SENIOR HIGH SCHOOL
General Physics1
Quarter 1 – Module 2:
Title: Vectors
Science – Grade 12
Alternative Delivery Mode
Quarter 1 – Module 2: Vectors
First Edition, 2020
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12
General Physics1
Quarter 1 – Module 2:
Vectors
Introductory Message
For the facilitator:
Welcome to the General Physics 1 12 Alternative Delivery Mode (ADM) Module on
Vectors!
This module was collaboratively designed, developed and reviewed by educators both
from public and private institutions to assist you, the teacher or facilitator in helping
the learners meet the standards set by the K to 12 Curriculum while overcoming their
personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of the
module:
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module. You
also need to keep track of the learners' progress while allowing them to manage their
own learning. Furthermore, you are expected to encourage and assist the learners as
they do the tasks included in the module.
2
For the learner:
Welcome to the General Physics 1 12 Alternative Delivery Mode (ADM) Module on
Vectors!
The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner is
capable and empowered to successfully achieve the relevant competencies and skills at
your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know
What I Know
What’s In
This will give you an idea of the skills or
competencies you are expected to learn in the
module.
This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New
In this portion, the new lesson will be
introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity or a situation.
What is It
This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More
This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.
What I Have Learned
This
includes
questions
or
blank
sentence/paragraph to be filled in to process
what you learned from the lesson.
What I Can Do
This section provides an activity which will
help you transfer your new knowledge or skill
into real life situations or concerns.
3
Assessment
This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
Additional Activities
In this portion, another activity will be given
to you to enrich your knowledge or skill of the
lesson learned. This also tends retention of
learned concepts.
Answer Key
This contains answers to all activities in the
module.
At the end of this module you will also find:
References
This is a list of all sources used in developing
this module.
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not hesitate
to consult your teacher or facilitator. Always bear in mind that you are not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
4
What I Need to Know
This module was designed and written with you in mind. It is here to help you master
the Vectors. The scope of this module permits it to be used in many different learning
situations. The language used recognizes the diverse vocabulary level of students. The
lessons are arranged to follow the standard sequence of the course. But the order in
which you read them can be changed to correspond with the textbook you are now
using.
The module is divided into one lesson with subtopics, namely:
●
Lesson 1 – Vectors
✔ Vectors and scalars
✔ Addition of Vectors
After going through this module, you are expected to:
1.
2.
3.
4.
5.
define scalar and vector quantity;
differentiate vector and scalar quantities;
classify the physical quantities as scalar and vector quantity;
determine the magnitude and direction of a given vector; and
perform addition of vectors
5
What I Know
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.
1. Which of the following is an example of a vector quantity?
a. acceleration
c. volume
b. mass
d. temperature
2. Displacement is a
a. base quantity
c. scalar quantity
b. derived quantity
d. vector quantity
3. Identify the following quantities as scalar or vector: the mass of an object, the
number of leaves on a tree and wind velocity.
a. vector, scalar, scalar
c. scalar, scalar, vector
b. vector, scalar, vector
d. scalar, vector, vector
4. If two forces 20 N towards North and 12 N towards South are acting on an
object. What will be the resultant force?
a. 32 N North
b. 20 N South
c. 32 N South
d. 8 N North
5. A student adds two displacement vectors with magnitudes of 3 m and 4 m
respectively. Which one of the following could not be a possible choice for the
resultant?
a. 1.3 m
b. 3.3 m
c. 5 m
d. 6.8 m
6. Find the displacement a hiker walks if he travels 9.0 km north, and then
turns around and walks 3.0 km south?
a. 0.5 km
c. 6.0 km
b. 3.0 km
d. 12.0 km
6
7. A runway dog walks 0.64 km due N. He then runs due W to a hot dog stand.
If the magnitude of the dog’s total displacement vector is 0.91 km, what is the
magnitude of the dog’s displacement vector in the due west direction?
a. 0.27 km
b. 0.33 km
c. 0.41 km
d. 0.52 km
8. An escaped convict runs 1.70 km due East of the prison. He then runs due
North to a friend’s house. If the magnitude of the convict’s total displacement
vector is 2.50 km, what is the direction of his total displacement vector with
respect to due East?
a. 340 SE
b. 430 SE
c. 470 NE
d. 560 NE
9. Two vectors A and B are added together to form a vector C. The relationship
between the magnitudes of the vectors is given by A + B = C. Which one of the
following statements concerning these vectors is true?
a. A and B must be displacements
b. A and B must have equal lengths
c. A and B must point in opposite directions
d. A and B point in the same direction
10. Which expression is FALSE concerning the vectors are shown in the sketch?
C
B
A
a. C = A + B
b. C + A = -B
c. A + B + C = 0
d. C  A + B
11. How to add vectors graphically?
a. put them in line
c. put them tip to tip
b. put them tail to tail
d. put them tip to tail
12. Which of the following is the definition of vector?
a. a quantity that has only magnitude
7
b. a quantity that has both magnitude and direction.
c. a quantity that has only one direction
d. a quantity that has magnitude but may or may not have direction
13.
Which of the following answer contains two scalar quantities and one vector
quantity?
a. mass, displacement, time
c. temperature, displacement, force
b. momentum, velocity, acceleration
d. time, length, mass
14. A boy walks far 5km along a direction 530 West of North. Which of the following
journeys would result in the same displacement?
15.
a. 4km N, 3 km W
c. 3 km N, 2 km W
b. 4 km W, 3 km W
d. 3 km N, 4 km W
Which procedure should NOT be considered in finding the resultant vector
graphically?
a. use component method
c. use ruler and protractor
b. use head to tail method
d. use scale
Lesson
Vectors
8
1
We come into contact with many physical quantities in the natural world on a
daily basis. For example, things like time, mass, weight, force, and electric charge, are
physical quantities with which we are all familiar. We know that time passes and
physical objects have mass. Things have weight due to gravity. We exert forces when we
open doors, walk along the street and kick balls. We experience electric charge directly
through static shocks in winter and through using anything which runs on electricity.
There are many physical quantities in nature, and we can divide them up into
two broad groups called vectors and scalars.
What’s In
Which of the following contains two vectors and a scalar?
a. distance, acceleration, speed
b. displacement, velocity, acceleration
c. distance, mass, speed
d. displacement, speed, velocity
Notes to the Teacher
It is significant that learners had background on the use ruler and
protractor in measurement.
9
What’s New
Scalar
A scalar is a physical quantity that has only a magnitude (size).
For example, a person buys a tub of margarine which is labelled with a mass of 500 g.
The mass of the tub of margarine is a scalar quantity. It only needs one number to
describe it, in this case, 500 g.
Vectors are different because they are physical quantities which have a size and a
direction. A vector tells you how much of something there is and which direction it is
in.
Vector
A vector is a physical quantity that has both a magnitude and a direction.
For example, a car is travelling east along a freeway at 100 km/h. What we have here is
a vector called the velocity. The car is moving at 100 km/h (this is the magnitude) and
we know where it is going – east (this is the direction). These two quantities, the
speed and direction of the car, (a magnitude and a direction) together form a vector we
call velocity.
Examples of scalar quantities:
●
mass has only a value, no direction
●
electric charge has only a value, no direction
Examples of vector quantities:
●
force has a value and a direction. You push or pull something with some strength
(magnitude) in a particular direction
●
weight has a value and a direction. Your weight is proportional to your mass
(magnitude) and is always in the direction towards the center of the earth.
10
What is It
Vectors are different to scalars and must have their own notation. There are many ways
of writing the symbol for a vector. In this book vectors will be shown by symbols with
an arrow pointing to the right above it. For example, F⃗, W⃗ and v⃗ represent the vectors
of force, weight and velocity, meaning they have both a magnitude and a direction.
Sometimes just the magnitude of a vector is needed. In this case, the arrow is omitted.
For the case of the force vector:
F⃗ represents the force vector
F represents the magnitude of the force vector
Graphical representation of vectors
Vectors are drawn as arrows. An arrow has both a magnitude (how long it is) and a
direction (the direction in which it points). The starting point of a vector is known as
the tail and the end point is known as the head.
Another common method of expressing directions is to use the points of a compass:
North, South, East, and West. If a vector does not point exactly in one of the compass
directions, then we use an angle. For example, we can have a vector pointing 40° North
of West. Start with the vector pointing along the West direction (look at the dashed arrow
below), then rotate the vector towards the north until there is a 40° angle between the
vector and the West direction (the solid arrow below). The direction of this vector can
also be described as: W 40° N (West 40° North); or N 50° W (North 50° West).
Downloaded from
and-scalars-0
https://www.siyavula.com/read/science/grade-10/vectors-and-scalars/20-vectors-
Drawing vectors
11
In order to draw a vector accurately we must represent its magnitude properly and
include a reference direction in the diagram. A scale allows us to translate the length of
the arrow into the vector's magnitude. For instance, if one chooses a scale of 1 cm = 2
N (1 cm represents 2 N), a force of 20 N towards the East would be represented as an
arrow 10 cm long pointing towards the right. The points of a compass are often used to
show direction or alternatively an arrow pointing in the reference direction.
Method: Drawing Vectors
1. Decide upon a scale and write it down.
2. Decide on a reference direction
3. Determine the length of the arrow representing the vector, by using the scale.
4. Draw the vector as an arrow. Make sure that you fill in the arrow head.
5. Fill in the magnitude of the vector.
Vector Addition
Graphical techniques involve drawing accurate scale diagrams to denote individual
vectors and their resultants. We will look at just one graphical method: the head-to-tail
method.
Method: Head-to-Tail Method of Vector Addition
1. Draw a rough sketch of the situation.
2. Choose a scale and include a reference direction.
3. Choose any of the vectors and draw it as an arrow in the correct direction and of the
correct length – remember to put an arrowhead on the end to denote its direction.
4. Take the next vector and draw it as an arrow starting from the arrowhead of the first
vector in the correct direction and of the correct length.
5. Continue until you have drawn each vector – each time starting from the head of the
previous vector. In this way, the vectors to be added are drawn one after the other headto-tail.
6. The resultant is then the vector drawn from the tail of the first vector to the head of
the last. Its magnitude can be determined from the length of its arrow using the scale.
Its direction too can be determined from the scale diagram.
12
What’s More
Activity 1
Categorize each quantity as being either a vector or a scalar.
1. 10 km
2. 60 km/h South
3. 40 mi downward
4. 50 calories
5. 250 bytes
6. 500 m/s NE
7. -9.8 m/s2
8. 1000 kg
9. 1 hour
10. 120 m/s SW
____________________
____________________
____________________
____________________
____________________
____________________
____________________
____________________
____________________
____________________
Activity 2
Determine the magnitude and direction of the following vectors using a ruler and
protractor. Use the scale:1 cm = 10 m/s
1.
2.
13
3.
4.
Activity 3
Accurately draw scaled vector diagram to represent the magnitude and direction of the
following vectors on a graphing paper.
1. 50 m 300
Scale: 1cm = 10m
2.
60 m 1500
Scale: 1cm = 10m
14
3.
140 m/s 2000
Scale: 1cm = 20m
4.
120 m/s 2400
Scale: 1cm = 15m/s
5.
35 m/s 2700
Scale: 1cm = 5m/s
Activity 4
Determine the resultant of the following:
1.
30 cm W and 75 cm N
2.
2km E and 4.5 km S
15
What I Have Learned
1. A scalar is a physical quantity with magnitude only.
2. A vector is a physical quantity with magnitude and direction.
3. Vectors may be represented as arrows where the length of the arrow indicates
the magnitude and the arrowhead indicates the direction of the vector.
4. The resultant vector is the single vector whose effect is the same as the
individual vectors acting together.
16
What I Can Do
Give the magnitude and direction from your house to school.
resultant vector.
17
Calculate the
Assessment
Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.
1. Which of the following is an example of a vector quantity?
a. acceleration
c. volume
b. mass
d. temperature
2. Displacement is a
a. base quantity
b. derived quantity
c. scalar quantity
d. vector quantity
3. Identify the following quantities as scalar or vector: the mass of an object, the
number of leaves on a tree and wind velocity.
a. vector, scalar, scalar
c. scalar, scalar, vector
b. vector, scalar, vector
d. scalar, vector, vector
4. If two forces 20 N towards North and 12 N towards South are acting on an
object. What will be the resultant force?
a. 32 N North
b. 20 N South
c. 32 N South
d. 8 N North
5. A student adds two displacement vectors with magnitudes of 3 m and 4 m
respectively. Which one of the following could not be a possible choice for the
resultant?
a. 1.3 m
b. 3.3 m
c. 5 m
d. 6.8 m
6. Find the displacement a hiker walks if he travels 9.0 km north, and then
turns around and walks 3.0 km south?
a. 0.5 km
c. 6.0 km
b. 3.0 km
d. 12.0 km
7. A runway dog walks 0.64 km due N. He then runs due W to a hot dog stand.
If the magnitude of the dog’s total displacement vector is 0.91 km, what is the
magnitude of the dog’s displacement vector in the due west direction?
a. 0.27 km
b. 0.33 km
c. 0.41 km
d. 0.52 km
8. An escaped convict runs 1.70 km due East of the prison. He then runs due
North to a friend’s house. If the magnitude of the convict’s total displacement
18
vector is 2.50 km, what is the direction of his total displacement vector with
respect to due East?
a. 340 SE
b. 430 SE
c. 470 NE
d. 560 NE
9. Two vectors A and B are added together to form a vector C. The relationship
between the magnitudes of the vectors is given by A + B = C. Which one of the
following statements concerning these vectors is true?
a. A and B must be displacements
b. A and B must have equal lengths
c. A and B must point in opposite directions
d. A and B point in the same direction
10. Which expression is FALSE concerning the vectors are shown in the sketch?
C
B
A
a. C = A + B
b. C + A = -B
c. A + B + C = 0
d. C  A + B
11. How to add vectors graphically?
a. put them in line
c. put them tip to tip
b. put them tail to tail
d. put them tip to tail
12. Which of the following is the definition of vector?
a. a quantity that has only magnitude
b. a quantity that has both magnitude and direction.
c. a quantity that has only one direction
d. a quantity that has magnitude but may or may not have direction
13.
Which of the following answer contains two scalar quantities and one vector
quantity?
a. mass, displacement, time
c. temperature, displacement, force
19
b. momentum, velocity, acceleration
d. time, length, mass
14. A boy walks far 5km along a direction 530 West of North. Which of the following
journeys would result in the same displacement?
15.
a. 4km N, 3 km W
c. 3 km N, 2 km W
b. 4 km W, 3 km W
d. 3 km N, 4 km W
Which procedure should NOT be considered in finding the resultant vector
graphically?
a. use component method
c. use ruler and protractor
b. use head to tail method
d. use scale
Additional Activities
20
A. Draw each of the following vectors to scale. Indicate the scale that you have used.
Use graphing paper, pencil, pen, ruler and protractor.
1. 12 km south
2. 1.5 m N 450 W
3. 1 m/s 200 E of N
4. 50 km/h
5. 5 mm
B. Harold walks to school by walking 600 m Northeast and then 500 m N 40° W.
Determine his resultant displacement by using accurate scale drawings.
C. A frog is trying to cross a river. It swims at 3 m/s in a northerly direction towards
the opposite bank. The water is flowing in a westerly direction at 5 m/s. Find the frog's
resultant velocity by using appropriate calculations. Include a rough sketch of the
situation in your answer.
D. Adrianne walks to the shop by walking 500 m Northwest and then 400 m N 30°
Determine her resultant displacement by doing appropriate calculations.
Answer Key
21
What I Know
B
22
What's More
Activity 1
Assessment
B
1. scalar
D
C
D
2. vector
3. vector
C
4. scalar
D
B
D
5. scalar
6. vector
B
7. vector
C
C
C
8. scalar
9. scalar
C
10. vector
B
C
Activity 2
1. 30 m/s 450 N of E
B
C
2. 30 m/s 450 S of E
C
D
3. 30 m/s 200 S of E
4. 30 m/s 200 S of W
C
D
Activity 4
B
A
1. 80.78 cm 980 N of W
2. 4.92 cm 200 S of E
B
A
D
References
Tabujara Jr., Geronimo D. K-12 Compliant Worktext for Senior High School General
Physics 1. Manila, Philippines: JFS Publishing Services
23
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