2.1 Vector Methods In One Dimension

Question 1

What is one of the fastest-growing sports in the world today?

Answer 1

Snowshoeing

Snowshoeing is noted for its minimal equipment requirements and ease of learning.

Question 2

What are the cardiovascular benefits of snowshoeing?

Answer 2

You can burn up to 1000 calories per hour

This makes snowshoeing an excellent cross-training program for athletes.

Question 3

What allows athletes to explore different terrains and gain a greater appreciation of the outdoors?

Answer 3

Snowshoeing

It also helps athletes test their limits, especially in endurance races.

Question 4

In which dimension can the motions in a snowshoe race be broken up?

Answer 4

One-dimensional

This section focuses on studying motion in one dimension using vectors.

Question 5

What do vector diagrams help visualize?

Answer 5

The motion of an object

Properly drawn vector diagrams enable accurate addition of vectors and determination of an object’s position.

Question 6

What does a line segment with an arrowhead represent in a vector diagram?

Answer 6

A vector quantity

The point of origin is called the tail, and the terminal point is the tip.

Question 7

What indicates the direction of a vector in a vector diagram?

Answer 7

The arrowhead

The length of the line segment depends on the vector’s magnitude.

Question 8

Fill in the blank: The length of the line segment in a vector diagram depends on the vector’s _______.

Answer 8

[magnitude]

This relationship is crucial for accurately representing vector quantities.

Question 9

True or False: Vector diagrams can only represent motion in two dimensions.

Answer 9

False

This section specifically addresses one-dimensional motion using vectors.

Question 10

What are some adjectives used to describe the direction of an object’s motion?

Answer 10

Forward, backward, up, down, into, out of, left, right

These adjectives help in clearly defining the direction of motion.

Question 11

What compass directions are commonly used in vector diagrams?

Answer 11

North [N], South [S], East [E], West [W]

These directions can be used to describe motion in a more standardized manner.

Question 12

Which directions are usually designated as positive in this unit?

Answer 12

Forward, up, right, north, east

Positive directions are chosen for consistency in vector representation.

Question 13

What is important to communicate when solving problems involving vectors?

Answer 13

The reference direction must be consistent and clearly communicated

This ensures clarity in the solution process and avoids confusion.

Question 14

What are collinear vectors?

Answer 14

Vectors that lie along the same straight line

They may point in the same or in opposite directions.

Question 15

How can vectors be added?

Answer 15

Graphically and algebraically

Vectors can be added as long as they represent the same quantity or measurement.

Question 16

What must be true for vectors to be added together?

Answer 16

They must represent the same types of quantities and have the same units

This is similar to adding like terms in mathematics.

Question 17

What is the sum of a series of vectors called?

Answer 17

Resultant vector

It is drawn from the tail of the first vector to the tip of the last vector.

Question 18

Fill in the blank: A vector drawn from the tail of the first vector to the tip of the last vector is called a _______.

Answer 18

resultant vector

This concept is crucial in understanding how to combine multiple vectors.

Question 19

What should you do before adding vectors with different units?

Answer 19

Convert the units of one of the vectors

This ensures that both vectors are expressed in the same units for accurate addition.

Question 20

What is the process for adding vectors?

Answer 20

Connect them tip to tail

The plus sign in a vector equation indicates to connect the vectors in a vector diagram.

Question 21

What is the total distance covered by the rugby team?

Answer 21

115 m

This includes all the forward and backward movements combined.

Question 22

What is the displacement of the rugby team after all sprints?

Answer 22

35 m [forward]

Displacement considers the net change in position, not the total distance traveled.

Question 23

How do you subtract collinear vectors graphically?

Answer 23

Two methods:
* Add the negative of one vector to the other tip to tail
* Connect the vectors tail to tail

The negative of a vector points in the opposite direction of the original vector.

Question 24

In the first method of vector subtraction, what is the equation used?

Answer 24

Ad = d1 - d2

This equation represents the resultant vector as the difference between two vectors.

Question 25

What does the negative of a vector create?

Answer 25

A new vector that points in the opposite direction ## Footnote This is essential for graphical vector subtraction.

Question 26

What is the scale conversion for measuring the resultant vector in Figure 2.9?

Answer 26

Convert the measured value using the scale and include the direction ## Footnote This process is crucial for accurately determining the magnitude and direction of vectors.

Question 27

Fill in the blank: To find the magnitude of the resultant vector, you measure with a _______.

Answer 27

ruler ## Footnote Measuring with a ruler helps determine the length of the vector in a diagram.

Question 28

What is the significance of the tip of the last vector in vector addition?

Answer 28

It indicates where the resultant vector ends ## Footnote The tip of the last vector connects to the resultant vector, showing the overall direction and magnitude.

Question 29

What is the definition of displacement?

Answer 29

Final position minus initial position ## Footnote Displacement is calculated using the formula Ad = d - d.

Question 30

In the example of sprinting drills, how far does the sprinter run initially?

Answer 30

40.0 m [N]

Question 31

What is the total distance the sprinter covers after running, walking, and sprinting?

Answer 31

160.0 m [N]

Question 32

How far is the sailboat initially positioned from the buoy?

Answer 32

15 m [right]

Question 33

What distance does the sailboat sail to determine its displacement?

Answer 33

35 m [left]

Question 34

Calculate the sailboat's displacement algebraically.

Answer 34

-50 m

Question 35

In terms of direction, what does a negative displacement indicate?

Answer 35

To the left

Question 36

What is the first movement of the basketball player in the give and go?

Answer 36

0.75 m [right]

Question 37

What is the second movement of the basketball player in the give and go?

Answer 37

3.50 m [left]

Question 38

What distance does the bricklayer's hand sweep back and forth?

Answer 38

1.70 m

Question 39

How many times does the bricklayer sweep her hand back and forth?

Answer 39

Four times

Question 40

Fill in the blank: To find displacement algebraically, use the equation Ad = d - _______.

Answer 40

d

Question 41

When finding displacement graphically, how are the position vectors arranged?

Answer 41

Tail to tail

Question 42

What does the resultant vector represent in the graphical method of finding displacement?

Answer 42

The displacement from the tip of the initial position vector to the tip of the final position vector

Question 43

What scale is used in the graphical representation of displacement?

Answer 43

1.0 cm : 10 m

Question 44

True or False: The sailboat's displacement is 50 m to the right.

Answer 44

False

Question 45

How do you find displacement for collinear vectors?

Answer 45

By subtracting initial position from final position.

Question 46

What is one method to subtract vectors graphically?

Answer 46

By connecting them tail to tail.

Question 47

What is another method to subtract vectors graphically?

Answer 47

By reversing the direction of the initial position vector.

Question 48

In which chapter is the direction for displacement discussed?

Answer 48

Chapter 1.

Question 49

The direction for displacement is given with respect to _______.

Answer 49

[initial position].