Choose the best answer

1. Which of the following physical quantities is a vector?
   
   1. Speed
      
   2. Velocity
      
   3. Time
      
   4. Length
      
   5. Temperature
      
   Answer: B
   

2. The default angle (angle measured with respect to the positive x-axis) for the
   vector A = 2 m north is
   
   1. 270 deg
      
   2. 90 deg
      
   3. 0 deg
      
   4. 180 deg
      
   5. -90 deg
      
   Answer: B
   

3. The default angle (angle measured with respect to the positive x-axis) for
   the vector A = 4 m 20 deg west of north is
   
   1. 70 deg
      
   2. 110 deg
      
   3. 20 deg
      
   4. 160 deg
      
   5. -20 deg
      
   Answer: B
   

4. Using the scale 1 cm for 10 m ⁄ s, the vector A = 12 m ⁄ s east, can be
   graphically represented by an arrow of length
   
   1. 2.4 cm
      
   2. 1.2 cm
      
   3. 0.833 cm
      
   4. 0.6 cm
      
   5. 12 cm
      
   Answer: B
   

5. If the vector A = 90 m ⁄ s 25 deg west of south, using the scale 1 cm for 30 m ⁄ s, the vector 0.8A can be
   graphically represented by an arrow of length _________ and default angle
   (angle measured with respect to the positive x-axis) ___________.
   
   1. 2.4 cm, 245 deg
      
   2. 1.2 cm, 205 deg
      
   3. 1.2 cm, 245 deg
      
   4. 2.4 cm, 205 deg
      
   5. 4.8 cm, 25 deg
      
   Answer: A
   

6. If the vector A = 100 m ⁄ s south, using the scale 1 cm for 30 m ⁄ s, the vector -0.8A can be
   graphically represented by an arrow of length _________ and default angle
   (angle measured with respect to the positive x-axis) ___________.
   
   1. 0.3 cm, 90 deg
      
   2. 2.667 cm, 90 deg
      
   3. 2.667 cm, -90 deg
      
   4. 1.333 cm, 90 deg
      
   5. 1.333 cm, -90 deg
      
   Answer: B
   

7. Given the vectors A = 8 m west and B = 7 m south, using graphical
   addition determine which of the following most likely represent
   the magnitude and direction of the sum vector (A + B ) respectively.
   (You should be able to answer it with sketches not drawn to scale.)
   
   1. 15 m, 221.186 deg
      
   2. 10.63 m, 41.186 deg
      
   3. 15 m, 318.814 deg
      
   4. 10.63 m, 318.814 deg
      
   5. 10.63 m, 221.186 deg
      
   Answer: E
   

8. Given the vectors A = 10 m west and B = 3 m north, using graphical
   method determine which of the following most likely represent
   the magnitude and direction of the difference vector, A - B, respectively.
   (You should be able to answer it with sketches not drawn to scale.)
   
   1. 10.44 m, 196.699 deg
      
   2. 10.44 m, 16.699 deg
      
   3. 13 m, 196.699 deg
      
   4. 10.44 m, 343.301 deg
      
   5. 13 m, 343.301 deg
      
   Answer: A
   

9. Determine the x and y components of the vector
   A = 100 m west.
   
   1. ( 100 m, 0 m )
      
   2. ( 0 m, 100 m )
      
   3. ( 0 m, -100 m )
      
   4. ( -100 m, 0 m )
      
   5. ( -100 m, 100 m )
      
   Answer: D
   

10. Determine the x and y components of the vector
    A = 660 m 60 deg west of north.
    
    1. ( -571.577 m, 54.446 m )
       
    2. ( -571.577 m, 330 m )
       
    3. ( -757.786 m, 330 m )
       
    4. ( -757.786 m, 54.446 m )
       
    5. ( -94.304 m, 221.305 m )
       
    Answer: B
    

11. Calculate the magnitude of a vector whose x and
    y components are -4 m and -9 m respectively.
    
    1. 13 m
       
    2. 5 m
       
    3. 97 m
       
    4. 9.849 m
       
    5. 3.606 m
       
    Answer: D
    

12. Calculate the direction (angle with respect to the positive x axis)
    of a vector whose x and y components are 14 m and 9 m respectively.
    
    1. 32.735 deg
       
    2. 57.699 deg
       
    3. 7.928 deg
       
    4. 15.637 deg
       
    5. 57.265 deg
       
    Answer: A
    

13. Calculate the magnitude and direction (with respect to the positive x axis)
    of a vector whose x and y components are -10 m and 19 m respectively.
    
    1. 23.618 m, 117.759 deg
       
    2. 23.618 m, 112.759 deg
       
    3. 21.471 m, 112.759 deg
       
    4. 21.471 m, 117.759 deg
       
    5. 21.471 m, -62.241 deg
       
    Answer: D
    

14. Given the vectors A = 10 m 30 deg
    north of east and B = 60 m 80 deg south of west,
    find the x and y components of their sum vector A + B.
    
    1. ( -1.036 m, -47.646 m )
       
    2. ( -1.759 m, -61.096 m )
       
    3. ( -2.396 m, -54.088 m )
       
    4. ( -1.759 m, -54.088 m )
       
    5. ( -2.396 m, -61.096 m )
       
    Answer: D
    

15. Given the vectors A = 30 m 70 deg north of west and B = 80 m 60 deg
    north of west , find the magnitude and direction (with respect to the positive x axis)
    of their sum vector A + B.
    
    1. 109.668 m, 168.59 deg
       
    2. 109.668 m, 117.277 deg
       
    3. 18.292 m, 117.277 deg
       
    4. 109.668 m, 134.386 deg
       
    5. 18.292 m, 168.59 deg
       
    Answer: B