1. Vectors

2. Vectors – Have both magnitude (value) and direction.
Scalars – Only have magnitude, no direction
Position
Velocity
Acceleration
Force
Distance
Speed
Mass
Time

3. Vectors can be written in two forms:
1. Magnitude and Direction:
20m/s at 50°
2. Component form:
< 12.9, 15.3 > m/s

4. Magnitude and direction form component form
20m/s at 50° =
<12.9, 15.3>m/s
50°
270°
180°
90° 0°
20sin50
≈15.3m/s
20cos50
≈ 12.9m/s

5. Magnitude and direction form component form
50m/s at 200° =
<-47, -17>m/s
50cos200
≈ -47m/s
200°
50sin200
≈ -17m/s

6. Magnitude and direction form component form
<12.9, 15.3>m/s =
20m/s at 50°
20m/s
15.3m/s
50°
12.9 m/s

7. Magnitude and direction form component form
<-40, 20>m/s =
45 m/s at 153°
45m/s
20m/s
153°
-27°
-40 m/s

8. Adding Vectors
A boat with a speed of 3m/s travels downstream in a river flowing at 4m/s. What is the boats velocity relative to shore?
3m/s
4m/s
4m/s
3m/s
4m/s
3m/s
7m/s

9. Adding Vectors
A boat with a speed of 3m/s travels upstream in a river flowing at 4m/s. What is the boats velocity relative to shore?
-3m/s
4m/s
4m/s
-3m/s
4m/s
-3m/s
1m/s

10. Adding Vectors
A boat with a speed of 3m/s travels straight across a river flowing at 4m/s. What is the boats velocity relative to shore?
4m/s
3m/s

11. 5m/s
3m/s θ
4m/s
3m/s
5m/s θ
4m/s

12. Adding Vectors
A boat with a speed of 3m/s travels at an angle of 60º across a river flowing at 4m/s. What is the boats velocity relative to shore?
4m/s
3m/s
60º

13. 4m/s at 0º = < 4 , 0 > + + = < 1.5 , 2.6 > 3m/s at 60º
= < 4 , 0 >
3sin60º =2.6 + +
3m/s at 60º
= < 1.5 , 2.6 >
4m/s
< 5.5, 2.6 >
3cos60º =1.5
6.08 m/s
2.6 θ
5.5
6.08m/s at 25.3º

14. 3m/s
60º
6.08 m/s
25.3º
4m/s
3m/s
60º
6.08 m/s
25.3º
4m/s

15. Steps to Add Vectors Draw a diagram.
Break all vectors into component form.
Add components.
Write in magnitude and direction form.
Done