A bridge with a parabolic shape has an opening 122 feet wide at the base of the bridge (where the bridge meets the water), and the height in the center of the bridge is 34 feet. A sailboat whose mast reaches 25 feet above the water is traveling under the bridge 15 feet from the center of the bridge. Will it clear the bridge without scraping its mast? Justify your answer.
A) Yes. The opening height is 25 feet, and the mast is 31.9 feet.
B) No. The opening height is 25 feet, and the mast is 31.9 feet.
C) Yes. The opening height is 31.9 feet, and the mast is 25 feet.
D) Yes. The opening height is 27 feet, and the mast is 25 feet.

Question

Quizplus · Accepted Answer

The bridge's shape can be described by a parabolic equation, and given the dimensions, we can determine the height at any point along the width. At 15 feet from the center, the height clearance is calculated to be more than the mast height of 25 feet, thus allowing the sailboat to pass without scraping.

A Bridge with a Parabolic Shape Has an Opening 122