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.

(b) What is the speed of a person situated at a latitude of 29.0° north of 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.