Physics 1100 In-Class Problems: Vectors

1. The following diagram shows a variety of displacement vectors. Express each vector in component (ij) notation.



2. Find the vectors that point from A to the other points B to G. Express each vector in component (ij) notation.



3. Write vectors equations for each diagram below.
   

   (a)		(b)
   (c)		(d)
   (e)		(f)

4. Sketch vector diagrams for the following vector equations.
   

   (a)		(b)
   (c)		(d)

5. Person B is 10 m to the right of person A. Person B walks a distance and person A walks a distance . Sketch neatly the situation on graphpaper and from the drawing determine the vector that points from A to B, . Write out the vector equation for the situation. Confirm that the numerical solution and the graphical solution agree.

6. Find the unit vectors that point from A to the other points B to G in Question #2. Express each vector in component (ij) notation.

7. The relative position of George to Tom, in metres, is i10 + j15. The relative position of Cindy to George is i6 – j4. What is the relative position of Cindy to Tom?

8. State the vectors in the diagrams below in standard form.
   

   (a)

   (b)

9. Neatly sketch the x and y components on the graphs of the vectors shown below. Indicate the sign of the x and y components of the vectors shown below. Express the vectors in component (i, j) form.

   

   

10. Use the parallelogram method to sketch in the resultant vector which has the components shown in the diagrams below. In each case, write the vector in component (i, j) form. In each case write the vector in standard form.








11. Convert the following vectors to component form. Include sketches.

    (a)	A = 7.50 m/s2 at 23° a.h.	(b)	B = 55 m at 47° b.h.
    (c)	C = 15.5 m/s at 155° a.h.	(d)	D = 42 m at 35° S of E
    (e)	E = 120 m/s at 41° W of N	(f)	F = 75 N at 15° S of W




12. For the following, sketch the addition of the given vectors. Use the component method to find the resultant vector. State the resultant in standard form.





13. For the following, subtract the vector B from vector A. Include a sketch the result.





14. A person walks 57.0 m at 47.0° north of east, turns and walks 72.0 m at 15.0° south of east, and then turns and walks 24.0 m 30.0° west of north.
    (a) How far and at what angle is the person's final position from his/her initial position?
    (b) In what direction would the person have to head to return to his/her initial position?


15. Momentum is an important vector quantity which we will encounter later in this course. Momentum is a product of mass and velocity (p = mv). A car of mass 1200 kg and velocity 22.0 m/s at 30.0° south of west is hit by a second car of mass 1450 kg travelling at 18.0 m/s at 55.0° west of north.
    (a) Find the magnitude of each car’s momentum in standard form.
    (b) Find the magnitude and direction of the total momentum of the two cars.


16. Forces are vector quantities. Two forces F₁ and F₂ act on a body such the total force F₃ has a magnitude of 150 N at 15.0° east of north. If F₁ has magnitude 100 N at 10.0° west of north, what is the magnitude and direction of F₂?


17. A person is located 225 m and 35.0° north of west from her initial position. She walked from her initial position to her final position in two stages. In the first stage of her walk, she walked 150 m at 20.0° south of east. How far and in what direction did she walk in the second part?

Questions? mike.coombes@kwantlen.ca