when a long-range cannonball is fired towards the equator from a northern (or southern) latitude, it lands west of its "intended" longitude. Why?

Answer 1

its east-west velocity is less than the velocity of points on the equator.

its angular velocity is the same at any latitude, but the higher the latitude, the less its linear speed, because the radius of its circle is less.

in 2-D, consider a ball on a rotating platform. If pushed toward the rim, its path will curve, rather than heading straight out along a radius.