Two-Dimensional Kinematics

In two dimensions, the position can no longer be wholly described by a scalar.

Instead, we use a vector to describe the position of an object in two dimensions.

Where and are the unit vectors in the x and y directions respectively.

Therefore, the velocity and acceleration can be derived from the position vector:

Where and are the x and y components of the velocity, and and are the and components of the acceleration.

Projectile Motion

Projectile motion is the motion of an object that is thrown or projected into the air.

The graph above shows the trajectory of a projectile in two dimensions. Two paths are shown: the predicted parabolic path and the actual path.

Factors affecting the actual orbit include:

Air resistance, where , where is the drag coefficient, is the velocity, and is the unit vector in the direction of the velocity.
The Coriolis effect, where the Earth's rotation causes the path of the projectile to curve.
The Magnus effect, where the spin of the projectile causes it to curve.

Usually in projectile motion, we ignore every factor except for gravity.