Question

1. a country road passes through a parabolic arch used to support a train bridge. the arch is 10 m wide at the base and the maximum height of the arch is 4 m. can a tractor pulling a trailer loaded with hay bales safely pass through the center of the arch if the trailer is 2.5 m wide and height of the hay bales is 3.5 m above the ground? (4 marks)

Explanation:

Model the parabolic arch

Using the Parabolic Arch Modeling knowledge point

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Determine the clearance width boundary

Using the Parabolic Arch Modeling knowledge point

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Calculate the arch height at the trailer edge

Using the Parabolic Arch Modeling knowledge point

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Compare heights for safe passage

Using the Parabolic Arch Modeling knowledge point

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Answer:

Yes, the tractor pulling the trailer loaded with hay bales can safely pass through the center of the arch. At the outer edge of the trailer (\(1.25\text{ m}\) from the center), the height of the parabolic arch is \(3.75\text{ m}\), which provides a clearance of \(0.25\text{ m}\) above the \(3.5\text{ m}\) tall load.