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How do Newton’s laws apply to projectile motion?

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Title page of Isaac Newton's Philosophiae Naturalis Principia Mathematica, 1687, featuring large Latin text and publication details in a bordered layout. — Newton’s laws of motion The title page of Isaac Newton's *Philosophiae Naturalis Principia Mathematica* (1687; *Mathematical Principles of Natural Philosophy*), the work in which the physicist introduced his three laws of motion.

Newton’s laws of motion provide the theoretical foundation for understanding projectile motion by treating the horizontal and vertical components of the motion as independent processes.12

Horizontal Motion: According to Newton’s first law (the law of inertia), an object in motion remains in motion at a constant velocity unless acted upon by an external force. In the absence of air resistance, there are no horizontal forces acting on a projectile, so it maintains a constant horizontal speed throughout its flight.12
Vertical Motion: Newton’s second law explains that the force of gravity acting on the projectile causes a constant downward acceleration. This results in the vertical motion of a freely falling body.13

By combining these independent motions—constant horizontal velocity and uniform vertical acceleration—the resulting trajectory of a projectile is mathematically described as a parabola. While these principles are essential for understanding the underlying physics, actual trajectories often deviate due to air resistance, which acts as an additional force that must be considered for precise predictions.1