Question 1

You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

Accepted Answer

A)  87 m 
B)  50 m 
C)  94 m 
D)  46 m 
A)  87 m 
B)  50 m 
C)  94 m 
D)  46 m

Question 2

Which of the following is an accurate statement?

Accepted Answer

A)  The magnitude of a vector can be zero even though one of its components is not zero. 
B)  It is possible to add a scalar quantity to a vector. 
C)  Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. 
D)  Rotating a vector about an axis passing through the tip of the vector does not change the vector. 
E)  The magnitude of a vector is independent of the coordinate system used. 
A)  The magnitude of a vector can be zero even though one of its components is not zero. 
B)  It is possible to add a scalar quantity to a vector. 
C)  Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. 
D)  Rotating a vector about an axis passing through the tip of the vector does not change the vector. 
E)  The magnitude of a vector is independent of the coordinate system used.

Question 3

For the vectors shown in the figure, express vector   
in terms of vectors   
and   
.

Accepted Answer

The answer of For the vectors shown in the figure,...

Question 4

A teacher sends her students on a treasure hunt. She gives the following instructions:
1. Walk 300 m north
2. Walk 400 m northwest
3. Walk 700 m east-southeast and the treasure is buried there.
As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?

Accepted Answer

A)  187 m in a direction 67.3° north of east 
B)  481 m in a direction 40.9° north of east 
C)  399 m in a direction 52.5° north of east 
D)  284 m in a direction 28.2° west of north 
E)  The treasure position cannot be reached in one straight walk. 
A)  187 m in a direction 67.3° north of east 
B)  481 m in a direction 40.9° north of east 
C)  399 m in a direction 52.5° north of east 
D)  284 m in a direction 28.2° west of north 
E)  The treasure position cannot be reached in one straight walk.

Question 5

If the eastward component of vector   is equal to the westward component of vector  
And their northward components are equal. Which one of the following statements about these two vectors is correct?

Accepted Answer

A)  Vector   is parallel to vector   . 
B)  Vectors   and   point in opposite directions. 
C)  Vector   is perpendicular to vector   . 
D)  The magnitude of vector   is equal to the magnitude of vector   . 
E)  The magnitude of vector   is twice the magnitude of vector   . 
A)  Vector   is parallel to vector   . 
B)  Vectors   and   point in opposite directions. 
C)  Vector   is perpendicular to vector   . 
D)  The magnitude of vector   is equal to the magnitude of vector   . 
E)  The magnitude of vector   is twice the magnitude of vector   .

Question 6

An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point.

Accepted Answer

A)  79 km 
B)  81 km 
C)  82 km 
D)  78 km 
E)  76 km 
A)  79 km 
B)  81 km 
C)  82 km 
D)  78 km 
E)  76 km

Question 7

An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?

Accepted Answer

A)  5.5 m/s 
B)  8.7 m/s 
C)  12 m/s 
D)  15 m/s 
A)  5.5 m/s 
B)  8.7 m/s 
C)  12 m/s 
D)  15 m/s

Question 8

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

Accepted Answer

A)  8.9 m/s 
B)  220 m/s 
C)  435 m/s 
D)  444 m/s 
A)  8.9 m/s 
B)  220 m/s 
C)  435 m/s 
D)  444 m/s

Question 9

If   = +4  
- 2  
- 3  
And  
= -4  
-2  
- 3  
, which of the following numbers is closest to the magnitude of  
-  
?

Accepted Answer

A)  8 
B)  7 
C)  9 
D)  10 
E)  11 
A)  8 
B)  7 
C)  9 
D)  10 
E)  11

Question 10

Under what condition is |   -  
| = A + B?

Accepted Answer

A)  The magnitude of vector   is zero. 
B)  Vectors   and   are in opposite directions. 
C)  Vectors   and   are in the same direction. 
D)  Vectors   and   are in perpendicular directions. 
E)  The statement is never true. 
A)  The magnitude of vector   is zero. 
B)  Vectors   and   are in opposite directions. 
C)  Vectors   and   are in the same direction. 
D)  Vectors   and   are in perpendicular directions. 
E)  The statement is never true.

Question 11

As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are   = 80.0 N,  
= 60.0 N, and  
= 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

Accepted Answer

A)  180 N at an angle 60.0° with respect to +x-axis. 
B)  60.0 N at an angle 90.0° with respect to +x-axis. 
C)  20.0 N at an angle 34.3° with respect to +x-axis. 
D)  35.5 N at an angle 34.3° with respect to +x-axis. 
E)  40.0 N at an angle 60.0° with respect to +x-axis. 
A)  180 N at an angle 60.0° with respect to +x-axis. 
B)  60.0 N at an angle 90.0° with respect to +x-axis. 
C)  20.0 N at an angle 34.3° with respect to +x-axis. 
D)  35.5 N at an angle 34.3° with respect to +x-axis. 
E)  40.0 N at an angle 60.0° with respect to +x-axis.

Question 12

If all the components of a vector are equal to 1, then that vector is a unit vector.

Accepted Answer

A) True 
 B)False

Question 13

Vector   
has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector   
has a magnitude of 25.0 cm and points along the negative x-axis. Vector   
has a magnitude of 40.0 cm and points at 45° below the negative x-axis.
(a) Determine the x and y components of Vector   
.
(b) Determine the x and y components of Vector   
.
(c) Determine the x and y components of Vector   
.
(d) Determine x and y components of the sum of these three vectors.
(e) Determine the magnitude and direction of the sum of these three vectors.

Accepted Answer

(a) @#IMG-DLM& = 65 cm, @#IMG-DLM& = 38 cm
(b) @#IMG-DLM& =

Exam 3: Vectors and Coordinate Systems

You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

Which of the following is an accurate statement?

For the vectors shown in the figure, express vector in terms of vectors and .

If the eastward component of vector is equal to the westward component of vector And their northward components are equal. Which one of the following statements about these two vectors is correct?

An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point.

An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

If = +4 - 2 - 3 And = -4 -2 - 3 , which of the following numbers is closest to the magnitude of - ?

Under what condition is | - | = A + B?

As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

If all the components of a vector are equal to 1, then that vector is a unit vector.

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

Nuclear Physics

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