Summary - Perpendicular Forces

A force does not produce any effect on the motion of an object in a perpendicular direction. The most important application of this principle is that the horizontal motion of a projectile has zero acceleration, while the vertical motion has an acceleration equal to g. That is, an object's horizontal and vertical motions are independent. The arc of a projectile is a parabola.

Motion in three dimensions is measured using three coordinates, x, y, and z. Each of these coordinates has its own corresponding velocity and acceleration. We say that the velocity and acceleration both have x, y, and z components.

Newton's second law is readily extended to three dimensions by rewriting it as three equations predicting the three components of the acceleration,

a_x = F_x,total/m ,
a_y = F_y,total/m ,
a_z = F_z,total/m ,

and likewise for the first and third laws.