Question 1

Components: 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 2

Addition and subtraction: You walk 53 m to the north, then turn 60° to your right and walk another   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 3

Addition and subtraction: 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 4

Components: 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 5

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

Accepted Answer

The answer of Addition and subtraction: For the vectors shown...

Question 6

Unit vectors: 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 7

Addition and subtraction: 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 8

Components: 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 9

Vector (cross) product: If two vectors are perpendicular to each other, their cross product must be zero.

Accepted Answer

A) True 
 B)False

Question 10

Components: 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 11

Scalar (dot) product: Two boys searching for buried treasure are standing underneath the same tree. One boy walks   east and then   north. The other boy walks   west and then   north. Find the scalar product of their net displacements from the tree.

Accepted Answer

The answer of Scalar (dot) product: Two boys searching for...

Question 12

Components: 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 13

Components: 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) A_x = 65 cm, A_y = 38 cm (b) B

Question 14

Addition and subtraction: 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

Question 15

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

Accepted Answer

A) True 
 B)False

Exam 2: Motion Along a Straight Line

Components: Which of the following is an accurate statement?

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

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

Components: 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.

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

Unit vectors: What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ?

Addition and subtraction: Under what condition is | - | = A + B?

Components: 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 (cross) product: If two vectors are perpendicular to each other, their cross product must be zero.

Scalar (dot) product: Two boys searching for buried treasure are standing underneath the same tree. One boy walks east and then north. The other boy walks west and then north. Find the scalar product of their net displacements from the tree.

Components: 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?

Addition and subtraction: 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?

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

Motion in Two or Three Dimensions

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Applying Newtons Laws

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The First Law of Thermodynamics

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