Vector Addition

This web page is designed to provide some additional practice with the use of scaled vector diagrams for the addition of two or more vectors. Your time will be best spent if you read each practice problem carefully, attempt to solve the problem with a scaled vector diagram, and then check your answer. You are cautioned to avoid making a quick reference to the solution prior to making your own attempt at the solution. Such a habit is likely to fail at nurturing the ability to draw a scaled vector addition diagram. If the solution to these practice problems are still not meaningful, you are encouraged to obtain some on-line help specific to the skill of head-to-tail vector addition. Visit The Physics Classroom Tutorial to learn more.

1. Add the following vectors and determine the resultant.

3.0 m/s, 45 deg and 5.0 m/s, 135 deg

2. Add the following vectors and determine the resultant.

5.0 m/s, 45 deg and 2.0 m/s, 180 deg

3. Add the following vectors and determine the resultant.

6.0 m/s, 225 deg and 2.0 m/s, 90 deg

4. Add the following vectors and determine the resultant.

4.0 m/s, 135 deg and 4.0 m/s, 315 deg

5. Add the following vectors and determine the resultant.

5.0 m/s, 45 deg and 2.5 m/s, 135 deg

6. Add the following vectors and determine the resultant.

7.0 m/s, 0 deg and 2.0 m/s, 90 deg

7. Add the following vectors and determine the resultant.

8.0 m/s, 330 deg and 4.0 m/s, 45 deg

8. Add the following vectors and determine the resultant.

2.0 m/s, 150 deg and 4.0 m/s, 225 deg

9. Add the following vectors and determine the resultant.

3.0 m/s, 45 deg and 5.0 m/s, 135 deg and 2.0 m/s, 60 deg

10. Add the following vectors and determine the resultant.

2.0 m/s, 315 deg and 5.0 m/s, 180 deg and 2.0 m/s, 60 deg

11. Add the following vectors and determine the resultant.

4.0 m/s, 90 deg and 2.0 m/s, 0 deg and 2.0 m/s, 210 deg

12. Add the following vectors and determine the resultant.

2.5 m/s, 45 deg and 5.0 m/s, 270 deg and 5.0 m/s, 330 deg

NOTE: Since your answers were determined using a scaled vector diagram, small errors in the measurement of the direction and magnitude of any one of the vectors may lead to small differences between your answers and the correct ones which are shown here. Do not have a cow.

1. 3.0 m/s, 45 deg + 5.0 m/s, 135 deg = 5.83 m/s, 104 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

2. 5.0 m/s, 45 deg + 2.0 m/s, 180 deg = 3.85m/s, 66.5 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

3. 6.0 m/s, 225 deg+ 2.0 m/s, 90 deg= 4.80 m/s, 207.9 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

4. 4.0 m/s, 135 deg+ 4.0 m/s, 315 deg = 0 m/s (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

5. 5.0 m/s, 45 deg+ 2.5 m/s, 135 deg= 5.59 m/s, 71.6 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

6. 7.0 m/s, 0 deg+ 2.0 m/s, 90 deg= 7.28 m/s, 15.9 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

7. 8.0 m/s, 330 deg+ 4.0 m/s, 45 deg= 9.83m/s, 352.2 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

8. 2.0 m/s, 150 deg+ 4.0 m/s, 225 deg= 4.91m/s, 201.8 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

9. 3.0 m/s, 45 deg+ 5.0 m/s, 135 deg+ 2.0 m/s, 60 deg= 7.40m/s, 93.2 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

10. 2.0 m/s, 315 deg+ 5.0 m/s, 180 deg+ 2.0 m/s, 60 deg= 2.61m/s, 173 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

11. 4.0 m/s, 90 deg+ 2.0 m/s, 0 deg+ 2.0 m/s, 210 deg= 3.01 m/s, 84.9 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

12. 2.5 m/s, 45 deg+ 5.0 m/s, 270 deg+ 5.0 m/s, 330 deg= 8.37 m/s, 316.8 deg (Note: the resultant is drawn in red.)

Return to Questions

Get on-line help at The Physics Classroom Tutorial

Return to: Physics Help