Chapter 12.4, Problem 22E

a.

To determine

To find value of h and v

Answer to Problem 22E

The h in feet is 129.75 and v in feet is 75.

Explanation of Solution

Given:

Angle of inclination of escalator $=30°$

The slope distance $=150$ feet.

Calculation:

As per the given problem,

We can apply principle of trigonometry,

We know that $\text{sin}\theta \text{=}\frac{perpendicular}{hypotenuse}\text{ cos}\theta \text{=}\frac{base}{hypotenuse}\text{}\text{ tan}\theta \text{=}\frac{perpendicular}{base}$

Or $\text{ cos30}°\text{=}\frac{\text{h}}{150}\text{}\text{ [where hypotenuse=150ft and }\theta \text{=30}°\text{]}$

h $=\frac{\sqrt{3}}{2}=\frac{\text{h}}{150}\text{ [cos30=}\frac{\sqrt{3}}{2}]$

  $\begin{array}{l}\text{h}=\frac{\sqrt{3}}{2}\times 150\\ \text{h=129}\text{.75}\text{feet}\end{array}$

Now the vertical distance ,

  $\begin{array}{l}\sin 30°=\frac{\text{v}}{150}\\ \frac{1}{2}=\frac{\text{v}}{150}\text{ [sin30=}\frac{1}{2}]\\ \text{v=}\frac{150}{2}\\ \text{v=75}\text{feet}\end{array}$

Conclusion:

The horizontal distance h is 129.75feet and vertical distance v is 75 feet

b.

To determine

The translation from top to bottom of escalator in feet

Answer to Problem 22E

The distance is 150feet

Explanation of Solution

Given:

  $\begin{array}{l}\text{vertical distance=75 feet}\\ \text{horizontal distance= 129}\text{.75 feet}\\ \text{slope distance=150 feet}\end{array}$

Calculation:

The translation distance from top to bottom of the escalator is 150 feet./

Since for translation,only the slope distance is considered,

Therefore

Translation in feet is 150.

Conclusion:

The translation from top to bottom of escalator is 150 feet