.

Calculation: From (1) the depth of the water can be evaluated by plugging speed $\left(v\right)$ equal to 145 kilometer per hour. Therefore from (1),

  $\begin{array}{c}\left(145\right)=356\sqrt{d}\mathrm{......}\left(\text{F}orv=145\right)\\ {\left(145\right)}^2={\left(356\right)}^{2}d\mathrm{......}\left(\text{Square both sides}\right)\\ d={\left(\frac{145}{356}\right)}^2\\ d=\mathrm{0.16......}\left(\text{Simplified}\right)\end{array}$