The Earth rotates about its axis once every 23 hours, 56 minutes, and 4 seconds, and the radius of the Earth is 3960 miles. Find the linear speed of a point on the equator in miles per hour (mi/h).
Answer (3)
The linear speed of a point on the Earth's surface can be found using the formula for the circumference of a circle (2πr), and the time it takes the Earth to rotate once on its axis (23 h 56 min 4 s). The speed is the circumference divided by the period of rotation. ;
23 h 56 min 4 s = ( 23 + 60 56 + 3600 4 ) h = ( 3600 82800 + 3600 3360 + 3600 4 ) h = 3600 86164 h ≈ 23.93 h L = 2 π R ; R = 3960 mi → L = 2 π ⋅ 3960 mi = 7920 πmi ≈ 7920 ⋅ 3.14 mi = 24868.8 mi v = 23.93 24868.8 mi / h ≈ 1039.231 mi / h ← an s w er
The linear speed of a point on the equator of the Earth is approximately 1039.23 miles per hour. This is calculated using the distance traveled in one rotation and the time taken for that rotation. The distance is derived from the circumference of the Earth, which is approximately 24868.8 miles.
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