Vectors
Vectors – Have both
magnitude (value) and
direction.
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Position
Velocity
Acceleration
Force
Scalars – Only have
magnitude, no direction
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Distance
Speed
Mass
Time
Vectors can be written in two forms:
1. Magnitude and Direction:
20m/s at 50°
2. Component form:
< 12.9, 15.3 > m/s
Magnitude and direction form
20m/s at 50° =
component form
<12.9, 15.3>m/s
90°
20sin50
≈15.3m/s
180°
50°
20cos50
≈ 12.9m/s
270°
0°
Magnitude and direction form
50m/s at 200° = <-47, -17>m/s
50cos200
≈ -47m/s
50sin200
≈ -17m/s
200°
component form
Magnitude and direction form
component form
<12.9, 15.3>m/s = 20m/s at 50°
m
v  12.9  15.3  20
s
 15.3 
tan   

 12.9 
1  15.3 
  tan 

 12.9 
  50
2
20m/s
15.3m/s
50°
12.9 m/s
2
Magnitude and direction form
component form
<-40, 20>m/s = 45 m/s at 153°
m
v  (40)  20  45
s
2
20m/s
45m/s
-27° 153°
-40 m/s
2
 20 
tan   

  40 
1  20 
  tan 

  40 
  27 
180  27  153
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?
4m/s
3m/s
4m/s
3m/s
4m/s
3m/s
7m/s
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?
4m/s
-3m/s
4m/s
-3m/s
4m/s
-3m/s
1m/s
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
5m/s
3m/s
θ
4m/s
5m/s
3m/s
θ
4m/s
m
v  3 4 5
s
2
2
3
tan  
4
1  3 
  tan  
4
  37 
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
60º
3sin60º =2.6
4m/s
60º
4m/s at 0º
+
3m/s at 60º
= < 4 , 0 >
+
+
= < 1.5 , 2.6 >
< 5.5, 2.6 >
3cos60º =1.5
m
v  5.5  2.6  6.08
s
2
2.6
θ
5.5
2.6
tan  
5 .5
1  2.6 
  tan 

 5. 5 
  25.3
6.08m/s at 25.3º
2
25.3º
4m/s
60º
25.3º
4m/s
60º
Steps to Add Vectors
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Draw a diagram.
Break all vectors into component form.
Add components.
Draw a diagram.
Write in magnitude and direction form.
Done