BRIDGE CONSTRUCTION Your team is working for the transport authorities of a certain city. You have to
analyze two construction projects for a new bridge over the river in said city. The
spacing between the bridge supports needs to be 1050 feet and the height at the center of the arch
350 cakes. One company has suggested that the structure be in the shape of a parabola; other
company suggests a semi-ellipse. The engineering team will determine the relative resistances of
the two projects; your job is to find if there is any difference in the widths of the
channel.
An empty oil tanker needs a clearance of 280 feet to pass under the bridge.
You must find the width of the channel in each of the proposals.
1. To determine the equation of a parabola with these characteristics, first place the
parabola on coordinate axes in a convenient position and draw it.
2. What is the equation of the parabola? (If you use decimal point in the equation, approximate to
six decimal places. If you use fractions, your answer will be more exact.)
3. If the shape of the satellite dish supports, how wide will the channel it will pass through
the oil tanker?
4. To determine the equation of a semi-ellipse with these characteristics, place the
semi-ellipse on coordinate axes in a convenient position and draw it.
5. What is the equation of the ellipse? How wide will the canal need to be for the
Petroleum ship?
6. Now that you know which of the two alternatives provides the widest channel, consider other
factors. His department is also in charge of verifying the depth of the channel, the
amount of river traffic and other details. For example, if there was a flood in the river and
the water level will rise 10 feet, how would free space be affected? Take a decision
about which project you think would be best as far as your department is concerned and
explain your decision.