The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. (a) Assuming the earth is a sphere with a radius of 6.38 106 m, determine the speed of a person situated at the equator.
My physics optional extra work: This would be helpful so I can compare the solutions here as I do the work by myself.
To determine the speed of a person situated at the equator, we need to calculate the linear velocity associated with the Earth's rotation.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius of the Earth is given as 6.38 * 10^6 m.
Therefore, the circumference of the Earth at the equator is:
C = 2π(6.38 * 10^6 m) = 40.07 * 10^6 m
The Earth completes one rotation in 24 hours, which is equivalent to 24 * 60 * 60 = 86,400 seconds.
Now, to calculate the speed of a person at the equator, we divide the circumference of the Earth by the time taken for one rotation:
Speed = Circumference / Time = 40.07 * 10^6 m / 86,400 s ≈ 463.04 m/s
Therefore, the speed of a person situated at the equator is approximately 463.04 m/s.
Please note that this calculation assumes a perfectly spherical Earth and uniform rotation, and it neglects factors such as the Earth's elliptical shape and variations in rotation speed at different latitudes.