Question

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.

Answer 1

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!