Despite being associated with Coriolis, the phenomenon that actually affect the vertical component of the trajectory is called Eötvös Effect. The rotation of the Earth generates a centrifugal force, the same that pushes you to the side when you make a sharp turn with your car. This force act perpendicular to the Earth rotatory axis, adding or subtracting to the gravity force. When an object flies eastward, in the same direction of Earth's rotation, centrifugal force acts opposite of gravity, pushing it away from the Earth's surface. If the object flies westward, in the opposite direction of the Earth rotation, centrifugal force pushes the object toward the ground concurrently to gravity force. Thus, bullets fired to the east always fly a little higher, and, conversely, bullets fired to the west always travel somewhat low.
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