The velocity of New York in space (due to rotation)

[Kanimoto]

QUESTION IS:

The latitude of New York City is 40° 45'. Find the velocity of New York in space due to the rotation of the earth on its axis. For this problem, use 4000 miles for the earth's radius.

I know this problem can be solved with a triangle inscribed in a circle, but I have no idea where to start, so if someone could help then thank you.

 

[stapel]

My guess: Draw a circle to represent a "side view" of the Earth. The point marking "New York" will be somewhere between "one o'clock" and "two o'clock".

Draw the horizontal radius line from the center to the Equator, on the side with New York's dot.

Draw a radius line to New York's dot. Note that the latitude gives the angle between the two radius lines.

Draw the vertical line from the center to the North Pole. Use the previous step to find the angle thus formed.

Draw the horizontal line from New York's dot back to the vertical line. You now have a right triangle with one known side length (the radius line) and one known angle (the one you just found).

Use trig to find the length of the base (the horizontal line) of the triangle. Note that this forms the radius of the rotational arc that New York describes over the course of one day (that is, one rotation).

Find the circumference of this circle, in miles. Note that this radial length is covered in twenty-four hours.

Divide to find the miles-per-hour.

Eliz.

 

[Kanimoto]

That helps a lot! Thanks.