Chapter 4.4, Problem 88E

(a)

To determine

To find: The time for one full respiratory cycle.

Answer to Problem 88E

The time for one full respiratory cycle is 6 second.

Explanation of Solution

Given information:

The velocity of airflow is

  $v=0.85\sin \left(\frac{\pi t}{3}\right)$

Calculation:

Calculate the velocity of airflow,

It is know that the period for a function of the form $y=a\sin bx$ is given by

Period $=\frac{2\pi }{b}$

The time for 1 full respiration cycle to the period of the model,

  $\begin{array}{c}Period=\frac{2\pi }{\left(\frac{\pi }{3}\right)}\\ =\frac{6\pi }{\pi }\\ =6\end{array}$

Therefore the time for one full cycle is 6 second.

(b)

To determine

To find: The number of cycle per minute.

Answer to Problem 88E

The number of cycle per minute is 10.

Explanation of Solution

Given information:

The velocity of airflow

  $v=1.75\sin \frac{\pi t}{2}$

Calculation:

Calculate the full cycle requires 4sec , then number of cycle in 1minute will be,

  $\begin{array}{c}n=\frac{60}{10}\left(1\right)\\ =10\end{array}$

Therefore, the number of cycles per minute is 10.

(c)

To determine

To graph: The equation $v=1.75\sin \frac{\pi t}{2}$ .

Answer to Problem 88E

The graph of the equation $v=1.75\sin \frac{\pi t}{2}$ , is shown in Figure (1).

Explanation of Solution

Given information:

The velocity of airflow is

  $v=1.75\sin \frac{\pi t}{2}$

Calculation:

Draw the graph of the equation $v=1.75\sin \frac{\pi t}{2}$ .

  

Figure-(1)

Therefore, the graph of the equation $v=1.75\sin \frac{\pi t}{2}$ , is shown in Figure (1)