A new bridge is to be constructed over the East River in New York City. Two...

A new bridge is to be constructed over the East River in New York City. Two structural possibilities exist: the support could be in the shape of a parabola or the support could be in the shape of a semi-ellipse.

The space between the supports needs to be 1050 feet.

The height at the center of the arch needs to be 350 feet. Determine the equation of a parabola with these characteristics. (Hint: Place the vertex of the parabola at the origin to simplify calculations).

Part 1

a. What is your equation for the parabola? An empty tanker, 520 feet wide and 260 feet high needs to pass beneath the bridge.

b. Can the tanker pass under this bridge? Justify your answer. Determine the equation of a semi-ellipse with the same characteristics. (Hint: Place the center of the semi-ellipse at the origin to simplify calculations)

Part 2

a. What is the equation for the semi-ellipse? Show the work required to determine the equation.

b. Will the tanker (520 feet wide and 260 feet high) be able to pass under this bridge? Justify your answer.

Part 3

a. If the river were to flood and rise 10 feet, how would the channel widths and the clearances of the two bridges be affected? Explain, using numbers, how the width of the channel would be affected for each bridge.

b. With all things considered, which bridge design would you choose? Explain your reasoning.

Solutions

Expert Solution

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Ally Wells answered 2 months ago

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