1. Unit 3-1: 2-Dimensional Vectors

2. A vector is any quantity that has both magnitude and direction. A 2-Dimensional vector is drawn at some angle with the length of the arrow drawn to scale. Vectors are now designated as being however magnitude at whatever angle.

3. Each 2-Dimensional vector can be broken into its components. –Components are entirely in the x or y dimension. –The reason for the components is because motion in the y dimension is independent of motion in the x dimension. –In other words, if something is moving to the right and then is dropped so that it falls, it will continue moving at the same exact velocity to the right while it is accelerating towards the ground.

4. We determine components by drawing the vector out on graph paper with a ruler and a protractor. –The scale we will be using will be constant throughout this unit: 1 square on the graph paper is going to represent 6m/s. Also measured out, 1cm is 10m/s 0.6cm is exactly 1 square on the graph paper.

5. To draw a vector and determine its components, we do the following: –Choose a starting point and measure out the angle with a protractor. –Draw the vector by connecting the starting point with the angle measured out. –After the vector is drawn, you can draw the x component by drawing from the starting point horizontally to where the vector ends. The y component is drawn vertically. –We calculate the x and y component by counting the squares and converting to m/s. We designate the direction of the x and y components with a positive or negative sign.

6. Lets try to get the components of a few examples: –40m/s at 30°: x = ______ y = _______ –60m/s at 190°: x = ______ y = ______ –75m/s at 290°: x = ______ y = ______

7. Drawing a vector from its components is also doable: –Draw out the x component horizontally and then draw out the y component vertically. –Connect the vector from the beginning of the x component to the end of the y component. –Measure the vector and convert it using the scale and measure the angle.

8. Lets try to build a few vectors: –x = 15m/s y = 35m/s –x = 30m/s y = -40m/s –x = -30m/s y = 60m/s

9. Adding vectors is also doable using graphical analysis: Use “Tip to Tail, Drawn to Scale” –Draw out the first vector to scale, –From the end of the first vector, draw out the second vector to scale. –Connect the beginning of the first vector to the end of the second. –Measure the length of the vector and measure the angle.

10. Let’s look at a few examples: –Add: 40m/s at 45° and 70m/s at 60° Resultant: ___________________ –Add: 50m/s at 30° and 20m/s at 200° Resultant: __________________ –Add: 25m/s at 180° and 55m/s at 30° Resultant: __________________