The Johnstown inclined plane in johnstown, pennsylvania, is a cable car that transports people up and down the side of a hill. during the cable car's climb, you move about 17 feet upward for every 25 feet you move forward. at the top of the incline, the horizontal distance from where you started is about 500 feet.
another cable car incline in pennsylvania, the monongahela incline, climbs at a slope of about 0.7 for a horizontal distance of about 517 feet. compare this climb to that of the johnstown inclined plane. which is steeper? JUSTIFY your answer.
Please help?
The slope of the first hill is 17/25.
The slope of the 2nd hill is 0.7.
Which slope is greater? This is the slope of the steeper hill.
To compare the steepness of the Johnstown inclined plane and the Monongahela incline, we can calculate the slopes of both cable cars.
The slope of a line is determined by the ratio of the vertical change (rise) to the horizontal change (run). In this case, the vertical change is the change in height (upward distance) and the horizontal change is the horizontal distance travelled.
For the Johnstown inclined plane:
Vertical change (rise) = 17 feet
Horizontal change (run) = 25 feet
Slope = rise / run = 17/25
For the Monongahela incline:
Vertical change (rise) = 0.7
Horizontal change (run) = 517 feet
Slope = rise / run = 0.7/517
To compare the slopes, we need to determine which slope is greater.
Let's calculate the slopes:
Slope of Johnstown Inclined Plane = 17/25 = 0.68
Slope of Monongahela Incline = 0.7/517 = 0.001354
The slope of the Johnstown inclined plane is approximately 0.68, while the slope of the Monongahela incline is approximately 0.001354.
Since the slope of the Johnstown inclined plane is significantly larger than that of the Monongahela incline, we can conclude that the Johnstown inclined plane is steeper.
Justification:
The slope of a line represents the "steepness" of the line. In this case, the slope is the ratio of the vertical change to the horizontal change. A higher slope value indicates a steeper incline. Therefore, because the slope of the Johnstown inclined plane is greater than the slope of the Monongahela incline, we can conclude that the Johnstown inclined plane is steeper.
To compare the steepness of the two inclines, we need to calculate the slope of each incline and compare the values.
Let's start by calculating the slope of the Johnstown Inclined Plane.
Slope is equal to the vertical change divided by the horizontal change. In this case, we know that for every 17 feet upward, we move 25 feet forward.
Vertical change = 17 feet
Horizontal change = 25 feet
Slope = vertical change / horizontal change
Slope = 17 / 25
Slope ≈ 0.68
Now, let's calculate the slope of the Monongahela Incline.
Here, we are given that the slope is approximately 0.7 for a horizontal distance of 517 feet.
Slope = 0.7
Horizontal change = 517 feet
To find the vertical change, we can multiply the slope by the horizontal change:
Vertical change = Slope * Horizontal change
Vertical change = 0.7 * 517
Vertical change ≈ 361.9 feet
Therefore, the Monongahela Incline has a vertical change of approximately 361.9 feet for a horizontal distance of 517 feet.
Now, we can compare the slopes of the two inclines.
The slope of the Johnstown Inclined Plane is approximately 0.68, while the slope of the Monongahela Incline is approximately 0.7.
Since the slope of the Monongahela Incline (0.7) is greater than the slope of the Johnstown Inclined Plane (0.68), we can conclude that the Monongahela Incline is steeper.
In summary, the Monongahela Incline is steeper than the Johnstown Inclined Plane based on the comparison of their slopes.