My vertical may not be yours

Graphic - localvertical

By ‘vertical’ we mean the line singled out by a pendulum at rest, or a ‘plumb-line, or a freely falling object. This is the direction of the gravitational force due to the earth. This force is always towards the earth’s centre. But this means something different at different points on the earth’s surface. A’s ‘vertical’ is not the same as B’s.

The implication is that we can expect to get away with using the ‘constant acceleration’ equations to describe motion near the surface of the earth only if the motion we describe is confined to a very small region of the earth’s surface. For motion on a larger scale we need to allow for the variation of the direction and possibly the magnitude of the force as the object moves.