During ordinary projectile motion with negligible air resistance, why is momentum conserved in the horizontal direction but not in the vertical direction, unless Earth is included in the system?

1. Momentum along a given direction is conserved only when the net external force along that same direction is zero. 2. For a projectile with negligible air resistance, no horizontal force acts, so horizontal momentum stays unchanged. 3. Gravity provides a constant nonzero vertical force, so the projectile's own vertical momentum keeps changing throughout the flight. 4. Including Earth in the system accounts for the equal and opposite vertical force on Earth, restoring overall conservation for the combined system. 5. This shows momentum can be conserved along one axis while not being conserved along another, rather than being an all-or-nothing property of the whole motion. _Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.3 Conservation of Momentum_