1. Created for C.V.C.A. Physics by Dick Heckathorn 26 September 2K+4
Vector Addition
Created for C.V.C.A. Physics by
Dick Heckathorn
26 September 2K+4

2. Vector Addition
In this problem we will add three displacement vectors, first by using a scale drawing and then by using a TI-83 calculator program called ‘VADD’.

3. The Problem
A police cruiser chasing a speeding motorist traveled 60 km [S], then 35 km [E 45o N], and finally 50 km [W].
What is the total displacement of the cruiser?
If the chase took 1.3 hr, what was the average speed and the average velocity for the trip?
Practice problem #1, page 94 from Fundamentals of Physics: Combined Course

4. Selecting a Scale
Select a scale that will allow you to draw an arrow to represent each displacement.
This scale must be large enough to be easy to work with, yet not so large that the drawing will exceed the work area.

5. A metric scale will be most useful if it is divisible by ten.
Selecting a Scale
A metric scale will be most useful if it is divisible by ten.
Possible scale: 1 cm = 10 km

6. Drawing the Vectors and finding the resultant

7. Represent the second displacement 35 km
Drawing Vectors W E
Represent the second displacement km
E 45o N
Represent the third displacement 50 km [W]
orientated in a north-south orientation with the arrow at the south end
by an arrow 6 cm long
Represent the first displacement 60 km [S]
Draw a line from the tail of the first vector to the head of the last vector.
by an arrow 3.5 cm long, with its tail connected to the head of the first vector.
by an arrow 5 cm long in a west direction.
Place an arrow on the end of the line where the line meets the head of the third vector.
Resultant 1 N 3 E S 2 W E

8. Find Resultant DisplacementW E
Resultant
Convert this length to the magnitude of the resultant.
Measure the length of the line with your ruler
Measured length is 4.3 cm
The resultant is
43 km

9. Find Resultant DirectionW E
Resultant
Then express the direction using proper notation.
Measure the angle that the resultant is from south.
Measured angle is
43 km
36o
S 36o W

10. The displacement of the cruiser is:
43 km S 36o W

11. Finding Average Speed
The total distance traveled is:
60 km + 35 km + 50 km = 145 km
The time of travel is: 1.3 hrs

12. Finding Average Velocity
The time of travel is: 1.3 hrs
The displacement is: 43 km S 36o W

13. Note...
The vector quantity, displacement, was divided by a scalar quantity, time.
When dividing a vector quantity by a scalar quantity, the answer is also a vector quantity with the same direction as the original vector quantity.

14. Using ‘Vector’ Program
1. ‘PROG’, ‘VADD__’, ‘ENTER’, ‘ENTER’
2. Select: 1: RESULTANT, ‘ENTER’

15. Using ‘Vector’ Program
3. NUMBER OF VECTORS: Enter ‘3’
4. Note...one will need to know the magnitude and direction of each vector.

16. Determining Direction
All vector directions must be specified as relative to a reference direction.
Use ‘East’ as your reference direction.

17. Determining Direction
Angles measured counter-clockwise will be identified as positive and angles measured clockwise will be identified as negative.

18. Determining Direction
To determine the direction of each vector, first draws the coordinates.

19. N W E S

20. Determining Direction
Next, sketch each vector on the coordinate reference frame with the tail of each vector at the origin of the coordinate system.

21. N 2 3 W E 1 S

22. Determining Direction
Finally, determine the number of degrees each vector is from the reference direction which we have selected as East.

23. N 2 3 W E 1
#1 = -90o
#2 = 45o
#3 = 180o S

24. Enter Vector Data Into the Calculator
When prompted for magnitude and direction, enter the following:
R Angle
#1 60, -90o
#2 35, 45o
#3 50, 180o

25. Take time to inspect the drawn vectors to see that they agree with reality.
When ‘Enter’ is pressed, one should see the three vectors drawn on the screen.

26. When ‘Enter’ is pressed, the resultant vector is drawn.

27. When ‘Enter’ is pressed again, the following is shown:

28. Interpreting the Information
Convert the direction to desired notation of:
Reference direction, angle, direction
-125.6o
S 35.6o W
The displacement is then:
43.4 km, S 35.6o W

29. Interpreting the Information
Once the displacement is found, one finds the average speed and average velocity as discussed previously.
That is all that there is to it.

30. That’s all folks!

31. Interpreting the Information
When ‘Enter’ is pressed, one should see the three vectors drawn on the screen.
Take time to inspect the drawn vectors to see that they agree with reality.

32. Interpreting the Information
When ‘Enter’ is pressed again, the magnitude and direction of the resultant is shown as:
43.4 (km), o

33. Interpreting the Information
When ‘Enter’ is pressed, the resultant vector is drawn.