Name_______________________________
Date_________________
DISCOVERY LAB: VECTORS
1. For the following questions, which of the following statements involve vector
quantities, and which involve scalar quantities?
a) I ran two miles at the lake. ______________
b) I ran two miles due north along the lake. ______________
c) The plane flew at a speed of 90 knots on a heading of 600 east of north.
______________
d) The car was traveling at 60 mph._________________
e) The temperature was minus 20 degrees. ______________
f) The cart moved 20 meters in the negative x direction. ___________
2. Vector A points due west, while vector B points due south. They both have a
magnitude of 4.0 cm. Using a ruler,
Draw the graphical addition of A + 2B to scale. Label A, 2B, (A + 2B).
Draw the graphical subtraction, (A – B) to scale. Label A, B, A - B.
Measure the length of each vector to 1 decimal place:
A + 2B __________
A – B ___________
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3. Vectors A and B are shown in the drawing below. Vector R (not shown) is the
resultant vector where R = A + B. Indicate the signs (negative or positive) of the
following scalar components:
Ax ____Ay ____Bx ____
By ____
Rx ____
Ry, ____
Exercises 4-6: Draw and label x- and y- components of the vector shown:
Exercises 7-9: Draw and label x- and y- components of the vector and determine
their numerical values (including sign!):
2
10. A common objective in physics is to calculate the components
of the gravity vector parallel and perpendicular to a hill or incline.
The vector F points in the “true vertical” direction (represented by
the long end of the paper). The axes are tilted so that the x axis
represents the hill’s orientation with respect to horizontal.
a. Draw the F vector on the diagram of tilted coordinate axes
below (F must remain true vertical at all times):

F
b. Draw the components FX and FY on the diagram:
c. Calculate the numerical value and sign of FX and FY:
y
FX = _______
x
FY = ________
20°
Exercises 11-16: Draw and label the vector with these components. Write the
magnitude of the vector below, along with the appropriate acute angle.
Ax = -3, Ay = 2
Bx = -3, By = -1
θ = ________
θ = ________
Cx = -2, Cy = 0
* θ = ________
* not acute in this case!
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Ax = -1, Ay = 2
A = ________
θ = ________
Bx = 0, By = -2
Cx = 3, Cy = -2
B = ________
C = ________
θ = ________
θ = ________
Exercises 17-19: In each case, the vector A is 5 units long and is directed
300 above true horizontal. Determine the components Ax and Ay for the three
coordinate systems shown below. Show your work below the figure.
Exercises 20-22 use graphical representation of vector addition. For each
force, determine the x and y components by counting the number of squares to
the nearest half. Include the appropriate “+” and “-“signs. Then, add the total
number x and y squares from all the forces and draw the net force vector on
the graph provided.
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EXAMPLE
x
y
F1 (N)
0
2
F2 (N)
-2.5
0
F3 (N)
0
-3
F4 (N)
3.5
-3.5
Fnet (N)
1
-4.5
#20
x
y
x
y
F1 (N)
F2 (N)
F3 (N)
F4 (N)
Fnet (N)
#21
F1 (N)
F2 (N)
F3 (N)
F4 (N)
Fnet (N)
5
#22
x
y
F1 (N)
F2 (N)
F3 (N)
F4 (N)
Fnet (N)
Exercises 23-25 review the addition of vectors (in this case force vectors)
using the mathematical procedure of vector addition. The procedure for all of
these problems is shown below.
1.
Enter the vector components in the table for each force vector. Put in the
appropriate “+” and “ – ” signs based on quadrant.
2.
Add components in the last row of the table.
3.
Find the magnitude and acute angle above/below positive/negative x axis
and enter it below the table.
4.
Draw the net force vector on the graph provided.
EXAMPLE
x component
y component
F1 (N)
40 cos 45o
28.3
0
40 sin 45o
28.3
30
-50 cos 30o
-43.3
-15
-50 sin 30o
-25
33.3
F2 (N)
F3 (N)
Fnet (N)
Fnet = 36.5 N Θ = 66o above –x axis
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#23
x
component
y
component
F1 (N)
F2 (N)
F3 (N)
Fnet (N)
Fnet =
#24
Θ=
x
component
y
component
F1 (N)
F2 (N)
F3 (N)
Fnet (N)
Fnet =
#25
Θ=
x
component
y
component
F1 (N)
F2 (N)
F3 (N)
Fnet (N)
Fnet =
Θ=
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