Concept explainers
a.
Find the vertical rise of the inclined plane.
a.

Answer to Problem 73E
Explanation of Solution
Given information:
The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The r
Find the vertical rise of the inclined plane.
Calculation:
The figure of the Johnstown inclined Plane in Pennsylvania is given below. It is one of the longest and the steepest hoist in the world. The railway cars travel a distance of
We have to find the vertical rise of the inclined plane.
Let
Now, from the above figure we can see that the length of the hypotenuse is
The side opposite to the angle
Now , we know that the trigonometric function which involves these two sides, that is the hypotenuse and the opposite to the angle is the sine function given by.
Substituting the values in the above gven formula of sin, we have,
Or
Hence, the vertical rise of the plane is
b.
Find the elevation of the lower end of the inclined plane.
b.

Answer to Problem 73E
Explanation of Solution
Given information:
The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The r
Find the elevation of the lower end of the inclined plane.
Calculation:
The total height of the plane above the sea level is
From part a we see that the height of the plane is
Hence, the elevation of the lower end of the inclined plane is
c.
Find the rate at which they rise vertically.
c.

Answer to Problem 73E
Explanation of Solution
Given information:
The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The r
The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically.
Calculation:
The cars move up the mountain at a rate
Hence, the rate at which cars rise vertically is given by the following equation,
Or
Hence, the rate at which cars rise vertically is
Chapter 4 Solutions
EBK PRECALCULUS W/LIMITS
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