**Forces in Two Dimensions**

Forces are vectors and can be added and subtracted like any other vector.

Force vectors can be resolved into two perpendicular components in the x and y directions.

The two force components are given by the following equations:

**Example 1:**

A force of 25N acts on an object at an angle of 30° above the horizontal. Calculate the horizontal and vertical components of this force:

Firstly, draw a diagram to represent the force and its components:

**Example 2:**

A force of 15N north and a force of 9N east act on an object. Calculate the resultant force acting on the object:

Firstly, draw a diagram to represent the forces:

To determine the resultant force:

Then we solve the angle,

Therefore, the resultant force is 17.49N at an angle of 59.04° in the east direction above the horizontal.