Admmodule Stem Gp12v Ia 8 9
Admmodule Stem Gp12v Ia 8 9
Admmodule Stem Gp12v Ia 8 9
General Physics1
Quarter 1 – Module 2:
Title: Vectors
Science – Grade 12
Alternative Delivery Mode
Quarter 1 – Module 2: Vectors
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work
of the Government of the Philippines. However, prior approval of the government agency or
office wherein the work is created shall be necessary for exploitation of such work for profit.
Such agency or office may, among other things, impose as a condition the payment of
royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,
trademarks, etc.) included in this module are owned by their respective copyright holders.
Every effort has been exerted to locate and seek permission to use these materials from
their respective copyright owners. The publisher and authors do not represent nor claim
ownership over them.
General Physics1
Quarter 1 – Module 2:
Vectors
Introductory Message
For the facilitator:
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:
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:
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.
What I Need to Know This will give you an idea of the skills or
competencies you are expected to learn in
the module.
3
process what you learned from the lesson.
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.
5
What I Know
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.
2. Displacement is a
a. base quantity c. scalar quantity
b. derived quantity d. vector quantity
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
10. Which expression is FALSE concerning the vectors are shown in the
sketch?
a. C = A + B b. C + A = -B c. A + B + C = 0 d. C A + B
7
12. Which of the following is the definition of vector?
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?
14. A boy walks far 5km along a direction 53 0 West of North. Which of the
following journeys would result in the same displacement?
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
15. Which procedure should NOT be considered in finding the resultant vector
graphically?
8
Lesson
1 Vectors
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
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.
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:
11
Drawing vectors
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.
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.
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.
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 head-to-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
5. 35 m/s 2700
Scale: 1cm = 5m/s
14
Activity 4
1. 30 cm W and 75 cm N
15
What I Have Learned
16
What I Can Do
Give the magnitude and direction from your house to school. Calculate the
resultant vector.
17
Assessment
Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.
2. Displacement is a
a. base quantity c. scalar quantity
b. derived quantity d. vector quantity
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
18
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
10. Which expression is FALSE concerning the vectors are shown in the
sketch?
a. C = A + B b. C + A = -B c. A + B + C = 0 d. C A + B
d. a quantity that has magnitude but may or may not have direction
19
13. Which of the following answer contains two scalar quantities and one vector
quantity?
14. A boy walks far 5km along a direction 53 0 West of North. Which of the
following journeys would result in the same displacement?
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
15. Which procedure should NOT be considered in finding the resultant vector
graphically?
20
Additional Activities
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.
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.
21
Answer Key
2. D 1. scalar 2. D
2. vector
3. C 3. C
3. vector
4. D 4. D
4. scalar
5. B 5. B
5. scalar
6. C 6. vector 6. C
7. C 7. vector 7. C
8. scalar
8. B 8. B
9. scalar
9. C 9. C
10. vector
10. C 10. C
Activity 2
11. D 1. 30 m/s 450 N of E 11. D
22
References
Tabujara Jr., Geronimo D. K-12 Compliant Worktext for Senior High School
General Physics 1. Manila, Philippines: JFS Publishing Services
23
For inquiries or feedback, please write or call: