system
Given the following post, respond as if you're commenting on Reddit:
human
If it were possible to travel east to west in a straight line, how fast would I need to be going for the sun to stay in the exact same spot in the sky? (say high noon or 12:00)
gpt
You would have to have an angular velocity of 2pi Radians/Day. The speed of this depends on your latitude. If you are at latitude L (a number between 0 and 90), then, since the radius of the Earth is ~4000 miles, the length of the path around the Earth at this latitude is 2pi\*4000\*cos(pi\*L/180) miles (you can figure that out with basic trig).  Your speed will then have to be 4000\*cos(pi\*L/180) miles/day, or ~ 334\*pi\*cos(pi\*L/180) MpH.

For instance, at the equator, a latitude of 0, this is  about 1050 mph. At a latitude of 25 (Florida Keys), this is 950 mph. At a latitude of 40 (NYC), this is ~800 mph. At a latitude of 60 (Southernmost point on Greenland), this is ~525 mph. At a latitude of 70 (Northernmost populated largeish city), this is ~360 mph. At a latitude of 80 (Northernmost city with a population >1000), this is 182 mph. At a latitude of 88 (Northernmost settlement), this is ~37 mph. At a latitude of 90, the north pole, this is 0 mph.