Question 1

The magnitude of a vector can never be less than the magnitude of one of its components.

Accepted Answer

A) True 
 B)False  True

Question 2

Vector   = -1.00  
+ -2.00  
And vector  
= 3.00  
+ 4.00  
. What are the magnitude and direction of vector  
= 3.00  
+ 2.00  
?

Accepted Answer

A)  3.61 in a direction -56.3° counterclockwise from the positive x-axis 
B)  3.61 in a direction 56.3° counterclockwise from the positive x-axis 
C)  3.61 in a direction 33.7° counterclockwise from the positive x-axis 
D)  5.00 in a direction 56.3° counterclockwise from the positive x axis 
E)  6.72 in a direction 34.4° counterclockwise from the positive x-axis 
A)  3.61 in a direction -56.3° counterclockwise from the positive x-axis 
B)  3.61 in a direction 56.3° counterclockwise from the positive x-axis 
C)  3.61 in a direction 33.7° counterclockwise from the positive x-axis 
D)  5.00 in a direction 56.3° counterclockwise from the positive x axis 
E)  6.72 in a direction 34.4° counterclockwise from the positive x-axis C

Question 3

Vectors   and  
Are shown in the figure. Vector  
Is given by  
=  
-  
. The magnitude of vector  
Is 16.0 units, and the magnitude of vector  
Is 7.00 units. What is the angle of vector  
, measured counterclockwise from the +x-axis?

Accepted Answer

A)  16.9° 
B)  22.4° 
C)  73.1° 
D)  287° 
E)  292° 
A)  16.9° 
B)  22.4° 
C)  73.1° 
D)  287° 
E)  292° D

Question 4

The components of vector   are  
= -3.5 and  
= -9.7, and the components of vector  
Are  
= -6 and  
= +8.1. What is the angle (less than 180 degrees) between vectors  
And  
?

Accepted Answer

A)  124° 
B)  56° 
C)  17° 
D)  163° 
E)  106° 
A)  124° 
B)  56° 
C)  17° 
D)  163° 
E)  106°

Question 5

If the magnitude of vector   
is less than the magnitude of vector   
, then the x component of   
is less than the x component of   
.

Accepted Answer

A) True 
 B)False

Question 6

Vectors   and  
Are shown in the figure. What is  
?

Accepted Answer

A)  31.8 
B)  -32.0   - 2.00   
C)  1028 
D)  34.0 
E)  -2.00   - 32.0   
A)  31.8 
B)  -32.0   - 2.00   
C)  1028 
D)  34.0 
E)  -2.00   - 32.0

Question 7

Vectors   and  
Are shown in the figure. Vector  
Is given by  
=  
-  
. The magnitude of vector  
Is 16.0 units, and the magnitude of vector  
Is 7.00 units. What is the magnitude of vector  
?

Accepted Answer

A)  9.00 
B)  9.53 
C)  15.5 
D)  16.2 
E)  17.5 
A)  9.00 
B)  9.53 
C)  15.5 
D)  16.2 
E)  17.5

Question 8

Vector   has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector  
.

Accepted Answer

A)  Ax = 3.83 and Ay = 3.21 
B)  Ax = 3.83 and Ay = -3.21 
C)  Ax = -3.21 and Ay = -3.83 
D)  Ax = -3.21 and Ay = 3.83 
E)  Ax = 4.29 and Ay = 2.16 
A)  Ax = 3.83 and Ay = 3.21 
B)  Ax = 3.83 and Ay = -3.21 
C)  Ax = -3.21 and Ay = -3.83 
D)  Ax = -3.21 and Ay = 3.83 
E)  Ax = 4.29 and Ay = 2.16

Question 9

Vector   
has a magnitude of 5.5 cm and points along the x-axis. Vector   
has a magnitude of 7.5 cm and points at +30° above the negative x-axis.
(a) Determine the x and y components of Vector   
.
(b) Determine the x and y components of Vector   
(c) Determine x and y components of the sum of these two vectors.
(d) Determine the magnitude and direction of the sum of these two vectors.

Accepted Answer

(a) @#IMG-DLM& = 5.5 cm, @#IMG-DLM& = 0
(b) @#IMG-DLM& = -6.

Question 10

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

Accepted Answer

A)  63° N of E 
B)  50° N of E 
C)  57° N of E 
D)  69° N of E 
A)  63° N of E 
B)  50° N of E 
C)  57° N of E 
D)  69° N of E

Question 11

The components of vector   are  
= + 3.90 and  
= -4.00. What is the angle measured counterclockwise from the +x-axis to vector  
?

Accepted Answer

A)  314° 
B)  134° 
C)  224° 
D)  136° 
E)  46.0° 
A)  314° 
B)  134° 
C)  224° 
D)  136° 
E)  46.0°

Question 12

What is the magnitude of   +  
+  
, where  
= 1.00  
+ 4.00  
- 1.00  
,  
= 3.00  
- 1.00  
- 4.00  
And  
= -1.00  
+ 1.00  
?

Accepted Answer

A)  7.07 
B)  2.00 
C)  10.76 
D)  6.78 
E)  8.12 
A)  7.07 
B)  2.00 
C)  10.76 
D)  6.78 
E)  8.12

Question 13

In the figure, the magnitude of vector   
is 18.0 units, and the magnitude of vector   
is 12.0 units. What vector   
must be added to the vectors   
and   
so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   
by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

Accepted Answer

The answer of In the figure, the magnitude of vector...

Question 14

Vector   = -3.00  
+ 3.00  
And vector  
= 3.00  
+ 4.00  
. What is vector  
=  
+  
?

Accepted Answer

A)  0.00   + 3.00   
B)  7.00   + 7.00   
C)  -3.00   + 7.00   
D)  0.00   + 7.00   
E)  -3.00   -3.00   
A)  0.00   + 3.00   
B)  7.00   + 7.00   
C)  -3.00   + 7.00   
D)  0.00   + 7.00   
E)  -3.00   -3.00

Question 15

If A > B, under what condition is |   -  
| = A - B?

Accepted Answer

A)  The statement is never true. 
B)  Vectors   and   are in opposite directions. 
C)  Vectors   and   are in the same direction. 
D)  Vectors   and   re in perpendicular directions. 
E)  The statement is always true. 
A)  The statement is never true. 
B)  Vectors   and   are in opposite directions. 
C)  Vectors   and   are in the same direction. 
D)  Vectors   and   re in perpendicular directions. 
E)  The statement is always true.

Question 16

The components of vector   are  
= +2.2 and  
= -6.9 , and the components of vector  
Are given are  
= -6.1 and  
= -2.2. What is the magnitude of the vector  
-  
?

Accepted Answer

A)  9.5 
B)  6.1 
C)  9.9 
D)  91 
E)  0.76 
A)  9.5 
B)  6.1 
C)  9.9 
D)  91 
E)  0.76

Question 17

Vector   = 1.00  
+ -2.00  
And vector  
= 3.00  
+ 4.00  
. What are the magnitude and direction of vector  
=  
+  
?

Accepted Answer

A)  7.21 in a direction 33.7° counterclockwise from the positive x axis 
B)  6.00 in a direction 63.4° counterclockwise from the positive x axis 
C)  4.47 in a direction 6.34° counterclockwise from the positive x axis 
D)  4.47 in a direction 26.6° counterclockwise from the positive x axis 
E)  7.21 in a direction 56.3° counterclockwise from the positive x axis 
A)  7.21 in a direction 33.7° counterclockwise from the positive x axis 
B)  6.00 in a direction 63.4° counterclockwise from the positive x axis 
C)  4.47 in a direction 6.34° counterclockwise from the positive x axis 
D)  4.47 in a direction 26.6° counterclockwise from the positive x axis 
E)  7.21 in a direction 56.3° counterclockwise from the positive x axis

Question 18

Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes   = 1.0 N,  
= 8.0 N and  
= 7.0 N, where N is the standard unit of force, what is the component of the net force  
net =  
1 +  
2 +  
3 parallel to the floor?

Accepted Answer

A)  2.5 N 
B)  5.1 N 
C)  6.0 N 
D)  7.8 N 
A)  2.5 N 
B)  5.1 N 
C)  6.0 N 
D)  7.8 N

Question 19

If   
-   
= 0, then the vectors   
and   
have equal magnitudes and are directed in the opposite directions from each other.

Accepted Answer

A) True 
 B)False

Question 20

A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?

Accepted Answer

A)  8.8 m 
B)  8.1 m 
C)  66 m 
D)  10 m 
A)  8.8 m 
B)  8.1 m 
C)  66 m 
D)  10 m

Exam 3: Vectors and Coordinate Systems

The magnitude of a vector can never be less than the magnitude of one of its components.

Vector = -1.00 + -2.00 And vector = 3.00 + 4.00 . What are the magnitude and direction of vector = 3.00 + 2.00 ?

Vectors and Are shown in the figure. Vector Is given by = - . The magnitude of vector Is 16.0 units, and the magnitude of vector Is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis?

The components of vector are = -3.5 and = -9.7, and the components of vector Are = -6 and = +8.1. What is the angle (less than 180 degrees) between vectors And ?

If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of .

Vectors and Are shown in the figure. What is ?

Vectors and Are shown in the figure. Vector Is given by = - . The magnitude of vector Is 16.0 units, and the magnitude of vector Is 7.00 units. What is the magnitude of vector ?

Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector .

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

The components of vector are = + 3.90 and = -4.00. What is the angle measured counterclockwise from the +x-axis to vector ?

What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 And = -1.00 + 1.00 ?

Vector = -3.00 + 3.00 And vector = 3.00 + 4.00 . What is vector = + ?

If A > B, under what condition is | - | = A - B?

The components of vector are = +2.2 and = -6.9 , and the components of vector Are given are = -6.1 and = -2.2. What is the magnitude of the vector - ?

Vector = 1.00 + -2.00 And vector = 3.00 + 4.00 . What are the magnitude and direction of vector = + ?

If - = 0, then the vectors and have equal magnitudes and are directed in the opposite directions from each other.

A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?

Concepts of Motion

Kinematics in One Dimension

Kinematics in Two Dimensions

Force and Motion

Dynamics I: Motion Along a Line

Newtons Third Law

Dynamics Ii: Motion in a Plane

Impulse and Momentum

Energy

Work

Rotation of a Rigid Body

Newtons Theory of Gravity

Oscillations

Fluids and Elasticity

A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

Traveling Waves

Superpositions

Wave Optics

Ray Optics

Optical Instruments

Electric Charges and Forces

The Electric Field

Gausss Law

The Electric Potential

Potential and Field

Current and Resistance

Fundamentals of Circuits

The Magnetic Field

Electromagnetic Induction

Electromagnetic Fields and Waves

Ac Circuits

Relativity

The Foundations of Modern Physics

Quantization

Wave Functions and Uncertainty

One-Dimensional Quantum Mechanics

Atomic Physics

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