Question 1

On occasion, the notation   will be a shorthand notation for   .
-The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true? ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 2

On occasion, the notation   will be a shorthand notation for   .
-If   and   , what is the magnitude of the vector   ?

Accepted Answer

A) 42 
B) 22 
C) 64 
D) 90 
E) 13 
A) 42 
B) 22 
C) 64 
D) 90 
E) 13 C

Question 3

On occasion, the notation   will be a shorthand notation for   .
-Given that   and   , what is   ? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 4

On occasion, the notation   = [A, θ] will be a shorthand notation for   .
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).
- The total displacement of the sailboat, the vector sum of its displacements OB, BC, CD and DE, is

Accepted Answer

A) 1732 m, East. 
B) 2000 m, Northeast. 
C) 6298 m, East. 
D) 8000 m, Southeast. 
E) 8000 m, East. 
A) 1732 m, East. 
B) 2000 m, Northeast. 
C) 6298 m, East. 
D) 8000 m, Southeast. 
E) 8000 m, East.

Question 5

On occasion, the notation   will be a shorthand notation for   .
-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   ?

Accepted Answer

A) 11 
B) 5.1 
C) 7.1 
D) 8.3 
E) 12.2 
A) 11 
B) 5.1 
C) 7.1 
D) 8.3 
E) 12.2

Question 6

On occasion, the notation   will be a shorthand notation for   .
-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)?

Accepted Answer

A) 247° 
B) 235° 
C) 243° 
D) 216° 
E) 144° 
A) 247° 
B) 235° 
C) 243° 
D) 216° 
E) 144°

Question 7

Anthony has added the vectors listed below and gotten the result   . What errors has he made? ​   ​
​

Accepted Answer

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. 
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.

Question 8

On occasion, the notation   will be a shorthand notation for   .
-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   ?

Accepted Answer

A) 2.0 
B) 3.0 
C) 4.0 
D) 5.0 
E) 6.0 
A) 2.0 
B) 3.0 
C) 4.0 
D) 5.0 
E) 6.0

Question 9

On occasion, the notation   = [A, θ] will be a shorthand notation for   .
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).
-The total distance it travels is

Accepted Answer

A) 1000 m. 
B) 1732 m. 
C) 2000 m. 
D) 6298 m. 
E) 8000 m. 
A) 1000 m. 
B) 1732 m. 
C) 2000 m. 
D) 6298 m. 
E) 8000 m.

Question 10

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
-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?

Accepted Answer

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. 
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.

Question 11

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?

Accepted Answer

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 
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

Question 12

On occasion, the notation   will be a shorthand notation for   .
The three forces shown act on a particle.
​   ​
Use this exhibit to answer the following question(s).
-What is the magnitude of the resultant of these three forces?

Accepted Answer

A) 27.0 N 
B) 33.2 N 
C) 36.3 N 
D) 23.8 N 
E) 105 N 
A) 27.0 N 
B) 33.2 N 
C) 36.3 N 
D) 23.8 N 
E) 105 N

Question 13

On occasion, the notation   will be a shorthand notation for   .
The three forces shown act on a particle.
​   ​
Use this exhibit to answer the following question(s).
-What is the direction of the resultant of these three forces?

Accepted Answer

A) 35° 
B) 45° 
C) 65° 
D) 55° 
E) 85° 
A) 35° 
B) 45° 
C) 65° 
D) 55° 
E) 85°

Question 14

On occasion, the notation   will be a shorthand notation for   .
-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)?

Accepted Answer

A) 225° 
B) 221° 
C) 230° 
D) 236° 
E) 206° 
A) 225° 
B) 221° 
C) 230° 
D) 236° 
E) 206°

Question 15

Vectors   and   have equal magnitudes. Which statement is always true?

Accepted Answer

A)    +   = 0 
B)    -   = 0 
C)    is perpendicular to   +   . 
D)    is perpendicular to   +   . 
E) The magnitude of   +   equals the magnitude of   . 
A)    +   = 0 
B)    -   = 0 
C)    is perpendicular to   +   . 
D)    is perpendicular to   +   . 
E) The magnitude of   +   equals the magnitude of   .

Question 16

On occasion, the notation   will be a shorthand notation for   .
-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   ?

Accepted Answer

A) 1.8 
B) 2.2 
C) 3.2 
D) 1.3 
E) 1.6 
A) 1.8 
B) 2.2 
C) 3.2 
D) 1.3 
E) 1.6

Question 17

On occasion, the notation   will be a shorthand notation for   .
-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   ?

Accepted Answer

A) 2.2 
B) 2.5 
C) 4.5 
D) 5.0 
E) 7.0 
A) 2.2 
B) 2.5 
C) 4.5 
D) 5.0 
E) 7.0

Question 18

On occasion, the notation   = [A, θ] will be a shorthand notation for   .
The vectors   and   are shown below.
​   ​
Use this exhibit to answer the following question(s).
-Which diagram below correctly represents   ?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

On occasion, the notation   will be a shorthand notation for   .
-If   = [15, 80°] and   , what is the magnitude of   ?

Accepted Answer

A) 15 
B) 35 
C) 32 
D) 5.0 
E) 23 
A) 15 
B) 35 
C) 32 
D) 5.0 
E) 23

Question 20

On occasion, the notation   will be a shorthand notation for   .
-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?

Accepted Answer

A) 0, 0 
B) 0, 8 
C) 0, 12 
D) 400 mi, 8 
E) 600 mi, 12 
A) 0, 0 
B) 0, 8 
C) 0, 12 
D) 400 mi, 8 
E) 600 mi, 12

Exam 3: Vectors

On occasion, the notation will be a shorthand notation for . -The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true? ​ ​

On occasion, the notation will be a shorthand notation for . -If and , what is the magnitude of the vector ?

On occasion, the notation will be a shorthand notation for . -Given that and , what is ? ​

On occasion, the notation will be a shorthand notation for . -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 ?

On occasion, the notation will be a shorthand notation for . -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)?

Anthony has added the vectors listed below and gotten the result . What errors has he made? ​ ​ ​

On occasion, the notation will be a shorthand notation for . -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 ?

On occasion, the notation = [A, θ] will be a shorthand notation for . 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). -The total distance it travels is

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . -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?

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?

On occasion, the notation will be a shorthand notation for . The three forces shown act on a particle. ​ ​ Use this exhibit to answer the following question(s). -What is the magnitude of the resultant of these three forces?

On occasion, the notation will be a shorthand notation for . The three forces shown act on a particle. ​ ​ Use this exhibit to answer the following question(s). -What is the direction of the resultant of these three forces?

On occasion, the notation will be a shorthand notation for . -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)?

Vectors and have equal magnitudes. Which statement is always true?

On occasion, the notation will be a shorthand notation for . -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 ?

On occasion, the notation will be a shorthand notation for . -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 ?

On occasion, the notation = [A, θ] will be a shorthand notation for . The vectors and are shown below. ​ ​ Use this exhibit to answer the following question(s). -Which diagram below correctly represents ?

On occasion, the notation will be a shorthand notation for . -If = [15, 80°] and , what is the magnitude of ?

Getting Started

One-Dimensional Motion

Two- and Three-Dimensional Motion

Newtons Laws of Motion

Applications of Newtons Laws of Motion

Gravity

Conservation of Energy

Energy in Nonisolated Systems

Systems of Particles and Conservation of Momentum

Collisions

Rotation I: Kinematics and Dynamics

Rotation II: a Conservation Approach

Static Equilibrium, Elasticity, and Fracture

Fluids

Oscillations

Traveling Waves

Superposition and Standing Waves

Temperature, Thermal Expansion, and Gas Laws

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Electric Forces

Electric Fields

Gausss Law

Electric Potential

Capacitors and Batteries

Current and Resistance

Direct Current Dc Circuits

Magnetic Fields and Forces

Gausss Law for Magnetism and Amperes Law

Faradays Law of Induction

Inductors and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Diffraction and Interference

Applications of the Wave Model

Reflection and Images Formed by Reflection

Refraction and Images Formed by Refraction

Relativity

Filters

On occasion, the notation will be a shorthand notation for . -The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

On occasion, the notation will be a shorthand notation for . -Given that and , what is ?

Anthony has added the vectors listed below and gotten the result . What errors has he made?

On occasion, the notation = [A, θ] will be a shorthand notation for . 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). -The total distance it travels is

On occasion, the notation will be a shorthand notation for . The three forces shown act on a particle. Use this exhibit to answer the following question(s). -What is the magnitude of the resultant of these three forces?

On occasion, the notation will be a shorthand notation for . The three forces shown act on a particle. Use this exhibit to answer the following question(s). -What is the direction of the resultant of these three forces?

On occasion, the notation = [A, θ] will be a shorthand notation for . The vectors and are shown below. Use this exhibit to answer the following question(s). -Which diagram below correctly represents ?