1)the gateway arch, which can be closely approximated by a parabola, is 630 feet high and 630 feet across at the base. The Gateway arch is the tallest man-made monument found in the United States in St. Louis Missouri. The maintenance crew is doing some work on the arch. The work will be done on the right side of the arch. In order to bring the equipment up the maintenance crew has constructed a temporary ramp from the ground on left side of the arch to the level where the work will be done on the right side. The ramp has a constant rate of rise of 1:5, which means 1 ft. up for every 5 ft. forward.
On the figure below, make a rough sketch of what you think the arch with the ramp would look like.
If the vertex of the parabola is at (0,630), then the arch is modeled by
y = (630/315^2)(315^2-x^2)
= 630 - 2/315 x^2
If the work is being done at a position c ft to the right of the vertex, it will be at the point (c,y(c)), on a line with slope 1/5.
Unfortunately, this makes for some very long ramps. If they're working at a point at height 376 ft (x=200), the ramp has to start out 1365 ft to the left of the arch. That's about 1/4 mile away!
I apologize, but as a text-based AI bot, I am unable to create visual sketches or images. However, I can provide you with a step-by-step description of the arch with the ramp.
1. Begin by sketching a horizontal line to represent the ground level.
2. Draw a vertical line from the center of the ground line to represent the height of the arch. This line should be 630 feet long.
3. At the top of the vertical line, draw a semi-circular shape to represent the arch. The diameter of this semi-circle should be 630 feet.
4. On the left side of the arch, draw a line that starts from the bottom left corner and gradually slopes upwards to the same level as the top of the arch. This line represents the temporary ramp.
5. Finally, label the ground level, the height and width of the arch, and any other relevant details or measurements.
Please note that this is a rough sketch and may not be to scale. It's recommended to consult an accurate diagram or image for a more precise representation of the Gateway arch with the ramp.
As an AI text-based bot, I'm unable to create visual sketches. However, I can help guide you through the process of visualizing the arch with the ramp.
To create a rough sketch, follow these steps:
1) Draw a horizontal line to represent the ground level.
2) Draw a vertical line from the center of the base line to represent the height of the arch (630 ft).
3) On the left side of the vertical line (base), draw a diagonal line moving upward to represent the ramp.
4) The diagonal line should have a slope of 1:5, meaning it rises 1 ft for every 5 ft of forward movement.
5) The diagonal line should intersect the vertical line (the height of the arch) at a point 1/5th of the way from the base to the top (126 ft up).
Remember, this sketch is a rough approximation. The Gateway Arch is more complex and has a more intricate shape, but this should give you a basic visual representation of the arch with the temporary ramp on the right side.