1. Vector Addition: Parallelogram Method Jerome walks 4 km north, and 8 km east. What is his displacement?

2. Graphical: Tip to Tail Method Jerome walks 4 km north, and 8 km east. What is his displacement?

3. Graphical Vector Addition: Parallelogram Method

4. Tip to Tail Method

5. A B C D R Tip to Tail method

6. Analytical vector addition 2km @ 75° 3km @ 20°

7. Analytical vector addition 2km @ 75° 3km @ 20°

8. cosθ = a/h a = h cosθ therefore a = h cosθ h = 3km a = 3 cos20 ° a = 2.82km sinθ = o/h o = h sinθ therefore o = h sinθ o = 3 sin20° o = 1.03km

9. Analytical vector addition 2km @ 75° 3km @ 20° Vector addition table VectormagAngle X Comp’t Y Comp’t 13202.821.03 2275 Res’t.521.93 3.342.96

10. Analytical vector addition Vector addition table VectormagAngle X Comp’t Y Comp’t 13202.821.03 2275 Res’t.521.93 3.342.96 R 2 = x 2 + y 2 R 2 = 3.34 2 + 2.96 2 R = 4.46 km 4.46 R

11. Analytical vector addition Vector addition table VectormagAngle X Comp’t Y Comp’t 13202.821.03 2275 Res’t.521.93 3.342.96 tanθ = opp/adj θ = tan -1 (y/x) θ = tan -1 (2.96/3.34) θ = 41.5˚ 4.46 R 41.5˚