Chapter 19, Problem 2E

(a)

To determine

The height of the pikes peak in $\text{km}$ and $\text{mi}$.

Answer to Problem 2E

The height of the pikes peak is $4.27\text{ km}$ or $2.65\text{mi}$.

Explanation of Solution

Given info: The height of the pikes peak is $\text{14000 ft}$.

Explanation:

The height of the pikes peak is $\text{14000 ft}$.

Convert the height from $\text{ft}$ into $\text{km}$.

$\text{1 ft = 0}\text{.000305 km}$

Use unitary method to find the height of the pikes peak in $\text{km}$.

Therefore, the height of the pikes peak in $\text{km}$ is as follows,

$\begin{array}{c}\text{14000 ft = }\left(\text{0}\text{.000305 km}\right)\left(\text{14000}\right)\\ =4.27\text{ km}\end{array}$

The height of the pikes peak is $\text{14000 ft}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the pikes peak in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the pikes peak in $\text{mi}$ is as follows,

$\begin{array}{c}4.27\text{ km = }\left(\frac{1}{1.61}\text{ mi}\right)\left(4.27\right)\\ =2.65\text{mi}\end{array}$

Conclusion:

Therefore, the height of the pikes peak is $4.27\text{ km}$ or $2.65\text{mi}$.

(b)

To determine

The height of the top of the Mt. Everest in $\text{km}$ and $\text{mi}$.

Answer to Problem 2E

The height of the top of the Mt. Everest is $8.845\text{ km}$ or $5.49\text{mi}$.

Explanation of Solution

Given info: The height of the top of the Mt. Everest is $\text{29000 ft}$.

Explanation:

The height of the top of the Mt. Everest is $\text{29000 ft}$.

Convert the height from $\text{ft}$ into $\text{km}$.

$\text{1 ft = 0}\text{.000305 km}$

Use unitary method to find the height of the top of the Mt. Everest in $\text{km}$.

Therefore, the height of the top of the Mt. Everest in $\text{km}$ is as follows,

$\begin{array}{c}\text{29000 ft = }\left(\text{0}\text{.000305 km}\right)\left(\text{29000}\right)\\ =8.845\text{ km}\end{array}$

The height of the top of the Mt. Everest is $\text{14000 ft}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the top of the Mt. Everest in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the top of the Mt. Everest in $\text{mi}$ is as follows,

$\begin{array}{c}8.845\text{ km = }\left(\frac{1}{1.61}\text{ mi}\right)\left(8.845\right)\\ =5.49\text{mi}\end{array}$

Conclusion:

Therefore, the height of the top of the Mt. Everest is $8.845\text{ km}$ or $5.49\text{mi}$.

(c)

To determine

The height of the commercial airline flight in $\text{km}$ and $\text{mi}$.

Answer to Problem 2E

The height of the commercial airline flight is $10.675\text{ km}$ or $6.63\text{mi}$.

Explanation of Solution

Given info: The height of the commercial airline flight is $\text{35000 ft}$.

Explanation:

The height of the commercial airline flight is $\text{35000 ft}$.

Convert the height from $\text{ft}$ into $\text{km}$.

$\text{1 ft = 0}\text{.000305 km}$

Use unitary method to find the height of the commercial airline flight in $\text{km}$.

Therefore, the height of the commercial airline flight in $\text{km}$ is as follows,

$\begin{array}{c}\text{35000 ft = }\left(\text{0}\text{.000305 km}\right)\left(\text{35000}\right)\\ =10.675\text{ km}\end{array}$

The height of the commercial airline flight is $\text{35000 ft}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the top of the Mt. Everest in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the commercial airline flight in $\text{mi}$ is as follows,

$\begin{array}{c}10.675\text{ km = }\left(\frac{1}{1.61}\text{ mi}\right)\left(10.675\right)\\ =6.63\text{mi}\end{array}$

Conclusion:

Therefore, the height of the commercial airline flight is $10.675\text{ km}$ or $6.63\text{mi}$.

(d)

To determine

The height of the supersonic transport flight in $\text{km}$ and $\text{mi}$.

Answer to Problem 2E

The height of the supersonic transport flight is $19.825\text{ km}$ or $12.31\text{mi}$.

Explanation of Solution

Given info: The height of the supersonic transport flight is $\text{65000 ft}$.

Explanation:

The height of the supersonic transport flight is $\text{65000 ft}$.

Convert the height from $\text{ft}$ into $\text{km}$.

$\text{1 ft = 0}\text{.000305 km}$

Use unitary method to find the height of the supersonic transport flight in $\text{km}$.

Therefore, the height of the supersonic transport flight in $\text{km}$ is as follows,

$\begin{array}{c}\text{65000 ft= }\left(\text{0}\text{.000305 km}\right)\left(\text{65000}\right)\\ =19.825\text{ km}\end{array}$

The height of the supersonic transport flight is $\text{35000 ft}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the supersonic transport flight in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the supersonic transport flight in $\text{mi}$ is as follows,

$\begin{array}{c}19.825\text{ km = }\left(\frac{1}{1.61}\text{ mi}\right)\left(19.825\right)\\ =12.31\text{mi}\end{array}$

Conclusion:

Therefore, the height of the supersonic transport flight is $19.825\text{ km}$ or $12.31\text{mi}$.

(e)

To determine

The height of the communications satellite in $\text{km}$.

Answer to Problem 2E

The height of the communications satellite is $\text{644 km}$.

Explanation of Solution

Given info: The height of the communications satellite is $400\text{mi}$.

Explanation:

The height of the communications satellite is $400\text{mi}$.

Convert the height from $\text{mi}$ into $\text{km}$.

$\text{1 mi }=\text{1}\text{.61 km}$

Use unitary method to find the height of the communications satellite in $\text{km}$.

Therefore, the height of the communications satellite in $\text{km}$ is as follows,

$\begin{array}{c}400\text{mi =}\left(\text{1}\text{.61 km}\right)\left(400\right)\\ =\text{644 km}\end{array}$

Conclusion:

Therefore, the height of the communications satellite is $\text{644 km}$.

(f)

To determine

The height of the E and F ion layers in $\text{mi}$.

Answer to Problem 2E

The height of the E layer is $62.1\text{ mi}$. The height of the F layer is $217.4\text{ mi}$.

Explanation of Solution

Given info: The height of the E layer is $\text{100 km}$. The height of the F layer is $\text{350 km}$.

Explanation:

The height of the E layer is $\text{100 km}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the E layer in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the E layer is as follows,

$\begin{array}{c}\text{100 km = }\left(\frac{\text{1}}{1.61}\text{ mi}\right)\left(100\right)\\ =62.1\text{ mi}\end{array}$

The height of the F layer is $\text{350 km}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the F layer in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the F layer is as follows,

$\begin{array}{c}\text{350 km = }\left(\frac{\text{1}}{1.61}\text{ mi}\right)\left(350\right)\\ =217.4\text{ mi}\end{array}$

Conclusion:

Therefore, the height of the E layer is $62.1\text{ mi}$. The height of the F layer is $217.4\text{ mi}$.

(g)

To determine

The height of the aurora displays in $\text{mi}$.

Answer to Problem 2E

The height of the E layer is $62.1\text{ mi}$. The height of the F layer is $217.4\text{ mi}$.

Explanation of Solution

Given info: The height of the aurora displays is $\text{500 km}$.

Explanation:

The height of the aurora displays is $\text{500 km}$.

Convert the height from $\text{km}$ into $\text{mi}$.

$\text{1}\text{.61 km = 1 mi}$

Use unitary method to find the height of the aurora displays in $\text{mi}$.

$\text{1 km = }\frac{\text{1}}{1.61}\text{ mi}$

Therefore, the height of the aurora displays is as follows,

$\begin{array}{c}\text{500 km = }\left(\frac{\text{1}}{1.61}\text{ mi}\right)\left(500\right)\\ =310.6\text{ mi}\end{array}$

Conclusion:

Therefore, the height of the aurora displays is $310.6\text{ mi}$.

(h)

To determine

The height of the syncom satellite in $\text{km}$.

Answer to Problem 2E

The height of the syncom satellite is $37030\text{ km}$.

Explanation of Solution

Given info: The height of the syncom satellite is $23000\text{mi}$.

Explanation:

The height of the syncom satellite is $23000\text{mi}$.

Convert the height from $\text{mi}$ into $\text{km}$.

$\text{1 mi }=\text{1}\text{.61 km}$

Use unitary method to find the height of the syncom satellite in $\text{km}$.

Therefore, the height of the syncom satellite in $\text{km}$ is as follows,

$\begin{array}{c}23000\text{mi =}\left(\text{1}\text{.61 km}\right)\left(23000\right)\\ =37030\text{ km}\end{array}$

Conclusion:

Therefore, the height of the syncom satellite is $37030\text{ km}$.

To determine

The comparison of different heights provided in the problem.

Answer to Problem 2E

In ascending order the heights can be arranged as follows,

pikes peak, the top of the Mt. Everest, the commercial airline flight, the supersonic transport flight, E layer, F layer, Aurora, communications satellite and syncom satellite.

Explanation of Solution

Given info: The heights of the pikes peak, Mt. Everest, commercial airline flight, supersonic transport flight, communications satellite, E layer, F layer, aurora displays and

syncom satellite are provided.

Explanation:

The height of the pikes peak is $4.27\text{ km}$ or $2.65\text{mi}$. The height of the top of the Mt. Everest is $8.845\text{ km}$ or $5.49\text{mi}$. The height of the commercial airline flight is $10.675\text{ km}$ or $6.63\text{mi}$. The height of the supersonic transport flight is $19.825\text{ km}$ or $12.31\text{mi}$.

The height of the communications satellite is $\text{644 km}$. The height of the E layer is $62.1\text{ mi}$. The height of the F layer is $217.4\text{ mi}$. The height of the aurora displays is $310.6\text{ mi}$. The height of the syncom satellite is $37030\text{ km}$.

Conclusion:

Therefore, in ascending order the heights can be arranged as follows,

pikes peak, the top of the Mt. Everest, the commercial airline flight, the supersonic transport flight, E layer, F layer, Aurora, communications satellite and syncom satellite.