12.2 Projectile motion
A projectile is any object that is thrown or launched. As with 1D kinematics problems, we’re not concerned with what caused the object to be launched, or how it was launched in the first place. All we care about is what happens after it has been launched. At that point, the only force acting on the object is gravity, when air resistance can be neglected.
Now, consider two identical projectiles: one dropped from rest and the other thrown horizontally from the same height, at the same time.
Newton’s first law (section 9.2) tells us that an object’s velocity only changes if there is some force applied to it. For both of the objects, the only force exerted is gravity, which only acts in the vertical direction. Therefore, only the vertical component of a projectile’s velocity changes. The acceleration in the vertical direction is g. There is zero acceleration in the horizontal direction. (Of course, these statements are only true as long as air resistance can be neglected.)
Returning to our two objects, we note that the vertical component of each object’s velocity is zero, the rate of change of each object’s velocity is the same, and they fall the same vertical distance—in the vertical direction everything is identical!
The vertical and horizontal components of motion are independent from one another. Solving two-dimensional problems is the same as solving one-dimensional problems, except that there is more information to work with. This is where proper organization becomes very important for helping you solve the problem efficiently.