LESSON 7 Adding Linear Vectors When you walk along a sidewalk, you are generally walking in a straight line. Every so often, you may choose to backtrack to look at something, but you will still be in a relatively straight line. We can look at these motions as individual vectors and add them together, i.e. add up the separate displacements. When we add vectors algebraically, we have to assign positive or negative values to the directions. We then add up the vectors, and indicate the final direction. Although a trip is made up of several different displacements, we can add them up to give us the resultant displacement (ΔdR), i.e. the final displacement. ΔdR = Δd1 + Δd2 + Δd3 + etc…

First, let’s break up the displacements according to position First, let’s break up the displacements according to position. Consider the diagram below. Consider a trip if Kyle goes to the store. What is his displacement? Remember, displacement is measured as a change in position.

Now consider a separate displacement, from when Kyle goes from the store to Kate’s house. What is this second displacement? Each trip is its own displacement, i.e. Δd1 and Δd2. To find Kyle’s resultant displacement we can either subtract his initial position and final position, or add his individual displacements together.

Calculate Kyle’s resultant displacement using his initial and final positions. Calculate Kyle’s resultant displacement using his individual displacements.

PROBLEM: Darren walks 26. 5 m [E] and then 12. 13 m [W] PROBLEM: Darren walks 26.5 m [E] and then 12.13 m [W]. Determine his resultant displacement.

PRACTICE: Dana leaves class and walks towards her locker to get books, which is 8.7 m [N]. She then walks 7.16 m [S] to visit her friend Tara. Dana forgets her calculator, and walks 7.16 m [N] back to her locker. She finally walks 9.8 m [N] to get to her math class. Calculate her resultant displacement. Use GAS.

SUMMARY OF ALGEBRAIC METHOD: Indicate which direction is positive and which is negative, e.g. "Let [E] be +”. Use GAS. Start by listing the givens and the unknown. Convert the directions according to the initial statement. Write the blank equation to solve for the resultant displacement (watch for decimal places when adding). Substitute the values and solve. Be aware of negative numbers. Convert your positive/negative number back to a direction in your final statement. Round your answer if necessary. H.W. Worksheet 7 – Adding Linear Vectors