PHYSICS FOR SCIENTISTS AND ENGINEERS 9TH EDITION BY SERWAY – TEST BANK
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Sample Test
Chapter 3—Vectors
MULTIPLE CHOICE
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
1. If
= [15, 80°] and , what is the magnitude of ?
|
a. |
15 |
|
b. |
35 |
|
c. |
32 |
|
d. |
5.0 |
|
e. |
23 |
ANS:
C
PTS:
2
DIF: Average
2. Vectors
and are shown. What is the magnitude of a vector if ?
|
a. |
46 |
|
b. |
10 |
|
c. |
30 |
|
d. |
78 |
|
e. |
90 |
ANS: A
PTS:
2
DIF: Average
3. If
and , what is the magnitude of the vector ?
|
a. |
42 |
|
b. |
22 |
|
c. |
64 |
|
d. |
90 |
|
e. |
13 |
ANS:
C
PTS:
2
DIF: Average
4. If
and , what is the direction of the vector ?
|
a. |
-49° |
|
b. |
-41° |
|
c. |
-90° |
|
d. |
+49° |
|
e. |
+21° |
ANS:
B
PTS:
2
DIF: Average
5. If
= [10 m, 30°] and = [25 m, 130°], what is the magnitude of the sum
of these two vectors?
|
a. |
20 m |
|
b. |
35 m |
|
c. |
15 m |
|
d. |
25 m |
|
e. |
50 m |
ANS:
D
PTS:
2
DIF: Average
6. If
= [10 m, 30°] and = [25 m, 130°], what is the direction of the sum
of these two vectors?
|
a. |
17° |
|
b. |
73° |
|
c. |
107° |
|
d. |
163° |
|
e. |
100° |
ANS:
C
PTS:
2
DIF: Average
7. A
vector, , when added to the vector yields a resultant vector which is in
the positive y direction
and has a magnitude equal to that of . What is the magnitude of ?
|
a. |
3.2 |
|
b. |
6.3 |
|
c. |
9.5 |
|
d. |
18 |
|
e. |
5 |
ANS:
A
PTS:
2
DIF: Average
8. If
vector is added to vector , the result is . If is subtracted from ,
the result is . What is the magnitude of ?
|
a. |
5.1 |
|
b. |
4.1 |
|
c. |
5.4 |
|
d. |
5.8 |
|
e. |
8.2 |
ANS:
B
PTS:
2
DIF: Average
9. If
= [2.5 cm, 80°], i.e., the magnitude and direction of are 2.5 cm
and 80°, = [3.5 cm, 120°], and , what is the direction of (to the
nearest degree)?
|
a. |
247° |
|
b. |
235° |
|
c. |
243° |
|
d. |
216° |
|
e. |
144° |
ANS:
D
PTS:
3
DIF: Challenging
10. If
vector is added to vector , the result is . If is subtracted from ,
the result is . What is the direction of (to the nearest degree)?
|
a. |
225° |
|
b. |
221° |
|
c. |
230° |
|
d. |
236° |
|
e. |
206° |
ANS:
B
PTS:
2
DIF: Average
11. A
vector is added to . The resultant vector is in the positive x direction and has
a magnitude equal to . What is the magnitude of ?
|
a. |
11 |
|
b. |
5.1 |
|
c. |
7.1 |
|
d. |
8.3 |
|
e. |
12.2 |
ANS:
D
PTS:
3
DIF: Challenging
12. A
vector is added to . The
resultant vector is in the positive x direction
and has a magnitude equal to that of . What is the direction of ?
|
a. |
74° |
|
b. |
100° |
|
c. |
-81° |
|
d. |
-62° |
|
e. |
106° |
ANS:
A
PTS:
3
DIF: Challenging
13. If
two collinear vectors and are added, the resultant has a magnitude
equal to 4.0. If is subtracted from , the resultant has a magnitude equal
to 8.0. What is the magnitude of ?
|
a. |
2.0 |
|
b. |
3.0 |
|
c. |
4.0 |
|
d. |
5.0 |
|
e. |
6.0 |
ANS:
A
PTS:
1
DIF: Easy
14. If
two collinear vectors and are added, the resultant has a magnitude
equal to 4.0. If is subtracted from , the resultant has a magnitude equal
to 8.0. What is the magnitude of ?
|
a. |
2.0 |
|
b. |
3.0 |
|
c. |
4.0 |
|
d. |
5.0 |
|
e. |
6.0 |
ANS:
E
PTS:
1
DIF: Easy
15. When
vector is added to vector , which has a magnitude of 5.0, the vector
representing their sum is perpendicular to and has a magnitude that is
twice that of . What is the magnitude of ?
|
a. |
2.2 |
|
b. |
2.5 |
|
c. |
4.5 |
|
d. |
5.0 |
|
e. |
7.0 |
ANS: A
PTS:
2
DIF: Average
16. Starting
from one oasis, a camel walks 25 km in a direction 30° south of west and then
walks 30 km toward the north to a second oasis. What distance separates the two
oases?
|
a. |
15 km |
|
b. |
48 km |
|
c. |
28 km |
|
d. |
53 km |
|
e. |
55 km |
ANS:
C
PTS:
2
DIF: Average
17. Starting
from one oasis, a camel walks 25 km in a direction 30° south of west and then
walks 30 km toward the north to a second oasis. What is the direction from the
first oasis to the second oasis?
|
a. |
21° N of W |
|
b. |
39° W of N |
|
c. |
69° N of W |
|
d. |
51° W of N |
|
e. |
42° W of N |
ANS:
D
PTS:
3
DIF: Challenging
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
Exhibit 3-1
The three forces shown act on a particle.
Use this exhibit to answer the following question(s).
18. Refer
to Exhibit 3-1. What is the magnitude of the resultant of these three forces?
|
a. |
27.0 N |
|
b. |
33.2 N |
|
c. |
36.3 N |
|
d. |
23.8 N |
|
e. |
105 N |
ANS:
D
PTS:
2
DIF: Average
19. Refer
to Exhibit 3-1. What is the direction of the resultant of these three forces?
|
a. |
35° |
|
b. |
45° |
|
c. |
65° |
|
d. |
55° |
|
e. |
85° |
ANS:
A
PTS:
3
DIF: Challenging
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
20. If
vector is added to vector , the result is a third vector that is
perpendicular to and has a magnitude equal to 3. What is the ratio of the
magnitude of to that of ?
|
a. |
1.8 |
|
b. |
2.2 |
|
c. |
3.2 |
|
d. |
1.3 |
|
e. |
1.6 |
ANS:
C
PTS:
2
DIF: Average
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
Exhibit 3-2
A child starts at one corner of a cubical jungle gym in a
playground and climbs up to the diagonally opposite corner. The original corner
is the coordinate origin, and the x, y and z axes are oriented
along the jungle gym edges. The length of each side is 2 m.
Use this exhibit to answer the following question(s).
21. Refer
to Exhibit 3-2. The child’s displacement is:
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
A
PTS: 1
DIF: Easy
22. Refer
to Exhibit 3-2. What is the child’s distance from her starting position?
|
a. |
2.8 m |
|
b. |
3.5 m |
|
c. |
6.0 m |
|
d. |
6.9 m |
|
e. |
12.0 m |
ANS:
B
PTS:
2
DIF: Average
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
23. The
displacement of the tip of the 10 cm long minute hand of a clock between 12:15
A.M. and 12:45 P.M. is:
|
a. |
10 cm, 90° |
|
b. |
10 cm, 180° |
|
c. |
10 cm, 4 500° |
|
d. |
20 cm, 180° |
|
e. |
20 cm, 540° |
ANS:
D
PTS:
1
DIF: Easy
24. A
student decides to spend spring break by driving 50 miles due east, then 50
miles 30 degrees south of east, then 50 miles 30 degrees south of that direction,
and to continue to drive 50 miles deviating by 30 degrees each time until he
returns to his original position. How far will he drive, and how many vectors
must he sum to calculate his displacement?
|
a. |
0, 0 |
|
b. |
0, 8 |
|
c. |
0, 12 |
|
d. |
400 mi, 8 |
|
e. |
600 mi, 12 |
ANS:
E
PTS:
2
DIF: Average
25. Given
that and , what is ?
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
A
PTS:
2
DIF: Average
26. Given
that and , what is ?
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
D
PTS:
2
DIF: Average
27. Given
that and , what is ?
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
A
PTS:
2
DIF: Average
28. The
diagram below shows 3 vectors which sum to zero, all of equal length. Which
statement below is true?
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
D
PTS:
1
DIF: Easy
29. Which
statement is true about the unit vectors , and ?
|
a. |
Their directions are
defined by a left-handed coordinate system. |
|
b. |
The angle between any two
is 90 degrees. |
|
c. |
Each has a length of 1 m. |
|
d. |
If is directed east
and is directed south, points up out of the surface. |
|
e. |
All of the above. |
ANS: B
PTS:
1
DIF: Easy
30. Vectors
and have equal magnitudes. Which statement is always true?
|
a. |
. |
|
b. |
. |
|
c. |
is perpendicular to . |
|
d. |
is perpendicular to . |
|
e. |
The magnitude of
equals the magnitude of . |
ANS:
C
PTS:
3
DIF: Challenging
31. When
three vectors, , , and are placed head to tail, the vector sum . If the
vectors all have the same magnitude, the angle between the directions of any
two adjacent vectors is
|
a. |
30° |
|
b. |
60° |
|
c. |
90° |
|
d. |
120° |
|
e. |
150° |
ANS:
D
PTS:
1
DIF: Easy
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
Exhibit 3-3
The vectors , , and are shown below.
Use this exhibit to answer the following question(s).
32. Refer
to Exhibit 3-3. Which diagram below correctly represents ?
|
a. |
d. |
||
|
b. |
e. |
||
|
c. |
|
||
ANS:
B
PTS:
2
DIF: Average
33. Refer
to Exhibit 3-3. Which diagram below correctly represents ?
|
a. |
d. |
||
|
b. |
e. |
||
|
c. |
|
||
ANS:
A
PTS:
2
DIF: Average
Instructions: On occasion, the notation
= [A, q] will be a shorthand
notation for .
Exhibit 3-4
The diagram below shows the path taken by a sailboat tacking
sideways because it cannot sail directly into the wind.
Use this exhibit to answer the following question(s).
34. Refer
to Exhibit 3-4. The total distance it travels is
|
a. |
1 000 m. |
|
b. |
1 732 m. |
|
c. |
2 000 m. |
|
d. |
6 298 m. |
|
e. |
8 000 m. |
ANS:
E
PTS:
1
DIF: Easy
35. Refer
to Exhibit 3-4. The total displacement of the sailboat, the vector sum of its
displacements OB, BC, CD and DE, is
|
a. |
1 732 m, East. |
|
b. |
2 000 m, Northeast. |
|
c. |
6 298 m, East. |
|
d. |
8 000 m, Southeast. |
|
e. |
8 000 m, East. |
ANS:
C
PTS:
1
DIF: Easy
Instructions: On occasion, the notation
= [A, q] will be a shorthand notation
for .
36. Dana
says any vector can be represented as the sum of two vectors: . Ardis
says any vector can be represented as the difference of two vectors: .
Which one, if either, is correct?
|
a. |
They are both wrong: every
vector is unique. |
|
b. |
Dana is correct: Any vector
can be represented as a sum of components and not as a difference. |
|
c. |
Ardis is correct: Any
vector can be represented as a difference of vector components and not as a
sum. |
|
d. |
They are both correct: A
difference of vectors is a sum . |
|
e. |
They are both wrong:
Vectors can be moved as long as they keep the same magnitude and direction. |
ANS:
D
PTS:
2
DIF: Average
37. The
vector has components +5 and +7 along the x and y axes respectively.
Along a set of axes rotated 90 degrees counterclockwise relative to the
original axes, the vector’s components are
|
a. |
-7; -5. |
|
b. |
7; -5. |
|
c. |
-7; 5. |
|
d. |
7; 5. |
|
e. |
7; 0. |
ANS:
B
PTS: 1
DIF: Easy
38. Anthony
has added the vectors listed below and gotten the result . What errors has he
made?
|
a. |
He lost the minus sign in
vector . |
|
b. |
He read the in
as . |
|
c. |
He lost the minus sign in
vector . |
|
d. |
All of the above are
correct. |
|
e. |
Only (a) and (b) above are
correct. |
ANS:
E
PTS:
2
DIF: Average
39. Given
the statement that , what can we conclude?
|
a. |
and . |
|
b. |
. |
|
c. |
and . |
|
d. |
Any one of the answers
above is correct. |
|
e. |
Only (a) and (b) may be
correct. |
ANS:
D
PTS:
2
DIF: Average
40. Adding
vectors and by the graphical method gives the same result for
+ and + . If both additions are done graphically from the
same origin, the resultant is the vector that goes from the tail of the first
vector to the tip of the second vector, i.e, it is represented by a diagonal of
the parallelogram formed by showing both additions in the same figure. Note that
a parallelogram has 2 diagonals. Keara says that the sum of two vectors by the
parallelogram method is . Shamu says it is . Both used the parallelogram
method, but one used the wrong diagonal. Which one of the vector pairs below
contains the original two vectors?
|
a. |
; |
|
b. |
; |
|
c. |
; |
|
d. |
; |
|
e. |
; |
ANS:
E
PTS:
3
DIF: Challenging
41. Given
two non-zero vectors, and , such that , the sum satisfies
|
a. |
. |
|
b. |
. |
|
c. |
. |
|
d. |
. |
|
e. |
. |
ANS: A
PTS:
2
DIF: Average
42. The
vector has components +5 and +7 along the x and y axes
respectively. If the vector is now rotated 90 degrees counterclockwise relative
to the original axes, the vector’s components are now
|
a. |
-7; -5. |
|
b. |
7; -5. |
|
c. |
-7; 5. |
|
d. |
7; 5. |
|
e. |
7; 0. |
ANS:
C
PTS:
1
DIF: Easy
43. The
rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point
are (r,
67.4°). What is the value of the polar coordinate r in this case?
|
a. |
1.92 |
|
b. |
4.62 |
|
c. |
12.0 |
|
d. |
13.0 |
|
e. |
More information is needed. |
ANS:
D
PTS:
2
DIF: Average
44. In
what quadrant are both the sine and tangent negative?
|
a. |
1st |
|
b. |
2nd |
|
c. |
3rd |
|
d. |
4th |
|
e. |
This cannot happen. |
ANS:
D
PTS:
1
DIF: Easy
PROBLEM
45. Two
vectors starting at the same origin have equal and opposite x components. Is it
possible for the two vectors to be perpendicular to each other? Justify your
answer.
ANS:
Yes. If the y components
are of the right magnitudes, the angle can be 90 degrees. (This will occur if
and A = B tan q1.)
PTS:
3
DIF: Challenging
46. A
vector starts at coordinate (3.0, 4.0) and ends at coordinate (-2.0, 16.0).
What are the magnitude and direction of this vector?
ANS:
13.0 m, 113°.
PTS:
2
DIF: Average
47. What
two vectors are each the same magnitude as and perpendicular to ?
ANS:
and .
PTS:
3
DIF: Challenging
Chapter 4—Motion in Two Dimensions
MULTIPLE CHOICE
1. At t = 0, a particle
leaves the origin with a velocity of 9.0 m/s in the positive y direction and
moves in the xy plane
with a constant acceleration of (2.0i –
4.0j)
m/s2. At the instant the x coordinate
of the particle is 15 m, what is the speed of the particle?
|
a. |
10 m/s |
|
b. |
16 m/s |
|
c. |
12 m/s |
|
d. |
14 m/s |
|
e. |
26 m/s |
ANS:
A
PTS: 2
DIF: Average
2. A
particle starts from the origin at t =
0 with a velocity of 6.0 m/s and moves in the xy plane with a
constant acceleration of (-2.0 + 4.0) m/s2. At
the instant the particle achieves its maximum positive x coordinate, how
far is it from the origin?
|
a. |
36 m |
|
b. |
20 m |
|
c. |
45 m |
|
d. |
27 m |
|
e. |
37 m |
ANS:
B
PTS:
2
DIF: Average
3. A
particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and
moves in the xy plane
with a constant acceleration of (3.0 – 2.0) m/s2. At
the instant the particle moves back across the x axis (y = 0), what is the value of its x coordinate?
|
a. |
65 m |
|
b. |
91 m |
|
c. |
54 m |
|
d. |
78 m |
|
e. |
86 m |
ANS: D
PTS:
2
DIF: Average
4. At t = 0, a particle
leaves the origin with a velocity of 5.0 m/s in the positive y direction. Its
acceleration is given by = (3.0 – 2.0) m/s2. At
the instant the particle reaches its maximum y coordinate how far is the particle
from the origin?
|
a. |
11 m |
|
b. |
16 m |
|
c. |
22 m |
|
d. |
29 m |
|
e. |
19 m |
ANS:
A
PTS:
2
DIF: Average
5. A
particle moves in the xy plane
with a constant acceleration given by . At t = 0, its position and velocity are
10 m and , respectively. What is the distance from the origin to the
particle at t =
2.0 s?
|
a. |
6.4 m |
|
b. |
10 m |
|
c. |
8.9 m |
|
d. |
2.0 m |
|
e. |
6.2 m |
ANS:
B
PTS: 3
DIF: Challenging
6. A
particle starts from the origin at t =
0 with a velocity of (16 – 12) m/s and moves in the xy plane with a
constant acceleration of = (3.0 – 6.0) m/s2.
What is the speed of the particle at t =
2.0 s?
|
a. |
52 m/s |
|
b. |
39 m/s |
|
c. |
46 m/s |
|
d. |
33 m/s |
|
e. |
43 m/s |
ANS:
D
PTS:
2
DIF: Average
7. At t = 0, a particle
leaves the origin with a velocity of 12 m/s in the positive x direction and
moves in the xy plane
with a constant acceleration of . At the instant the y coordinate of the
particle is 18 m, what is the x coordinate
of the particle?
|
a. |
30 m |
|
b. |
21 m |
|
c. |
27 m |
|
d. |
24 m |
|
e. |
45 m |
ANS:
C
PTS:
2
DIF: Average
8. The initial
speed of a cannon ball is 0.20 km/s. If the ball is to strike a target that is
at a horizontal distance of 3.0 km from the cannon, what is the minimum time of
flight for the ball?
|
a. |
16 s |
|
b. |
21 s |
|
c. |
24 s |
|
d. |
14 s |
|
e. |
19 s |
ANS: A
PTS:
3
DIF: Challenging
9. A
ball is thrown horizontally from the top of a building 0.10 km high. The ball
strikes the ground at a point 65 m horizontally away from and below the point
of release. What is the speed of the ball just before it strikes the ground?
|
a. |
43 m/s |
|
b. |
47 m/s |
|
c. |
39 m/s |
|
d. |
36 m/s |
|
e. |
14 m/s |
ANS:
B
PTS:
2
DIF: Average
10. A
baseball is hit at ground level. The ball is observed to reach its maximum
height above ground level 3.0 s after being hit. And 2.5 s after reaching this
maximum height, the ball is observed to barely clear a fence that is 97.5 m
from where it was hit. How high is the fence?
|
a. |
8.2 m |
|
b. |
15.8 m |
|
c. |
13.5 m |
|
d. |
11.0 m |
|
e. |
4.9 m |
ANS:
C
PTS:
2
DIF: Average
11. A
rock is projected from the edge of the top of a building with an initial
velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes
the ground a horizontal distance of 25 m from the base of the building. Assume
that the ground is level and that the side of the building is vertical. How
tall is the building?
|
a. |
25.3 m |
|
b. |
29.6 m |
|
c. |
27.4 m |
|
d. |
23.6 m |
|
e. |
18.9 m |
ANS: D
PTS:
2
DIF: Average
12. A
projectile is thrown from the top of a building with an initial velocity of 30
m/s in the horizontal direction. If the top of the building is 30 m above the
ground, how fast will the projectile be moving just before it strikes the
ground?
|
a. |
35 m/s |
|
b. |
39 m/s |
|
c. |
31 m/s |
|
d. |
43 m/s |
|
e. |
54 m/s |
ANS:
B
PTS:
2
DIF: Average
13. A
rifle is aimed horizontally at the center of a large target 60 m away. The
initial speed of the bullet is 240 m/s. What is the distance from the center of
the target to the point where the bullet strikes the target?
|
a. |
48 cm |
|
b. |
17 cm |
|
c. |
31 cm |
|
d. |
69 cm |
|
e. |
52 cm |
ANS:
C
PTS: 2
DIF: Average
14. A
rock is thrown from the edge of the top of a 100-ft tall building at some
unknown angle above the horizontal. The rock strikes the ground a horizontal
distance of 160 ft from the base of the building 5.0 s after being thrown.
Assume that the ground is level and that the side of the building is vertical.
Determine the speed with which the rock was thrown.
|
a. |
72 ft/s |
|
b. |
77 ft/s |
|
c. |
68 ft/s |
|
d. |
82 ft/s |
|
e. |
87 ft/s |
ANS:
C
PTS: 2
DIF: Average
15. An
airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m.
Assume that the ground is level. At what horizontal distance from a target must
the pilot release a bomb so as to hit the target?
|
a. |
3.0 km |
|
b. |
2.4 km |
|
c. |
3.3 km |
|
d. |
2.7 km |
|
e. |
1.7 km |
ANS:
D
PTS:
2
DIF: Average
16. An
object moving at a constant speed requires 6.0 s to go once around a circle
with a diameter of 4.0 m. What is the magnitude of the instantaneous
acceleration of the particle during this time?
|
a. |
2.2 m/s2 |
|
b. |
2.7 m/s2 |
|
c. |
3.3 m/s2 |
|
d. |
3.8 m/s2 |
|
e. |
4.4 m/s2 |
ANS:
A
PTS:
2
DIF: Average
17. A
particle moves at a constant speed in a circular path with a radius of 2.06 cm.
If the particle makes four revolutions each second, what is the magnitude of
its acceleration?
|
a. |
20 m/s2 |
|
b. |
18 m/s2 |
|
c. |
13 m/s2 |
|
d. |
15 m/s2 |
|
e. |
24 m/s2 |
ANS: C
PTS:
2
DIF: Average
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