Vector Direction

This web page is designed to provide some additional practice with the use of scaled vector diagrams for the representation of the magnitude and direction of a vector. Your time will be best spent if you read each practice problem carefully, attempt to solve the problem, 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 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 interpretting scaled vector diagrams. Visit The Physics Classroom Tutorial to learn more.

Determine the magnitude and direction of the following vectors in questions #1-6. Use the counter-clockwise (from East) convention discussed in class to determine the direction. Use the indicated scale and a scale conversion to determine the magnitude. Depress mouse on the "pop-up menu" to check the answers.

1. Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 45 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 24 m/s; 2.4 cm in length multiplied by the factor (10 m/s)/1 cm.

2. Given the SCALE: 1 cm = 50 km/hr, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 300 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 150 km/hr; 3.0 cm in length multiplied by the factor (50 km/hr)/1 cm.

3. Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 345 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 36 m/s; 3.6 cm in length multiplied by the factor (10 m/s)/1 cm.

4. Given the SCALE: 1 cm = 50 km/hr, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 210 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 200 km/hr; 4.0 cm in length multiplied by the factor (50 km/hr)/1 cm.

5. Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 120 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 37 m/s; 3.7 cm in length multiplied by the factor (10 m/s)/1 cm.

6. Given the SCALE: 1 cm = 50 km/hr, determine the magnitude and direction of this vector.

Depress mouse to see answer. The direction is 225 degrees (the counter- clockwise angle of rotation from due East). The magnitude is 160 km/hr; 3.2 cm in length multiplied by the factor (50 km/hr)/1 cm.

 

 

Use an accurately-drawn scaled vector diagram to represent the magnitude and direction of the following vectors in questions #7-12. Use the indicated scale and the counter-clockwise convention discussed in class. Click on the hot link to check the answers.

7. Given the SCALE: 1 cm = 10 m, represent the vector 50 m, 30-degrees by a scaled vector diagram.

8. Given the SCALE: 1 cm = 10 m, represent the vector 60 m, 150-degrees by a scaled vector diagram.

9. Given the SCALE: 1 cm = 20 m, represent the vector 140 m/s, 200-degrees by a scaled vector diagram.

10. Given the SCALE: 1 cm = 15 m/s, represent the vector 120 m/s, 240-degrees by a scaled vector diagram.

11. Given the SCALE: 1 cm = 5 m/s, represent the vector 35 m/s, 270-degrees by a scaled vector diagram.

12. Given the SCALE: 1 cm = 5 m/s, represent the vector 31 m/s, 310-degrees by a scaled vector diagram.

 

Answers and Solutions

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.

7. The vector 50 m, 30-degrees (SCALE: 1 cm = 10 m) would look like this:

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8. The vector 60 m, 150-degrees (SCALE: 1 cm = 10 m) would look like this:

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9. The vector 140 m, 200-degrees (SCALE: 1 cm = 20 m)would look like this:

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10. The vector 120 m/s, 240-degrees (SCALE: 1 cm = 15 m/s) would look like this:

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11. The vector 35 m/s, 270-degrees (SCALE: 1 cm = 5 m/s) would look like this:

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12. The vector 31 m/s, 310-degrees (SCALE: 1 cm = 5 m/s) would look like this:

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