He 40th parallel of north latitude runs across the United States through Philadelphia, Indianapolis, and Denver. At this latitude, Earth's radius is about 3030 miles. The earth rotates with an angular velocity of _π_ radians (or 15°) per 12 hour toward the east. If a jet flies due west with the same angular velocity relative to the ground at the equinox, the Sun as viewed from the jet will stop in the sky. How fast in miles per hour would the jet have to travel west at the 40th parallel for this to happen?

Question

Mathematics

Aleah Frederick

2 August, 23:20

He 40th parallel of north latitude runs across the United States through Philadelphia, Indianapolis, and Denver. At this latitude, Earth's radius is about 3030 miles. The earth rotates with an angular velocity of _π_ radians (or 15°) per 12 hour toward the east. If a jet flies due west with the same angular velocity relative to the ground at the equinox, the Sun as viewed from the jet will stop in the sky. How fast in miles per hour would the jet have to travel west at the 40th parallel for this to happen?

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Answers (1)

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Declan Olsen · Answer 1

Answer: Velocity = 153.4 rad/s

Step-by-step explanation: given that

Radius of the earth = 3030

Rotational radius = Rcos15

Rotational radius = 2926.76

The circumference = 2πR

Circumference = 2 * 22/7 * 2926.8

Circumference = 18389.3

the Earth completes one revolution in 24 hr

Let us divide the circumference by 12 hr to get the rotational velocity

Velocity = 18389.3/12

Velocity = 1532.4 rad/s