Chapter 3.2 – Adding Vectors

1. Adding Vectors Chapter 3.2 – Adding Vectors

2. Finding the Resultant of 1-D Vectors ( Vectors going east or west; north or south) • The Resultant is the result of adding two or more vectors together. • When you add vectors together, the resultant determines the overall magnitude and the direction of the addition of those vectors.

3. Finding the Resultant of 2-D Vectors –

4. There are a variety of methods for determining the magnitude and direction of the resultant. • The 2 Methods that we will learn how to use: • 1. Pythagorean Theorem (using Trig). • Can only be used if the vectors you are adding form right angles with each other. • 2. Head – to – Tail Method ( using graphs)

5. Calculating Resultants Using the “Head – To – Tail” Method • Add the vectors by first attaching them head to tail. • 2. Once all the vectors have attached head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish 3. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. 4. The direction of the resultant can be determined by using a protractor and measuring its counterclockwise angle from the horizon.

6. EXAMPLE #1 Add the following vectors together and find the resultant • 20 m, 45 deg. + 25 m, 300 deg. + 15 m, 210 deg. • Scale: 1 cm = 5m • The order in which you attach the vectors doesn’t matter as long as you don’t change their magnitude or direction.

7. Process • Attach your vectors “Head – to- Tail” • Draw the resultant in red. • Draw the resultant from the start to finish. • Measure the angle from the tail of your resultant

8. The order in which you add or attach) your vectors doesn’t matter, as long as you don’t change the magnitude or the direction.