Chapter 4.3, Problem 77E

a.

To determine

To find: the vertical rise of the inclined plane.

Answer to Problem 77E

  $\text{Vertical}\text{Rise}\text{of}\text{the}\text{inclined}\text{Plane}\approx$ 519.3 ft.

Explanation of Solution

Given information: The J inclined plane in P is one of the longest and steepest hoists in

world. The railway cars travel a distance of 896.5 feet at an angle of approximately ${35.4}^{\circ }$ rising to a height of 1693.5 feet above sea level.

Formula used:

  $\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}$.

Calculation:

  $\begin{array}{c}\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}.\\ \theta ={35.4}^{\circ }.\\ \sin ({35.4}^{\circ })=\frac{\text{Vertical}\text{Rise}\text{of}\text{the}\text{inclined}\text{Plane}}{896.5\text{ft}}.\\ \text{Vertical}\text{Rise}\text{of}\text{the}\text{inclined}\text{Plane}=896.5\times \sin ({35.4}^{\circ }).\\ \text{Vertical}\text{Rise}\text{of}\text{the}\text{inclined}\text{Plane}\approx 519.3\text{ft}\text{.}\end{array}$

b.

To determine

To find: the elevation of the lower end of the inclined plane.

Answer to Problem 77E

Elevation of the lower end is 1174.2 ft.

Explanation of Solution

Given information: The J inclined plane in P is one of the longest and steepest hoists in

world. The railway cars travel a distance of 896.5 feet at an angle of approximately ${35.4}^{\circ }$ rising to a height of 1693.5 feet above sea level.

Calculation:

Elevation of the Upper End is 1693.5 ft.

From part (a) $\text{Vertical}\text{Rise}\text{of}\text{the}\text{inclined}\text{Plane}$ is 519.3 ft.

Therefore the elevation of the lower end is 1693.5-519.3=1174.2 ft.

c.

To determine

To find: the rate at which they rise vertically when the cars move up the mountain at a rate of 300 feet per minute.

Answer to Problem 77E

  $\text{Rate}\text{of}\text{vertical}\text{rise}\approx 173.78\text{ft/min}\text{.}$

Explanation of Solution

Given information: The J inclined plane in P is one of the longest and steepest hoists in

world. The railway cars travel a distance of 896.5 feet at an angle of approximately ${35.4}^{\circ }$ rising to a height of 1693.5 feet above sea level.

Calculation:Formula used:$\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}$.

Calculation:

  $\begin{array}{c}\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}.\\ \theta ={35.4}^{\circ }.\\ \sin ({35.4}^{\circ })=\frac{\text{Rate}\text{of}\text{vertical}\text{rise}}{300\text{ft/min}}.\\ \text{Rate}\text{of}\text{vertical}\text{rise}=300\times \sin ({35.4}^{\circ }).\\ \text{Rate}\text{of}\text{vertical}\text{rise}\approx 173.78\text{ft/min}\text{.}\end{array}$