Launches often happen near the equator in order to take advantage of Earth's rotation speed. This is why more launches are towards the East than towards the West.

How can one calculate the speed of rotation of a point on the Earth's surface about the Earth's axis, given only a latitude?

While the simplest approach might be to assume the Earth is a sphere and it rotates once per day, it's rotation isn't exactly 24 hours, and the Earth is definitely not exactly a sphere!