Chapter 4.6, Problem 20E

To determine

To find: How fast the water level rising when it is $2ft$ deep.

Answer to Problem 20E

The answer:

  $\frac{dh}{dt}=\frac{1}{16}$ feet per minutes.

Explanation of Solution

Given information:

The figure is:

  

Calculation:

The equation is $V_w=\frac{1}{2}lwh$

Where,

  $\begin{array}{c}l=15\\ w=\frac{4}{3}h\end{array}$

Put, the value of $l,w$ and simplify:

  $\begin{array}{c}{V}_w=\frac{1}{2}(15)(h)\left(\frac{4}{3}h\right)\\ =10h^2\\ \Rightarrow \frac{d{V}_w}{dt}=20h\frac{dh}{dt}\\ \Rightarrow 2.5=20(2)\frac{dh}{dt}\\ \Rightarrow \frac{dh}{dt}=\frac{2.5}{40}\\ =\frac{1}{16}\text{ feet per minute}\end{array}$

Therefore, the required $\frac{1}{16}\text{ feet per minute}$ fast the water level rising when it is $2ft$ deep.