Chapter 4.5, Problem 88E

a.

To determine

Time for one full respiratory cycle.

Answer to Problem 88E

  $\boxed{4}$

Explanation of Solution

Given information:

For a person at rest, the velocity $v$ (in litres per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by (a) Find the time for one full respiratory cycle

  $v=0.85\sin \begin{array}{c}\pi t\\ 3\end{array}$

Where $t$ is the time (in seconds).

Find the time for one full respiratory cycle.

Calculation:

Let us consider the following model:

  $v=0.85\sin \begin{array}{c}\pi t\\ 3\end{array}$

Time for one full respiratory cycle is equal to the period of the model,

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

Hence, the time for one full respiratory cycle is $\boxed{6}$ seconds.

b.

To determine

Find the number of cycles per minute.

Answer to Problem 88E

  $\boxed{15}$

Explanation of Solution

Given information:

For a person at rest, the velocity $v$ (in litres per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by (a) Find the time for one full respiratory cycle

  $v=0.85\sin \begin{array}{c}\pi t\\ 3\end{array}$

Where $t$ is the time (in seconds).

Find the number of cycles per minute.

Calculation:

One full cycle requires $6$ sec., then the number of cycles in $1$ minute will be,

  $\begin{array}{c}60\\ 6\end{array}=10$

Hence, the number of cycles per minute is $\boxed{10}$ .

c.

To determine

Sketch the graph of the velocity function.

Answer to Problem 88E

  

Explanation of Solution

Given information:

For a person at rest, the velocity $v$ (in litres per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by (a) Find the time for one full respiratory cycle

  $v=0.85\sin \begin{array}{c}\pi t\\ 3\end{array}$

Where $t$ is the time (in seconds).

Sketch the graph of the velocity function.

Calculation:

The graph of $v=0.85\sin \begin{array}{c}\pi t\\ 3\end{array}$ is given below:

  

Hence, the result.