Sept 4 th Vectors in two dimensions

Vectors in 2 dimensions There are two common ways to express the direction of a vector. 10° E of N = N 10° E Sometimes you will also see vectors expressed as ‘bearing’ or ‘heading’. In this case North is 0° and the bearing increases in a clockwise direction. N 10° E = 10°

Adding Vectors The sum of two vectors is called the resultant. There are three ways to add two-dimensional vectors. Method #1: Graphically Using graph paper and a ruler, carefully draw the vectors in tip-to-tail position. Draw the resultant vector going from the tail of the first vector to the tip of the 2 nd vector Measure it carefully. Don’t forget to measure the angle.

Ex 3: Archie walks 4.2m [S38°W] and then walks 1.7m [N 25°E]. Use the Cosine and Sine laws to find his total displacement.

Method #3 - Components Two perpendicular vectors can be added using a combination of Pythagorean theorem and the tangent function. Ex: Joe walks 12.0m [S] and 5.0m[E]. Find his total displacement.

Since any two perpendicular vectors can be added using the Pythagorean theorem… Then any vector can be expressed as a sum of two perpendicular vectors

To add any two vectors, we can first break them down into their perpendicular component vectors. The components are easier to add. Instead of adding and directly, we express them as components and add the components. We can add the x-components and y- components separately, to get the components of the resultant.

Ex 2: Archie walks 4.2m [S38°W]. What are the x-and y-components of his displacement?

Archie then walks 1.7m [N 25°E]. Find his total displacement.