Chapter 1.1, Problem 54E

a

To determine

To find: the temperature outside of an airplane at height 500 ft.

Answer to Problem 54E

  $92.5°\text{F}$

Explanation of Solution

Given information:

For every 1000 feet ascends of an airplane, the temperatures decreases by $5°\text{F}$ .

Ground level temperature = $95°\text{F}$

Height of airplane $\left(d\right)$ = 500 ft

Temperature function $t\left(d\right)$ at d feet height is as follows:

  $t\left(d\right)=95-0.005d$ …. (1)

Calculation:

To get the temperature outside of airplane at 500 ft, substitute the $d=500\text{ ft}$ in equation (1) and simplify it as shown below.

  $\begin{array}{c}t\left(d\right)=95-0.005d\\ t\left(500\right)=95-0.005\left(500\right)\\ =95-2.5\\ =92.5°\text{F}\end{array}$

Thus, the temperature outside the airplane at 500 ft is $92.5°\text{F}$ .

b

To determine

To find: the temperature outside of an airplane at height 750 ft.

Answer to Problem 54E

  $91.25°\text{F}$

Explanation of Solution

Given information:

For every 1000 feet ascends of an airplane, the temperatures decreases by $5°\text{F}$ .

Ground level temperature = $95°\text{F}$

Height of airplane $\left(d\right)$ = 750 ft

Temperature function $t\left(d\right)$ at d feet height is as follows:

  $t\left(d\right)=95-0.005d$ …. (1)

Calculation:

To get the temperature outside of airplane at 750 ft, substitute the $d=750\text{ ft}$ in equation (1) and simplify it as shown below.

  $\begin{array}{c}t\left(d\right)=95-0.005d\\ t\left(750\right)=95-0.005\left(750\right)\\ =95-3.75\\ =91.25°\text{F}\end{array}$

Thus, the temperature outside the airplane at 750 ft is $91.25°\text{F}$ .

c

To determine

To find: the temperature outside of an airplane at height 1000 ft.

Answer to Problem 54E

  $90°\text{F}$

Explanation of Solution

Given information:

For every 1000 feet ascends of an airplane, the temperatures decreases by $5°\text{F}$ .

Ground level temperature = $95°\text{F}$

Height of airplane $\left(d\right)$ = 1000 ft

Temperature function $t\left(d\right)$ at d feet height is as follows:

  $t\left(d\right)=95-0.005d$ …. (1)

Calculation:

To get the temperature outside of airplane at 1000 ft, substitute the $d=1000\text{ ft}$ in equation (1) and simplify it as shown below.

  $\begin{array}{c}t\left(d\right)=95-0.005d\\ t\left(1000\right)=95-0.005\left(1000\right)\\ =95-5\\ =90°\text{F}\end{array}$

Thus, the temperature outside the airplane at 1000 ft is $90°\text{F}$ .

d

To determine

To find: the temperature outside of an airplane at height 5000 ft.

Answer to Problem 54E

  $70°\text{F}$

Explanation of Solution

Given information:

For every 1000 feet ascends of an airplane, the temperatures decreases by $5°\text{F}$ .

Ground level temperature = $95°\text{F}$

Height of airplane $\left(d\right)$ = 5000 ft

Temperature function $t\left(d\right)$ at d feet height is as follows:

  $t\left(d\right)=95-0.005d$ …. (1)

Calculation:

To get the temperature outside of airplane at 5000 ft, substitute the $d=5000\text{ ft}$ in equation (1) and simplify it as shown below.

  $\begin{array}{c}t\left(d\right)=95-0.005d\\ t\left(5000\right)=95-0.005\left(5000\right)\\ =95-25\\ =70°\text{F}\end{array}$

Thus, the temperature outside the airplane at 5000 ft is $70°\text{F}$ .

e

To determine

To find: the temperature outside of an airplane at height 30000 ft.

Answer to Problem 54E

  $-55°\text{F}$

Explanation of Solution

Given information:

For every 1000 feet ascends of an airplane, the temperatures decreases by $5°\text{F}$ .

Ground level temperature = $95°\text{F}$

Height of airplane $\left(d\right)$ = 30000 ft

Temperature function $t\left(d\right)$ at d feet height is as follows:

  $t\left(d\right)=95-0.005d$ …. (1)

Calculation:

To get the temperature outside of airplane at 30000 ft, substitute the $d=30000\text{ ft}$ in equation (1) and simplify it as shown below.

  $\begin{array}{c}t\left(d\right)=95-0.005d\\ t\left(5000\right)=95-0.005\left(5000\right)\\ =95-160\\ =-55°\text{F}\end{array}$

Thus, the temperature outside the airplane at 30000 ft is $-55°\text{F}$ .