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Answer :
Final answer:
The linear velocity of a point near the Earth's equator is 0.4704 km/s.
Explanation:
The linear velocity of a point near the equator can be calculated using the formula: v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the Earth.
Given that the radius of the Earth is 4000 miles, we first need to convert it to meters. 1 mile is equal to 1609.34 meters. Therefore, the radius of the Earth in meters would be 4000 miles * 1609.34 meters/mile = 6437.36 km.
The angular velocity can be calculated using the formula: ω = 2π/T, where T is the period of rotation of the Earth. The Earth completes one full rotation in 24 hours, so the period is 24 hours or 86400 seconds.
Now we can calculate the angular velocity: ω = 2π/86400 seconds = 0.0000727 rad/s.
Using the formula v = ωr, the linear velocity at a point near the equator is v = 0.0000727 rad/s * 6437.36 km = 0.4704 km/s.
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