Lesson #4

LESSON #4

E.Q: How do the properties and differences between vectors and scalars influence our understanding and description of the physical phenomena in the world?

Vectors​

Multiple Choice

Choose which is NOT a vector quantity

• volume

• velocity

• acceleration

• force

SI units and conversions

Other systems of units

1 meter = 1 x109 nanometers (nm)

1 miles (mi) = 1609.34 meter

1 kg = 2.20 lbs

1 year = 365.25 days

1 day = 24 hrs

1 hr = 3600 sec

1 min = 60 sec

Main conversions

The meters can
be change by
grams and the
conversions

will be the

same.

sinθ = Opposite _

Hypotenuse

cosθ = Adjacent _

Hypotenuse

tanθ = Opposite _

Adjacent

Equations for triangles

θ

This goes in the
section for side

equations

θ =sin-1 Opposite _

Hypotenuse

θ =cos-1 Adjacent _

Hypotenuse

θ =tan-1 Opposite _

Adjacent

Equations for triangles

θ

This goes in the
section for angle

equations

A lakefront drops off gradually at an angle. To provide
some info about the depth, a lifeguard rows straight
out from the shore a distance of 14m and drops a
weighted fishing line. By measuring its length, he
determines the depth to be 2.25m. (a) What is the
value of the angle? (b) What would be the depth of the
lake at a distance of 22m from the shore?

Example 2

Vectors

Vectors

1. Vector is a quantity that has magnitude and direction.

2. Scalar has magnitude without direction.

3. Magnitude = size (how big it is)

4. Direction = where the arrow is pointing (left, right, North,

South, 90 degrees, 240 degrees)

5. Resultant = final vector that results from the addition or

subtraction of multiple vectors

tail

head

vector

Mention different examples of:

Vectors

Scalars

Velocity
Displacement
Acceleration
Force
Impulse
Momentum

Time
Distance
Speed
Temperature
Work
Electrical Charge

EOC question

Remember to always use directions

90°

0°

180°

270°

Add this in
your notes.
Is REALLY
IMPORTANT
for vectors.

How to draw vectors?

Rules:
1. Draw the 1st vector.
2. The 2nd vector will always start where the 1st one

ends.

3. The resultant will form connecting the tail of the first

vector with head of the last one.

Ex.1:

A

B

Resultant

How to draw vectors?
Rules:
1. Draw the 1st vector.

2. The 2nd vector will always start where the 1st one

ends.

3. The resultant will form connecting the tail of the first

vector with head of the last one.

Ex. 2:
A

B
C

Resultant

Rules to add vectors mathematically

Rules to add vectors and scalars

Ex #1: A + B = R

Ex #2: A + (-B) = R

Ex #3: A + (-C) = 0

Ex #4: R = √A2 + B2

Find the values for
each examples if:
A = 12
B = 5
C = 12

Vector Practice Worksheet

� 1. If we add two displacement vectors with

magnitudes of 20 km and 9km. What will be
the maximum and minimum we can have?
Give ALL the possible answers (this means you
must find all the answers in different
directions).

Vector Practice Worksheet

�2. Add the following vectors. Use the

rules to draw them and add them
(mathematically). Find the magnitude of
the resultant vector and the direction.

�Vector A = 10 m North

�Vector B = 6m South

�Vector C = 13 m East

Vector Practice Worksheet

� 3. Train station #1 lies 13 km north

from train station #2. Train station
#3 lies 18.5km west away from
station #2. If we want to connect
stations 1 and 3, what will be
distance of the railroad track that
will connect them?

� Solve the problem, draw vectors

and give a direction to the resultant.

2

1

3

Check your answers

Problem #1 (Answer)

� If we add two displacement vectors with

magnitudes of 20 km and 9km. What will be
the maximum and minimum we can have?
Give all the possible answers (find different
directions).

� +/- 29 km
� +/- 11km
� 21.93 km

Problem #2 (Answer)

�Add the following vectors. Use the rules to draw

them and add them (mathematically). Find the
magnitude of the resultant vector and the
direction.

�Vector A = 10 m North

�Vector B = 6m South

�Vector C = 13 m East

� Answer: 13.6 m and the direction is 17.1°
� (internal angle will be 72.89°)

R

Problem #3 (Answer)

� Train station #1 lies 13 km north

from train station #2. Train station
#3 lies 18.5km west away from
station #2. If we want to connect
stations 1 and 3, what will be
distance of the railroad track that
will connect them?

� Solve the problem, draw vectors

and give a direction to the resultant.

�
� Answer: 22.61 km and the direction

is 35.1° from 3-1 and 54.9° from 1-3

2

1

3

R

Vectors Components

How do we find vector components?

Component in X

Component in Y

35°
A

Ax

35°

Ay

Component in Y

How do we find vector components?
(create a table in your notebook similar to this)

When you have components

When you have the angle and the
vector

Page 16 of the
notebook

How do we find vector components?
(create a table in your notebook similar to this)

When you have components (Ax and Ay)

When you have the angle and the
vector

� To find Ax we use: Ax = A cos Ѳ

� To find Ay we use: Ay = A sin Ѳ

A
Ay

Ax

Ay

Ax

A

Think about it...

Which of the following

vectors have the
same y-component
as vector a? How
long is the
y-component?

Solution

Answers:
b and c

Practice problems

1. Find the x and y components of a 10.5 m vector

with a 35º angle.

2. Find mathematically the components in x and y

for an applied force of 25 Newton at 56 degrees.
What will be the new force if the y-component is
doubled?

Practice Problems (Vector Jamboard)

3. Find the each component (x and y) of the
vectors if they have the following measures:

a. 467.54 m with an Ѳ = 48°

b. 23.09 Km with an Ѳ = 77°

4. If the horizontal component is 34.9m and the
vertical component is 53.2m, what will be the
magnitude and direction of the vector?

Practice problems (Answers)

1. Find the x and y components of a 10.5 m vector

with a 35º angle.
Ax =8.6m Ay =6.02m

2. Find mathematically the components in x and y

for an applied force of 25 Newton at 56 degrees.
What will be the new force if the y-component is
doubled?

Ax =13.98N Ay =20.73N / New A = 43.75N

Practice Problems (Answers)

Find the each component (x and y) of the vectors
if they have the following measures:

a. Ax = 312.85m, Ay =347.45m

b. Ax = 5.19km, Ay = 22.5km

If the horizontal component is 34.9m and the
vertical component is 53.2m, what will be the
magnitude and direction of the vector?

A = 63.63m, θ = 56.73°

Combination of multiple vectors at
different angles (Sec. 1.8)

IMPORTANT:If our vectors have different angles we

can’t add them directly. We have to find the
components first.

Find your cornell notes

Combination of multiple vectors at
different angles

Step #1: Find the individual components for each vector (A and B)

using trigonometric functions (sin and cos).

Components: Ax , Ay , Bx and By

Step #2: Add all the components in x together and all the y’s

together.

Rx = Ax + Bx and Ry = Ay + By

Test Review

Unit #1

Instructions

You will work with the review in your notebook.

Label the section you are working on.

The review is on Canvas in Unit #1 Module.

Do it on pages 18-19, find the

notebook presentation on

Canvas.

Kahoot practice review game

Link:
https://kahoot.it/challenge/05398496?challenge-
id=6750d3aa-b5f2-4304-9979-98458f673438_1
629915023358

Pin: 05398496

Test Today

Instructions:

Get your computer, calculator, notecards, scratch paper and pencil. Put your backpacks
at the back of the classroom.

Your test will be done through Lockdown Browser. Find it on your desktop.

I will provide you with the password as soon as everyone is ready.

When you finish your test, you can work on your notebook or missing work.

Remember the due date for the notebook is today but your late date is Monday. The due
date for missing work it TODAY.

Password

Test#12021A

Maybe I will use it or maybe I
won’t

Vector doodles review
We will fill out a section of this
document in class but you
must complete the rest as
review.

Drawing vectors section

How to draw vectors (this goes where the stairs are):

1.

Draw the compass

2.

Start at the center

3.

Measure the correct angle with a protractor

4.

Draw a thin straight line

5.

Measure with a ruler

6.

Finish with a small arrow

After the steps, at the end of the page, there is a practice problem.

This section explain
in more detail what
we discussed in the
last slides.

Adding vectors section

Steps:

Step #1: Draw the 1st vector using the proper steps.

Step #2: Begin the 2nd vector exactly where the 1st vector
ended.

Step #3: The resultant vector begins with the 1st vector
and ends with the 2nd.

Links

P-2 →https://tinyurl.com/P-2VectorsPractice

P-3→https://tinyurl.com/P-3VectorsPractice

P-4→https://tinyurl.com/P-4VerctorsPractice

P-5→https://tinyurl.com/P-5VectorsPractice

P-6→https://tinyurl.com/P-6VectorsPractice

P-7→https://tinyurl.com/P-7VectorsPractice

Bellwork from Monday August
23rd

What will be the size of a shadow cast by a
flag pole 5.5 m tall if the angle created by the
Sun and the floor is 38 degrees? Draw the
picture and solve.

Solve this in the small paper
you took at the beginning of

class. While you are working, I

will sign the HW.

Bellwork (Answer)

What will be the size of
a shadow cast by a flag
pole 5.5 m tall if the
angle created by the Sun
and the floor is 38
degrees? Draw the
picture and show work.

38°

5.5m

tanϴ = opp
adj
tan38 = 5.5m
x
X = 7.04m

x

● Homework #1: Scientific Method
● Go to Canvas to find it.
● Due date: Wednesday August 22nd

Scientific Method or Cycle of Scientific Thinking

1. Are your measurements (if you don’t understand the

difference, find the definition online):

● Precise?
● Accurate?
● Reliable?
2. Why?
3. You think your measurements will change if you remeasure the
objects with a ruler? Why?

Bellwork: As soon as you enter, take a bellwork
document and answer the following questions on
Thursday’s space

Change the next four slides to a quiz

Let’s Practice

▪ Mario studied how far room temperature water would spurt

out of a plastic milk carton when 3mm holes were punched at
different heights from the bottom of the container. Identify
the DEPENDENT variable

▪ 3mm holes
▪ Distant water traveled out of carton
▪ Different heights of the holes in the container
▪ Ice water from Iceland

Let’s Practice (Answer)

▪ Mario studied how far room temperature water would spurt

out of a plastic milk carton when 3mm holes were punched at
different heights from the bottom of the container. Identify
the DEPENDENT variable

▪ 3mm holes
▪ Distant water traveled out of carton
▪ Different heights of the holes in the container
▪ Ice water from Iceland

Let’s Practice

▪ Mr. McNiece wanted to see how different types of music

affected students’ pulse rates. He played different types of
music: heavy metal, rap, R&B, alternative, pop, country, and
classical. What CONSTANT should be considered when doing
this experiment?

▪ Amount of time the music was played
▪ Use all dead people
▪ Using a different student for each music type
▪ Types of music

Let’s Practice (Answer)

▪ Mr. McNiece wanted to see how different types of music

affected students’ pulse rates. He played different types of
music: heavy metal, rap, R&B, alternative, pop, country, and
classical. What CONSTANT should be considered when doing
this experiment?

▪ Amount of time the music was played
▪ Use all dead people
▪ Using a different student for each music type
▪ Types of music

Problem:

� Marcos wants to measure the movement of a slug moving in

a straight line on the sidewalk. He recorded the following
table. Find the displacement from 5 to 25 seconds. Find the
average velocity from 10 to 15 seconds

Time (sec)

Position (mm)

0

20

5

23.4

10

26.8

15

24.6

20

31.9

25

34

Bellwork (August 19, 2019)
(3 min)

List the main steps to the scientific method (6
steps at least).

I will need 4 students who
speak another language
besides english. You will
have to translate a
message you will receive in
a card in that language.

Class:

If they were scientists and
they need to share their
research, what will they do
to communicate with each
other?

Class role play

Finish presentations
As soon as you enter show the
work for your problem on the
board.

Bellwork (Aug 25)
5 min

● Find the x and y components of a

18.9 m vector with a 24.6º angle.

● How the main vector will change if

the components are reduced by
half? Is the direction going to
change?

Use any scratch paper you have
available to do it.

Bellwork (Answers)

● Find the x and y components of a 18.9

m vector with a 24.6º angle.
○ Ax = 17.18 m, Ay = 7.87 m

● How the main vector will change if the

components are reduced by half? Is
the direction going to change?
○ A = 9.45 m, The angle will not

change.

Bellwork (Tuesday August 20,2019)

1. Why do we need a common system in the

scientific community?

2. Summarize in 4 steps how would you

convert a number from one unit to the
other? If you want use 3km = _____mm as a
reference.

Activity #1: Scientific Method

Write LAB on the Thursday and Friday section of your bellwork.

Go to Canvas and create a copy of the document: Activity #1:
Scientific Method

This will be the format your group will follow for the assignment. One
member of the group will make a copy of it and share it with the rest.
This will be your first assignment and practice for future labs.

Title the assignment: P#_Class Assignment#1:Scientific Method_Last
names and Initials

Writing portion:

Purpose: You will develop your own experimental
procedure and measurements.

Your objective is to develop your own problem,
hypothesis, observations, experimental procedure, data
analysis and possible answers (“conclusions”).

At the end, you must have your own measuring system.

Instructions for the Activity #1: Scientific Method

Using the materials on the counter measure the
following objects (you can use each material once):

1. A shortest pinky fingernail (from your

table)

2. The length of the classroom
3. The height of a tallest person in the table
4. The vertical distance between each slat

from the window blinds

Activity (15 min)

List of materials to measure the
objects:

Paperclip

Pencil

Wood stick

Box of markers

Band-aid

Check your Activity #1 document

Make sure you have the measurements of each
object.

At least, 5 observations.

The problem and your predictions.

Write up to 4 steps to explain the process you
did in class.

You need

Computers

Notecards

Pencil

Calculators

**Backpack at the front of the classroom.

Quiz

Go on Canvas and find the quiz titled Quiz #1 in the
Modules section.

You will have 10 minutes to answer your quiz. You need
your conversion factors.

You will work on the version assigned to your seat
number. (Versions are on the next slide.)

Do the math on paper.

Versions

Version A

1

5

9

13

17

21

25

Version B

2

6

10

14

18

22

Version C

3

7

11

15

19

23

Version D

4

8

12

16

20

24

● Measure with a ruler in cm each object (box of

markers, pencil, etc.) you used on the activity.

● Record the actual measurement of the object.
● Create a conversion factor.
● Example: 1 eraser (horizontally) = 5.3 cm
● Convert each measurement you got to its actual

value in cm.

Activity: (Part II)

Height of the person = 28 ¾ erasers

Step #1: 28 ¾ erasers = 28.75 eraser

Step #2: Conversion factor → 1 eraser = 5.3cm

Step #3: Convert

28.75 erasers 5.3 cm = 152.4 cm

1 eraser

Example

Actual size is:
_________

Complete the following sections
in the Activity

● Your observations
● Your prediction (you can talked about what will happen if

you use a ruler instead of those materials)

● Procedure (at least 5 steps)
● Measurement scale (Ex. band-aid horizontally = 4.2cm)
● Conclusions (address you problem)
● Submit it through Canvas

Bellwork (Answers)

1. 2.36 Km = 2360m
2. 40 days = 3456000 seconds

Bellwork: (As soon as you enter, answer the
following questions on Monday’s section) (4 min)

Solve and show work:

1. 2.36 Km = _______m
2. 40 days = _______seconds

Each group will choose the problem and present it to the class.

Solving the problems

Bellwork (Thursday August 29, 2019)
(5 min) Start as soon as you enter!

� Find the resultant vector, the direction and

create the drawing for a person moving with
the following coordinates:

� 1050.6m with an Ѳ = 90°

� 30.5Km with an Ѳ = 180°

� 10 Km with an Ѳ = 360°

Bellwork (Thursday August 29, 2019)
Answer

Step #1: Convert the 1st coordinate from m to km.
Step #2: Draw your vectors.
Step #3: Classify your x’s and y’s based on your drawing. Subtract or add if
you have multiple vectors in the same axis.
Step #4: Use the total for your x’s and y’s and place it in the Pythagorean
theorem to find the magnitude of the resultant.
Step #5: Use the total for your x’s and y’s and find the direction using tan-1.
� Answer: 20.53 km and the direction is -87.1°

Bellwork (4 min)

What is the difference between a vector and a scalar?

Mention 2 examples of each.

Add the following vectors and determine the resultant
and its direction.

● 4.0 m/s, 90° and 2.0 m/s, 0° and 2.0 m/s, 270°

Bellwork (Answer)

Add the following vectors and determine the resultant and its
direction.

● 4.0 m/s, 90° and 2.0 m/s, 0° and 2.0 m/s, 270° (A: 2.83 m/s 45°)

Instructions

Go to the following link: https://tinyurl.com/Physics-InASecondLanguage
and read the article.

Discuss the following questions in your BBB group.

1.What is your perspective about the language barrier mention when we try to learn and teach
physics?

2.Do you think having a common language for scientific research affects the way we share
knowledge with other countries?

3.Why do you think was necessary to establish a common measuring system and language for
scientific research?

4.Is there any personal experience that relates to the article?

5.If you speak another language (other than english), try to talk using that language in you BBB small
group and see if other people can understand what you are saying.

Go on Canvas to find the EdPuzzle videos and answer
the questions.

Trigonometry (HW)

Example 1

R

A

B

Each vector has a
different magnitude
and direction. To add
them we have to look
for the components.

A=20

B=32

θa=50°

θb = 65°

Step #1:

Components

of A

Ax = A cosθ
Ay = A sinθ

A=20
θa=50°

Step #2:

Components of B

Bx = B cosθ
By = B sinθ

B=32
θb = 65°

If the components
are in the same
axis (x or y) they
will be grouped
together.

X components

Step #3: RX = AX + BX

Y components

Step #3: RY = AY + BY

Step #4:
The sum of the x'sand the y's creates
the components of the resultant.

To find the angle of the resultant:
θR = tan-1(Ry/Rx)

R = √Rx2 + Ry2

If you combine the vectors
components from A and B,

they will form the vector

component in x and y for the

resultant.

AX

BX

AY

BY

R

R = √Rx2 + Ry2
RX = AX + BX
RY = AY + BY

A=20

B=32

θa=50°

θb = 65°

Example 2

A

B

R

A=10

B=12

θa=30°

θb = 290°

Components
of A

A=10
θa=30°

Components
of B

By is going to
a negative direction

B=I2
θb = 290°

Displace the vector components

The blue
vector goes
on top of the red

Ry and R
will be negative
numbers.

Instructions

Go to the discussion board and answer the question.
After the discussion board we will complete the
problems we were working on yesterday.

When we finish the problems we will have a quiz.

Then we will do a vector review.

First test will be this Tuesday if nothing change.

Results

Ax =8.66 Ay = 5
Bx = 4.1 By = -11.28
Rx = 12.76
Ry = -6.28
R = 11.11
ϴR = -26.19° (334°)

A

B

C

R

Example 3

A=20

B=18

θa=30°

θb = 20°

C=44
θc=305°

A

B

C

R

Components
for A

A=20
θa=30°

A

B

C

R

Components
for B

B=18
θb = 20°

A

B

C

R

Components
for C

C=44
θc=305°

A

B

C

R

Displace the vectors

Ax

Bx

Cx

A

B

C

R

Displace the vectors

Ax

Bx

Cx

A

B

C

R

Transfer the resultant

Multiple Choice

What is the resultant of these two vectors?

• +17 m

• +3 m

• -17 m

• -3 m

Multiple Choice

The side of the right triangle of length A is __________ to angle α

• adjacent

• opposite

• hypotenuse

• inverse

Multiple Choice

The side of the right triangle of length B is called __________ to angle α

• adjacent

• opposite

• hypotenuse

• inverse

​Thank you !

Bellwork (Sept 6, 2019) 5 min

Find the direction of the resultant vector
made by the combination of the following
displacement vectors:

� A = 105.6m with an Ѳ = 45°

� B = 0.305Km with an Ѳ = 80°

� Put your homework on the side of your desk.