High School

What is the approximate linear velocity of a particle on the equator of the Earth, assuming the radius of the Earth is 4000 miles?

A. 1000 miles per hour
B. 2000 miles per hour
C. 3000 miles per hour
D. 4000 miles per hour

Answer :

Final answer:

The approximate linear velocity of a particle on the equator of the Earth is approximately 523.6 miles per hour.

Explanation:

The approximate linear velocity of a particle on the equator of the Earth can be calculated using the formula v = rω. Here, r represents the radius of the Earth and ω represents the angular velocity. The angular velocity of the Earth can be calculated using the formula ω = 2π/T, where T represents the period of rotation of the Earth. Since the period of rotation of the Earth is approximately 24 hours, the angular velocity would be approximately 2π/24 radians per hour. Substituting these values into the formula, we get v = (4000 miles) × (2π/24 radians per hour) = 523.6 miles per hour. Therefore, the approximate linear velocity of a particle on the equator of the Earth is approximately 523.6 miles per hour.

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