1. Motion in Two Dimensions

2. Example
What is the displacement of a person who walks 10.0 km (E) and then 5.00 km (N) ?
D1 + D2 = DR
Use a “tip to tail” method
Draw 1st vector (D1)
Draw 2nd vector (D2) placing its tail at the tip of the 1st vector

3. Draw the arrow from the tail of the 1st vector to the tip of the second. This is the resultant vector (sum of two vectors) - DR
The magnitude of DR is not equal to the sum of D1 and D2
If the two are not in the same direction the resultant is always smaller - D1 + D2 > DR
It is not important what order they are added in

4. Once the diagram is complete, solve for DR using the Pythagorean theorem
a2 + b2 = c2
= c c = 11.2 km

5. Solve for direction of travel using trig identities
Sin θ = opp/hyp cos θ = adj/hyp
Sin θ = 5/ θ = 27°
Final answer 11.2 km (27º N of E)

6. Vectors by Components
Tip to tail method will not be sufficient if the triangle formed is not a right triangle
A single angled vector can be expressed as two components
Finding the components is called Resolution of the vector

7. Example What are the components of 50 km (47º N of E)?
Single vector has a vertical and horizontal component – vx and vy
50km vy vx

8. Example
A mail carrier leaves the post office and drives 22.0 km (N), then 47 km (60º S of E). What is the displacement?

9. Step 1
Resolve the angled vector into its two components

10. Step 2
Total the vertical and horizontal components

11. Step 3
Draw the vector from the vertical and horizontal totals

12. Step 4
Solve as a right triangle vector