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. Tip to Tail method D B A C R

6. Analytical vector addition
75°
20°

7. Analytical vector addition
75°
20°

8. 3km @ 20° h = 3km cosθ = a/h sinθ = o/h therefore a = h cosθ
therefore o = h sinθ
a = 3 cos20°
o = 3 sin20°
a = 2.82km
o = 1.03km

9. Analytical vector addition
75°
20°
Vector addition table
Vector
mag
Angle
X Comp’t
Y Comp’t 1 3 20
2.82
1.03 2 75
Res’t
.52
1.93
3.34
2.96

10. Analytical vector addition
Vector addition table
Vector
mag
Angle
X Comp’t
Y Comp’t 1 3 20
2.82
1.03 2 75
Res’t
R2 = x2 + y2
R2 =
R = 4.46 km
.52
1.93
4.46
3.34
2.96

11. Analytical vector addition
Vector addition table
Vector
mag
Angle
X Comp’t
Y Comp’t 1 3 20
2.82
1.03 2 75
Res’t
tanθ = opp/adj
θ = tan-1(y/x)
θ = tan-1(2.96/3.34)
θ = 41.5˚
.52
1.93
4.46
41.5˚
3.34
2.96