1. GIG
Read the passage and mark your answers on your whiteboard. NOT ON THE PAPER.
Questions 3-4.

2. Adding and Subtracting Vectors

3. A Treasure Map
A treasure map tells you to start at the sycamore tree, walk 5 paces north and 3 paces east. Doing so gets you to the treasure.
If you walked directly from the tree to the treasure, would your displacement have changed?

5. Adding Vectors
Vectors can be visually represented with arrows. You can add vectors by placing the tip of one vector to the tail of another. The resultant vector is the displacement (magnitude) and direction (angle) of added vectors.

7. Adding the Components of the Vectors Works
You can break each vector into its x and y components and add them, and end up with the correct x,y coordinate for total displacement.

9. Subtracting Vectors
Sometimes a problem will ask you to subtract a vector. This means changing the sign of the vector’s x and y components (visually, turning the vector 180 degrees). Line up this reversed vector tip to tail with the others.

11. Sample Problem - Try Solving on Whiteboard
Find the magnitude and angle of displacement of a person who walks the following three paths on a flat field. First, he walks 25 m heading 49° north of east. Then, he walks 23 m heading 15° north of east. Finally, he turns and walks 32 m in a direction 68° south of east.
Break each vector into its components with trigonometry, then add them.

12. Sample Problem - Try Solving on Whiteboard
First vector - x component
25m(cos(49)) = 16.40m
First vector - y component
25m(sin(49)) = 18.87m

13. Sample Problem - Try Solving on Whiteboard
Second vector - x component
23m(cos(15)) = 22.22m
Second vector - y component
23m(sin(15)) = 5.953m

14. Sample Problem - Try Solving on Whiteboard
Third vector - x component
32m(cos(68)) = m
Third vector - y component
-32m(sin(68)) = m

15. Sample Problem - Try Solving on Whiteboard
Add the x and y components x y
16.40m
18.87m
22.22m
5.953m
11.99m
-29.67m
50.61m
-4.847m

16. Sample Problem - Try Solving on Whiteboard
Use the Pythagorean theorem to find the magnitude of total displacement.
50.61m2 + ( m)2 = displacement2 = m2
√ m2 = 50.84m

17. Sample Problem - Try Solving on Whiteboard
Finally, use the trigonometry to find the angle.
One option is tan θ = / θ = 5.471° S of E
** Enter tan-1(4.847/50.61) **
50.61m θ
4.847
50.84m

18. Sample Problem - Try Solving on Whiteboard
Put it all together with significant figures
Displacement = 51m
Angle = 5.5° south of east.

19. Final Result (Less Accurate Visual Addition Method)

20. Note that you can add the vectors in any order.

21. Read pages 121-126 in textbook
Discuss LessonCheck questions on page 126 with table partners.

22. Homework
Be prepared for 1-D motion test on block day.

23. Closure Answer on your whiteboard:
You drive 2.4 km heading 12 degrees north of west. How far west have you gone? How far north?

24. Closure Answer on your whiteboard:
You drive 2.4 km heading 12 degrees north of west. How far west have you gone? How far north?
2.4km(cos(12)) = 2.3km west
2.4km(sin(12)) = .50km north