Practice Problems: Vectors
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1. (easy) Vector A represents 5.0 m of displacement east.  If vector B represents 10.0 m of displacement west, find the addition of the two displacements (Resultant vector = R).

2. (easy) Vector A represents 5.0 m of displacement east.  If vector B represents 10.0 m of displacement north, find the addition of the two displacements (R).

3. (easy) Determine the x and y components of a displacement whose magnitude is 30.0 m at a 23° angle from the x-axis.

4. (moderate) A car moves 150.0 m at a 63° "north of east" (this simply means 63° from the x-axis). It stays at rest for a while then moves 300 m at 34° "south of west" (this means 214° from the x-axis.)  Find the total displacement of the car.

5. (easy) Two forces are being exerted on an object, but in different directions. For example, you and a friend might both be pulling on strings attached to a single block of wood. Find the magnitude and direction of the resultant force in the following circumstances.
a) The first force has a magnitude of 10 N and acts east. The second force has a magnitude of 4 N and acts west.
b) The first force has a magnitude of 10 N and acts east. The second force has a magnitude of 4 N and acts north.

6. (moderate) Find the equilibrant force for the system of forces described here:
Force A: 20 N at 20°
Force B: 40 N at 230°

7. (moderate) Two displacements with magnitudes of 10 m and 12 m can be combined to form resultant vectors with many different magnitudes. Which of the following magnitudes can result from these two displacments? 22 m, 2 m, 30.9 m, 15.6 m. For the possible resultants, what angle exists between the original displacements?

8. (moderate) Find the dot product (A • B) and the cross product magnitude |A x B| for these two vectors:
Vector A: magnitude of 15 units, angle of 10°
Vector B: magnitude of 150 units, angle of 80°

9. (moderate) If vector C has a magnitude 100 units pointing along the x-axis, and Vector D has a magnitude of 50 units, at what angle must it point so that the dot product of Vector C and Vector D has a magnitude of 250 units?

10. (moderate) A student carries a lump of clay from the ground floor door of a skyscraper (on Grant Street) to the elevator, 24 m away. She then takes the elevator to the 11th floor. Finally, she exits the elevator and carries the clay 12 m back toward Grant Street. Determine the total displacement for the clay if each floor is 4.2 m above the floor below.

Please supplement these problems with those found in your companion text.