Precalculus

Can someone check my answers please? Thank you :)

30. What is Earth's rotational speed at (a) Bangor, Maine (latitude 45 degrees N) and (b) Rio de Janeiro, Brazil (latitude 23 degrees S)? (It's given in the problem also that Earth's rotational speed at the equator is about 1,038 mph and Earth's radius is 3,963 miles.)

(a) 734 mph
(b) 899 mph

Are these answers correct?

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1. I would call the speeds tangential speed, since it is a speed measured along the tangent. A rotational speed is measured in radians/second, or degrees per minute, etc.

Assuming the earth is a perfect sphere, the tangential speed at latitude θ (north or south) is given by multiplying the speed at the equator (1038 mph) by the cosine of the latitude.
(a) 1038*cos(45)=734 mph
(b) 1038*cos(23)=952 mph.
Your answer of 899 was probably due to an error of the angle and corresponds to a latitude of 30 degrees south.

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