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9
SCIENCE
QUARTER 4
Week 1
Capsulized Self-Learning Empowerment
Toolkit
Schools Division Office of Zamboanga City
Region IX, Zamboanga Peninsula
Zamboanga City
“Unido, Junto avanza con el EduKalidad
Cree, junto junto puede!”
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
1
SUBJECT &
GRADE/LEVEL
Science 9
TOPIC/s
LEARNING
COMPETENCIES
QUARTER
4
WEEK
1
DAY
_______________________
dd/mm/yyyy
Free Fall
Projectile Motion
1. Relate uniformly accelerated motion to free fall.
2. Describe horizontal and vertical motions of a projectile.
(S9FE-IVa-34)
IMPORTANT: Do not write anything on this material. Write your answers on a separate
sheet. Do not forget to answer all the Self-Assessment Questions (SAQs).
UNDERSTAND
Observe the pictures given below. Describe each picture.
Free fall of an apple
Dropping a ball
Skydiving
Have you ever wondered how fast a heavy object falls compared to a
lighter one?
If you drop a book and a pencil at the same height and time, which
object do you think will hit the ground first? ______________Why?
________________
What do you think made the two objects fall? _________________
3m
3m
You have probably noticed that when a book and a pencil is dropped at the same
height and time, both hit the ground at the same time regardless of their masses. How is
that possible? Why did it happen?
Things fall because of the force of gravity. The object is in free fall when a falling
object is free of all restraints—no friction, with the air or otherwise—and falls under the
influence of gravity alone. The apple, skydiver and the ball in the figure above are in a
state of free fall. Their motion is classified as free fall motion and they are called free
falling objects.
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
2
What is Freely falling object?
A free-falling object is an object that is falling under the influence of gravity alone.
What are the important characteristics of true free-falling objects?
The following are the characteristics of objects that are under the state
of free fall:
1. Free-falling objects do not encounter air resistance.
2. All free-falling objects (on Earth) accelerate downwards at a rate of
9.8 m/s2.
The numerical value of the acceleration of free-falling objects is known as
the acceleration due to gravity - the acceleration for any object moving under
the influence of gravity alone. Physicists have a special symbol to denote it - the
symbol g. The numerical value for the acceleration of gravity is most accurately
known as -9.8 m/s2.
Free-falling objects are acted by gravity (force) alone. According to
Newton’s Law of Acceleration the object’s acceleration follows the direction
of the net force, in the case of free fall motion the net force equals gravity,
thus the object follows the direction of gravity which is “downward”, meaning
towards the center of the earth. Since acceleration is a vector quantity the acceleration
due to gravity g is more accurately equivalent to -9.8 m/s2. The acceleration due to gravity
is constant for a particular location on Earth.
g = -9.8 m/s2
Direction
or you may say
g = 9.8 m/s2, downward
Magnitude and unit
SAQ-1: What are free falling objects?
SAQ-2: Why is the magnitude of the acceleration due to gravity constant or uniform?
Hint: Relate it to Newton’s Law of Acceleration
Freefall is a special case of motion with constant acceleration because acceleration
due to gravity is always constant and downward. This is true even when an object is
thrown upward or has zero velocity.
The equations for uniformly accelerated motion are thus applicable to free fall motion
except that “a” is replaced by “g”.
Uniformly accelerated Motion
A
d= 𝒗𝒊 t +
𝟏
𝟐
a𝒕𝟐
Free Fall Motion
h= 𝒗𝒊 t +
𝟏
𝟐
g𝒕𝟐
B
𝒗𝒇𝟐 = 𝒗𝒊 𝟐 + 2ad
𝒗𝒇𝟐 = 𝒗𝒊 𝟐 + 2gh
C
𝒗𝒊 𝟐 = 𝒗𝒇 𝟐 – 2ad
𝒗𝒊 𝟐 = 𝒗𝒇𝟐 – 2gh
D
𝒗𝒇= 𝒗𝒊 + at
𝒗𝒇= 𝒗𝒊 + gt
E
𝒗𝒊 = 𝒗𝒇 - at
𝒗𝒊 = 𝒗𝒇 - gt
F
d=
𝒗𝒇 𝟐 −𝒗𝒊 𝟐
𝟐𝒂
h=
𝒗𝒇 𝟐 −𝒗𝒊 𝟐
𝟐𝒈
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
3
G
t=
𝒗𝒇 −𝒗𝒊
𝒂
𝟐𝒅
; if 𝒗𝒊= 0 t = √ 𝒂
Where
h – height of fall
𝒗𝒇 – final velocity
𝒗𝒊 – initial velocity
t=
𝒗𝒇 −𝒗𝒊
𝒈
𝟐𝒉
; if 𝒗𝒊= 0 t = √ 𝒈
t – time
SAQ-3: Observe the equations for free fall. Will the mass of the object affect its motion
when it falls? What factors will affect a free-falling object’s motion?
What happens to the object’s velocity when it falls?
Each successive second of the object’s fall, the
object’s speed increases by the same amount: 9.8 m/s.
The velocity of the ball is seen to increase as it falls as
shown in the diagram at the right.
What happens to the object’s velocity when it is
thrown up?
When an object is thrown up in the air, the objects's
velocity is initially upward. Since gravity pulls the object
toward the earth with a constant acceleration g, the
magnitude of velocity decreases as the ball approaches maximum height.
At the highest point in its trajectory, the object changes its direction of motion from
upward to downward, the ball has zero velocity and the magnitude of velocity increases
again as the ball falls back toward the earth (see figure 1).
The object slows down at the rate of 9.8
Figure 1. Direction of velocity and
acceleration for a ball thrown up
in the air.
𝑚
𝑠2
during the
upward part of its motion, the same acceleration it
experiences on the way down. The instantaneous
speed at points of equal elevation in the path is the
same whether the object is moving upward or
downward. The velocities are opposite because they
are in opposite directions. The downward velocities
have a negative symbol, meaning that they are moving
downward.
Acceleration from gravity is always constant and
downward, but the direction and magnitude of velocity
change.
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
4
Let’s Practice 1!
(Write your answer on the separate sheet/s of paper.)
PART A: FACT or BLUFF
Determine if each of the given statements below is a Fact or a Bluff. Tick the
appropriate box.
An object that is free falling is acted upon by the
force of gravity alone
FACT
BLUFF
A ball is thrown upwards and is rising towards its
maximum height. As it rises upwards it is not in a
state of free fall.
FACT
BLUFF
An object in free fall experiences an acceleration
which is independent on the mass of an object.
FACT
BLUFF
FACT
BLUFF
FACT
BLUFF
Free fall motion is a type of motion that is uniformly
accelerated.
An object in free fall is uniformly accelerating.
PART B: CONCEPT CHECK
Answer the question below in one to three sentences only.
Why is free fall motion considered as a special case of uniformly accelerated
motion?
PROJECTILE MOTION
What is Projectile Motion?
Projectile motion is the motion of an object thrown or projected into the air with a
constant initial velocity that follows a curved path. Below are some examples of objects
undergoing projectile motion.
Trajectory
Range
Any body that is given an initial velocity and then follows a direction entirely
determined by the effects of gravity and air resistance is referred to as a projectile. The
curve path followed by the projectile is called it’s trajectory. The maximum horizontal
distance that a projectile covers is called the range (R).
Projectile motion is two-dimensional. It is made of horizontal motion (along the xaxis) and vertical motion (along the y-axis). These two motions are independent of each
other.
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
5
Describing the motion of the projectile
If there were no gravity, a stone thrown
horizontally would move in a straight line path
and cover equal distances in equal time
intervals.
Gravity causes the projectile to move vertically
downward. The projectile at the same time moves
horizontally forward. The curved solid line shows the
resulting trajectory that combines horizontal and
vertical motions of the projectile.
The horizontal motion of the projectile is unaffected by the presence of gravity.
Gravity works downward and is unable to change the horizontal motion. Gravity causes
the projectile to accelerate at a constant rate. The acceleration of the projectile is equal to
𝒎
the acceleration due to gravity g (-9.8𝒔𝟐).
A horizontal force is needed to cause a horizontal acceleration (𝑎𝑥 ). Since there
is only a vertical force (gravity) acting upon a projectile, it does not accelerate
horizontally. Thus, 𝑎𝑥 equals zero.
SAQ-4: If the horizontal acceleration of the projectile equals zero, what does this imply
about its horizontal velocity?
SAQ-5: If a boy simply drops a baseball
a vertical distance of 5 m, it will hit the
ground in 1s. Suppose instead that he
throws the ball horizontally (Refer to the
figure on the right). How long would it
take the baseball to fall to the ground?
The equations used in free fall are applied to the vertical motion of the projectile.
For horizontally launched projectiles the following equattions are applied.
Equations for Horizontal Motion of a Equations for Vertical Motion of the
horizontally launched Projectile
Projectile
𝟏
𝒗𝒊𝒙 = 𝒗𝒇𝒙
h= 𝒗𝒊𝒚 t + g𝒕𝟐
𝟐
𝒅𝒙 = 𝒗𝒊𝒙 t
𝒗𝒇𝒚 𝟐 = 𝒗𝒊𝒚 𝟐 + 2gh
Range = 𝒗𝒊𝒙 𝑡
𝒗𝒊𝒚 𝟐 = 𝒗𝒇𝒚 𝟐 – 2gh
𝒗𝒇𝒚 = 𝒗𝒊𝒚 + gt
𝒗𝒊𝒚 = 𝒗𝒇𝒚 - gt
h=
𝒗𝒇𝒚 𝟐 −𝒗𝒊𝒚 𝟐
𝟐𝒈
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
6
t=
𝒗𝒇𝒚 −𝒗𝒊𝒚
𝒈
𝟐𝒉
; if 𝒗𝒊= 0 t = √ 𝒈
REMEMBER!!!
Projectile motion is a combination of horizontal motion with constant velocity and
vertical motion with constant acceleration (g).
Let’s Practice 2!
(Write your answer on a separate sheet/s of paper.)
𝑚
𝑣𝑖 = 2 𝑠
A
B
Use the figure above to answer the items that follow. Underline your answer.
1. The horizontal velocity at pt A is (less than, equal to, greater than) 𝑣𝑖 .
2. Compared to pt A the vertical velocity at pt B is (lesser, equal, greater).
3. The projectile is moving with a horizontal velocity that is (increasing, constant,
decreasing).
4. The vertical velocity at pt A is (less than, equal to, greater than) the acceleration
at pt B.
5. The projectile is moving with a vertical acceleration that is (increasing, constant,
decreasing).
REMEMBER
Key Points






A free-falling object is an object that is falling under the sole influence of gravity.
Any object that is moving and being acted upon only by the force of gravity is said
to be "in a state of free fall."
𝑚
A free-falling object will experience a downward acceleration of 9.8𝑠 2. Whether the
object is falling downward or rising upward towards its highest point of travel, if it is
𝑚
under the sole influence of gravity, then its acceleration value is 9.8𝑠 2 in the
downward direction.
Free Fall motion is a special case of uniformly accelerated motion because it is
𝑚
moving with a constant acceleration of -9.8𝑠 2 .
The motion of an object thrown or projected into the air, subject only to gravity's
acceleration, is known as projectile motion.
Projectile motion is a combination of horizontal motion with constant velocity (𝑎𝑥 =
𝑚
0) and vertical motion with constant acceleration (g = -9.8𝑠 2).
Important equations to remember
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
7
Free Fall Motion
𝟏


h= 𝒗𝒊 t + g𝒕𝟐
𝟐
𝒗𝒇𝟐 =𝒗𝒊 𝟐 + 2gh

𝒗𝒊 𝟐 = 𝒗𝒇𝟐 – 2gh

𝒗𝒇= 𝒗𝒊 + gt

𝒗𝒊 = 𝒗𝒇 - gt

h=

t=
𝒗𝒇 𝟐 −𝒗𝒊 𝟐
𝟐𝒈
𝒗𝒇 −𝒗𝒊
𝒈
𝟐𝒉
or t = √ 𝒈 (if 𝒗𝒊 = 0)
Equations for Horizontal Motion of a Equations for Vertical Motion of the
horizontally launched Projectile
Projectile
𝟏
𝒗𝒊𝒙 = 𝒗𝒇𝒙
h= 𝒗𝒊𝒚 t + g𝒕𝟐
𝟐
𝒅𝒙 = 𝒗𝒊𝒙 t
𝒗𝒇𝒚 𝟐 = 𝒗𝒊𝒚 𝟐 + 2gh
Range = 𝒗𝒊𝒙 𝑡
𝒗𝒊𝒚 𝟐 = 𝒗𝒇𝒚 𝟐 – 2gh
𝒗𝒇𝒚 = 𝒗𝒊𝒚 + gt
𝒗𝒊𝒚 = 𝒗𝒇𝒚 - gt
h=
t=
𝒗𝒇𝒚 𝟐 −𝒗𝒊𝒚 𝟐
𝟐𝒈
𝒗𝒇𝒚 −𝒗𝒊𝒚
𝒈
𝟐𝒉
; if 𝒗𝒊= 0 t = √ 𝒈
TRY
Let us see how much you have learned today!
Directions: Read each question carefully and choose the letter corresponding to your
answer. (Write your answer on a separate sheet of paper.)
1. When we say that free fall is a special case of uniformly accelerated motion, what does
it mean?
A. Objects that are freely falling are moving with constant acceleration.
B. Objects that are freely falling are moving with constant acceleration half the time.
C. Objects that are freely falling are moving with constant velocity.
D. Objects that are falling freely are affected alone by air resistance neglecting the
force of gravity
2. What happens to the velocity of a ball as it is dropped off from a cliff?
A. It decreases at a uniform rate.
B. It increases at a uniform rate.
C. It is constant.
D. It increases at a non-uniform rate.
For items 3-5. Refer to the problem below.
A ball is thrown straight up from point A, reaches a maximum
height at point B, and then falls back to point C, as illustrated by the
picture on the right.
3. Which of the following is true about the direction the ball’s velocity
and acceleration between A and B?
A.
B.
C.
D.
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
8
4. Which of the following is true about the direction the ball’s velocity and acceleration
between B and C?
A.
C.
B.
D.
5. Which of the following is true about the ball’s velocity and acceleration the highest point
B?
A. Its velocity and acceleration are both zero
B. Its velocity is up and non-zero constant and acceleration is zero
C. Its velocity is down and non-zero constant and acceleration is zero
D. Its velocity is zero and acceleration is down and non-zero constant
6. A ball is tossed straight up with an initial velocity of 5.0 m/s. What is the speed of the
ball at its maximum height?
A. 0.0m/s B. 5.0 m/s
C. 9.8 m/s D. 14.8 m/s
7. Four students were discussing projectile motion in the canteen after science class. Who
do you agree with?
Luz: “A projectile’s v x changes because of gravity, and its v y remains constant.”
Joseph: “Both vx and vy are constant.”
Tito: “A projectile has no acceleration in the vertical dimension but it does accelerate
horizontally.”
Jay: “A projectile has vertical acceleration and a constant horizontal velocity”
A. Luz
B. Joseph
C. Tito
D. Jay
8. A ball is projected horizontally with a velocity of 1·5 ms−1 from a cliff as shown.
The ball hits the ground 1.22 s after it leaves the cliff. The effects of air resistance are
negligible. What is the horizontal velocity of the projectile (ball) halfway through its fall?
𝑚
𝑚
𝑚
A. 1.5
B. lesser than 1.5
C. greater than 1.5
d. 0
𝑠
𝑠
𝑠
9. Two identical balls X and Y are projected horizontally from the edge of a cliff. The
path taken by each ball is shown.
Identify which of the following statements about the motion of the balls is/are correct.
I they take the same time to reach sea level.
II they have the same vertical acceleration.
III they have the same horizontal velocity.
A. I only
B. II only
C.I and II only
D. I and III only
WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School
9
10. Which of the following statements is true for both free fall and uniformly accelerated
motion?
A. Objects moving with these types of motion have constant acceleration.
B. Objects moving with these types of motion have constant velocity.
C. Objects moving with these types of motion have constant instantaneous speed.
D. Objects moving with these types of motion have zero acceleration.
Department of Education- Bureau of Learning Resources (DepEdBLR), Science Learner’s Module 9: Uniformly Accelerated Motion
[Philippines] Department of Education; 2017, 338p.
“Freefall Review (Article).” n.d. Khan Academy.
https://www.khanacademy.org/science/high-school-physics/onedimensional-motion-2/objects-in-freefall/a/freefall-ap1.
“Free Fall SlideShare,” SlideShare, November 27, 2016 Retrieved
fQuizizz.com. 2021. Projectile Motion Multiple Choice Practice Quiz. [online] Available at:
<https://quizizz.com/admin/quiz/5dea7b92864ff2001b06e1c0/proje
ctile-motion-multiple-choice-practice> [Accessed 13 May
2021].rom https://www.slideshare.net/KhanSaif2/1-free-fall69571245
REFERENCE/S
Grove.ea.dundeecity.sch.uk. 2021. [online] Available at:
<http://grove.ea.dundeecity.sch.uk/ourschool/departments/sciences/physics/departmentdocuments/national-5/dynamics/homework/homework-5>
[Accessed 13 May 2021].
“Kinematic Equations and Free Fall.” n.d.
Www.physicsclassroom.com.
https://www.physicsclassroom.com/class/1DKin/Lesson6/Kinematic-Equations-and-Free-Fall.
DISCLAIMER
"The Acceleration of Gravity." The Physics Classroom. Accessed
March 06, 2021.
https://www.physicsclassroom.com/class/1DKin/Lesson5/Acceleration-of-Gravity.
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WRITTEN BY: DOROTHY DEANNE S.T. ARANETA, SST – I, Culianan National High School
SHERRYL MAE F. BERMUDO, SST – II, Culianan National High School
JANICE G. GUBAN, SST – I, Culianan National High School