Component Addition

The Component Addition Concept Builder is comprised of nine problems in which two or more vectors must be added in order to determine the magnitude and direction of the resultant. Each problem is scaffolded and directed so that students gain the sense of how resultants can be determined from their compoents. There are three levels of difficulty with three different problems per level. Those three difficulty levels are differentiated as follows:
 
  • Apprentice Level: Question Groups 1-3; add 2 vectors
  • Masters Level: Question Groups 4-6; add 3 vectors
  • Wizard Level: Question Groups 7-9; add 4 vectors

Teachers are encouraged to view the questions in order to judge which level of difficulty is most appropriate for their classes. We recommend providing students two or more options. For instance, it might be profitable for a student to complete the Concept Builder at the Apprentice Level in order to gain some confidence and then to be challenged to complete the activity at the Masters Level.

The Physics Classroom grants teachers and other users the right to print these questions for private use. Users are also granted the right to copy the text and modify it for their own use. However, this document should not be uploaded to other servers for distribution to and/or display by others. The Physics Classroom website should remain the only website or server from which the document is distributed or displayed. We also provide a PDF that teachers can use under the same conditions. We have included a link to the PDF near the bottom of this page.

 


Component Addition of Vectors

 

The following diagram is used in all questions:
 

 
 

Question Groups 1-3 all use the following table:

 
 
Question Group 1

Question 1

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
D   +   G   =   ???
 
 

Question 2

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
D   +   G   =   ???
 
 

Question 3

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
D   +   G   =   ???
 
 
 
Question Group 2

Question 4

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
H   +   F   =   ???
 
 

Question 5

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
H   +   F   =   ???
 
 

Question 6

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
H   +   F   =   ???
 
 
 
Question Group 3

Question 7

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
C   +   G   =   ???
 
 

Question 8

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
C   +   G   =   ???
 
 

Question 9

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
C   +   G   =   ???
 
 
 
 
 
 

 

Question Groups 4-6 all use the following table:

 
 
Question Group 4

Question 10

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
B    +    C   +   G   =   ???
 
 

Question 11

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
B    +    C   +   G   =   ???
 
 

Question 12

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.

 
Scale: 1 square = 20 km along its edge
B    +    C   +   G   =   ???
 
 
 
Question Group 5

Question 13

Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.

 
Scale: 1 square = 5 km along its edge
H   +   F   +   I   =   ???
 
 
Question 14
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
H   +   F   +   I   =   ???
 
 
Question 15
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
H   +   F   +   I   =   ???
 
 
 
Question Group 6
Question 16
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
A   +   F   +   D   =   ???
 
 
Question 17
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
A   +   F   +   D   =   ???
 
 
Question 18
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
A   +   F   +   D   =   ???






Question Groups 7-9 all use the following table:
 

 
Question Group 7
Question 19
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
A   +   H   +   C   +   D   =   ???
 
 
Question 20
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
A   +   H   +   C   +   D   =   ???
 
 
Question 21
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
A   +   H   +   C   +   D   =   ???
 
 
 
Question Group 8
Question 22
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
H   +   B   +   G   +   I   =   ???
 
 
Question 23
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
H   +   B   +   G   +   I   =   ???
 
 
Question 24
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
H   +   B   +   G   +   I   =   ???
 
 
 
Question Group 9
Question 25
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 5 km along its edge
F   +   D   +   C   +   B   =   ???
 
 
Question 26
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 10 km along its edge
F   +   D   +   C   +   B   =   ???
 
 
Question 27
Use the diagram and scale to determine the magnitude and direction of the resultant for the vector addition equation. Begin with the table.
 
Scale: 1 square = 20 km along its edge
F   +   D   +   C   +   B   =   ???
 

 
The following graphic appears on all questions:
 

 



 



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