9

Science
Quarter 4 – Module 2:
Toss Me Up, Pull Me Down
Science – Grade 9
Quarter 4 – Module 2: Projectile
First Edition, 2021

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Published by the Department of Education – Region XI

Development Team of the Module

Writer: Ma. Jade Juanich-Pijan

Editor: Luz Gazo, Reynaldo Pardillo
Reviewers: Dinah G. Oani, Genevaive M. Pepito, Rhiza T. Erbina, Joyce C.
Unabia, Rudilyn M. Garcesa, Lady Luvimin T. Basuel
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Alma C. Cifra,
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Faye Genevieve P. Pasamonte

Printed in the Philippines by ________________________

Department of Education – Division of Davao City

Office Address: E. Quirino Avenue, Davao City

Telephone: (082) 227 4762
E-mail Address: lrms.davaocity@deped.gov.ph
 9

Science
Quarter 4 – Module 2:
Toss Me Up, Pull Me Down
Introductory Message
For the facilitator:
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 at home.
Furthermore, you are expected to encourage and assist the learners as
they do the tasks included in the module.

For the learner:

As a learner, you must learn to become responsible of your own
learning. Take time to read, understand, and perform the different
activities in the module.
As you go through the different activities of this module be
reminded of the following:
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 Let Us Try before moving on to the other
activities.
3. Read the instructions 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 done.
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!

ii
 Let Us Learn

A wonderful day to you young scientist! In this module, you will learn
about an object thrown with an initial horizontal velocity and acted upon by
the earth’s pull of gravity. You shall learn more about the projectile motion
(MELC 2).

Specifically, you are expected to:

• Define projectile motion
• Describe the horizontal and vertical motions of a projectile;
• Solve problems related and relevant to projectile motion.

Let Us Try!

Choose the best answer and write on a separate sheet of paper.

1. Ignoring air resistance, describe the velocity of an object falling toward

the surface of the earth.
A. Accelerating C. Uniformly decreasing
B. constant D. Cannot be determined

2. What factor(s) affect(s) the range of a projectile?

A. acceleration due to gravity C. initial velocity
B. Angle of release D. all the above

3 Which of the following movements best describes the two-dimensional

motion (vertical and horizontal) of an object moving under the influence
of gravity?
A. Circular motion C. Rectilinear motion
B. Projectile motion D. Rotational motion

4. Two balls of the same mass are released at the same time from the
same height. Ball A is thrown horizontally, while Ball B is simply
dropped vertically downward. Which statement best describes the
motion of the two balls?
A. Ball A will reach the ground first.
B. Ball B will reach the ground first.
C. Both balls will reach the ground at the same time.
D. Ball A has greater speed than ball B.

5. A basketball player throws a ball horizontally. Neglecting air resistance,

which statement best describes the ball’s motion after it is thrown?
A. Its vertical speed increases, and its horizontal speed decreases.

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 B. Its vertical speed decreases, and its horizontal speed increases.
C. Its vertical speed increases, and its horizontal speed is constant.
D. Its vertical speed is constant, and its horizontal speed increases.

Let Us Study

Examine the illustrations below.

A B C

Figure 1: Types of Projectiles

https://www.slideserve.com/rivka/projectile-motion

Take a look at Figure 1. Projectiles has a variety of examples.

A. An object at an elevated point dropped from rest is an example of a
projectile (provided that the influence of air resistance is negligible).
B. An object that is thrown vertically upward is also a projectile (provided
that the influence of air resistance is negligible).
C. And an object which is thrown upward at an angle with the horizontal
is also a projectile (provided that the influence of air resistance is
negligible).

A projectile is any object that once projected or dropped and continues to

move by virtue of its inertia and influenced only by the downward force of
gravity. Most of the projectile motion travels in a curved path called trajectory.

When an object moves both vertically and horizontally, it is called

PROJECTILE MOTION. A single force acts upon it – the force of gravity. If
there were any other force acting upon an object, then that object would not
be a projectile. It is very important to note that projectile motion is a combination
of vertical motion with constant acceleration and horizontal motion with
constant velocity.

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To illustrate further, examine the diagrams below.

Fig. 1A. A marble rolling across a shiny frictionless floor.

𝑣! = 0 𝑣" = 0

𝑣" = 𝑚𝑎𝑥
𝑣! = 𝑚𝑎𝑥

Fig. 1B. A ball tossed vertically

upward.
Fig. 1C. A ball dropped to the
ground.

Figure 2: Breaking it down in two: horizontal

and vertical components of
projectile motion.

These two (vertical and horizontal) motions are independent and that
they do not influence one another.

Figure 3 found in the next page, shows the trajectory of a projectile that
is being kicked at an angle above the horizontal. The horizontal component of
its velocity is constant. This implies that the initial horizontal velocity remains
the same in its entire motion. On the other hand, its vertical motion is under
the influence of gravity, therefore it is accelerating along the vertical axis and
its acceleration is the acceleration due to gravity, g, which is 9.8 m/s2. The
vertical velocity decreases as the object goes up because it goes against the
gravity and its velocity at the highest point is zero. As it goes down, its velocity

3
is in the same direction as the gravitational force, therefore it is accelerating
on its way down.

Figure 3: Horizontal (red arrows) and vertical (green arrows) components of projectile
Source: https://byjus.com/trajectory-formula/

Now, let us describe the motion of projectiles numerically. Let us

discover how the numerical values of the horizontal (x) and vertical (y)
components of velocity and displacement change with the change of time. (see
figure 4 below)

Try to consider a bullet launched from the top of a cement post.

Suppose that the bullet, launched horizontally with no upward angle, has an
initial speed of 15 m/s. The bullet would continue in motion at 15 m/s in the
horizontal direction keeping its horizontal velocity (𝑣! ) constant. This means
that the bullet covers equal distances in equal time intervals. The horizontal
distance traveled by a bullet after its fall at time (t) is called the horizontal
displacement, (𝑑! ) or range, (R). It is given by equation,
𝑅 = 𝑑! = 𝑣! 𝑡
However, the gravity causes the bullet to accelerate downward at a rate
of 9.8 m/s2. This means that the vertical velocity (vy) is changing by 9.8 m/s2
every second (1-second intervals of time). Vertical velocity is given by
equation vy = gt
The increase in speed in the vertical direction causes greater vertical
distances (dy) to be covered in each successive time interval. Thus, the height
h or vertical displacement through which a projectile falls during the time t is
described by equation,

𝑔𝑡 "
ℎ = 𝑑! =
2

4
 It is important to note that the horizontal motion of a projectile is
completely independent of the vertical motion. However, the velocity of a
projectile as it strikes the ground is the resultant of the horizontal (𝑣! ) and
vertical (𝑣" ) velocities as expressed in the equation below.

𝒗 = %𝒗𝒙 𝟐 + 𝒗𝒚 𝟐

Figure 4 shows that a bullet travels at constant speed all throughout

its horizontal motion, while its vertical velocity increases uniformly at 9.8
m/sec2 in every second.

𝑣" = −9.8 𝑚/𝑠 '

𝑣" = −19.6 𝑚/𝑠 '

𝑣" = −29.4 𝑚/𝑠 '

𝑣" = −39.2 𝑚/𝑠 '

𝑣" = −49.0 𝑚/𝑠 '

Figure 4: Numerical description of projectile motion

Table 1. Kinematics Equations for Projectile Motion

Horizontal Component of Motion Vertical Component of Motion
𝑎! = 0 , 𝑣! = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑎" = −𝑎& = 𝑔 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑔𝑡 '
Range, 𝑅 = 𝑑! = 𝑣! 𝑡 𝑑" =
2
Final velocity, 𝒗 = %𝒗𝒙 𝟐 + 𝒗𝒚 𝟐

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Sample Problem
A stone is thrown with an initial horizontal velocity of 10 m/sec from the top
of a tower 200 meters high.
1. What is the horizontal velocity of the stone 2 seconds after being
thrown?
2. How far does the stone travel horizontally after 2 seconds?
3. What is its velocity upon hitting the ground after 6 seconds?
4. How far has it gone vertically downward as it hits the ground in 6
seconds?
$
Given: ℎ𝑒𝑖𝑔ℎ𝑡 (ℎ), 𝑑! = 200 𝑚 and 𝑣# = 10
%

Solution 1:
The horizontal velocity remains constant (10 m/s) in its entire flight.
Solution 2:
The horizontal distance traveled after 2 seconds

𝑅𝑎𝑛𝑔𝑒 = 𝑑# = 𝑣# 𝑡
= 10 m/s (2 s)

𝑑# = 20 m
Solution 3:
Upon hitting the ground, horizontal velocity, vx = 10 m/s, and vertical velocity
is given by vy = gt = -9.8 (m/s2) t = 6 sec

vy = -9.8 m/s2 (6 s)
= -58.8 m/s
(the negative sign implies the downward direction of the vertical velocity)

Hence,
𝑣 = %𝑣! ' + 𝑣" '

= <(10𝑚/𝑠)' + (−58.8𝑚/𝑠)'

'
= %100𝑚' /𝑠 ' + 3457.44 𝑚 A𝑠 '

'
= %3557.44 𝑚 A𝑠 '

𝑣 = 59. 64 m/s

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Solution 4:

After hitting the ground in 6 seconds, the ball will travel vertical distance,

#$ !
𝑑" =
%

"
&.( ! . *!
= #
%

"
&.( ! . +* , !
= #
%

&'".) $
= "

𝑑𝑦 = 176.4 𝑚

In real daily life experiences, horizontal and vertical motions are
oftentimes combined. Projectile motion has many uses beyond just putting
away laundry; from plotting an airplane flight, launching a rocket to playing
basketball or any sports.

Let Us Practice
Activity 1: Daily Move

Direction: Enumerate at least five (5) situations in your life that exhibit
projectile motion.

1) _____________________________________________________________________
2) _____________________________________________________________________
3) _____________________________________________________________________
4) _____________________________________________________________________
5) _____________________________________________________________________

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 Let Us Practice More
Activity 2: Compare Me

You will need:

ü 2 plastic bottle caps
ü plastic ruler

What to do:
a) Place the ruler on the table as shown in the diagram above.
b) Put one plastic bottle cap on one edge of the ruler and the other plastic
bottle cap on the other end of the ruler.
c) Push the ruler forward such that both caps will fall.
d) Observe the two plastic bottle caps as they move and hit on the floor.
e) Did the plastic bottle caps hit the floor at different times or at the same
time? What makes you think so?

Points to consider:
1. One plastic bottle cap falls freely and the other is projected with an
initial horizontal velocity.
2. The projectile has travelled some horizontal distance from the point
of release.

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 f) Solve the problem below.

A ball is launched horizontally from the top of the cliff with an initial
velocity of 25 m/s. The trajectory of the ball is shown below.

𝒕 = 𝟎𝒔𝒆𝒄, 𝒗𝒚 = 𝟎𝒎/𝒔𝟐

𝑣! = 25 𝑚/𝑠 '

𝑣! = ________ 𝑚/𝑠 '

t = 1 s, vy = - 9.8 m/s2
𝑣! = _________ 𝑚/𝑠 '

t = 2 s, vy = - _____ m/s2
𝑣! = ________ 𝑚/𝑠 '

t = 3 s, vy = - ______ m/s2
𝑣! = ________ 𝑚/𝑠 '

𝒕 = 𝟒𝒔𝒆𝒄, 𝒗𝒚 = −______𝒎/𝒔𝟐 𝑣! = ________ 𝑚/𝑠 '

Figure
𝒕 = 𝟓𝒔𝒆𝒄, 6
𝒗𝒚 = −______𝒎/𝒔𝟐

For questions below, express your answers on the blanks provide for in figure
6.
A. What is the horizontal velocity(𝑣# ) of the ball in every time interval of 1
second?

B. What is the vertical velocity (𝑣! ) of the ball for every second of fall?

9
 Let Us Remember

v Objects thrown into the air that follows a curved path (trajectory) and
are influenced by gravity are called projectiles.
v A projectile motion is a combination of free fall and horizontal
motions that are independent of each other. It is a special kind of
motion wherein an object is moving in two dimensions.
v The curved or parabolic path of a projectile is known as the trajectory
of a projectile.
v Horizontal component of the projectile’s motion,
ü Its horizontal velocity, vx, is constant, which means that the
initial horizontal velocity in its entire motion, is equal to its final
horizontal velocity (vx = vf).
ü Its net force is zero
ü The object is not accelerating along horizontal and there is no
net force on the object along horizontal.
v On the other hand, its vertical component of motion
ü Under the influence of gravity.
ü Its motion is accelerating vertically and its acceleration due to
gravity is 9.8 m/s2.
ü The vertical velocity (vy) decreases as the object goes up and
becomes ZERO at the highest point of trajectory and increases
as it goes down.

Let Us Assess
Read the questions carefully. Choose the best answer and write it on a
separate sheet of paper.

1. Which of the following descriptions of moving objects accurately

portray a projectile?
A. A falling skydiver with an open parachute
B. An object upon which the only significant force is the force of
gravity
C. An object which is moving through air and touching any surface
D. Any object upon which air resistance is negligible

2. At what point in its path is the vertical component of the velocity (𝑣" )
of a projectile the smallest?
A. As it nears the top C. Halfway to the top
B. At the top D. The instant it is thrown

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3. Ball A is thrown horizontally, and ball B is dropped from the same
height at the same time.
A. Ball A reaches the ground C. Balls A & B reach the ground
first. at the same time.
B. Ball B reaches the ground D. Ball A has greater speed
first. when it reaches the ground.

4. At what point in its path is the horizontal component of the velocity (𝑣! )
of a projectile the smallest?
A. As it nears the top C. Halfway to the top
B. At the top D. It is the same throughout the
path

5. Which of the following statements are true of the vertical motion of

projectiles?
I. The vertical component of a projectile’s velocity is changing.
II. The vertical component of a projectile’s velocity is a constant value
of 9.8 m/sec.
III. The vertical component of a projectile’s velocity is changing at a
constant rate.
IV. The final vertical velocity of a projectile is always equal to the
initial vertical velocity.
A. Statements I, II and III C. Statements I and III
B. Statements II, III and IV D. Statements II and IV

6. The only force acting on a projectile is _________.

A. electricity C. surface friction
B. gravity D. tension

7. Which statement is not true of the time of flight for a projectile?

A. The time that a projectile is in the air is dependent upon the
horizontal component of the initial velocity.
B. The time that a projectile is in the air is dependent upon the
vertical component of the initial velocity.
C. A projectile that lands at the same height from where it was
projected, the time to rise to the peak is equal to the time to fall
from its peak to the original height.
D. For the same upward launch angles, projectiles will stay in the air
longer if the initial velocity is increased.

8. What do you call a projectile’s path through space?

A. flight path C. range
B. period D. trajectory

9. An object in free fall is also called___?

A. gravity C. projectile
B. projectile motion D. tide

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10. Objects will accelerate towards Earth at a constant rate of
A. 2.8 m/s2 C. 4.8 m/s2
B. 9.8 m/s2 D. 7.8 m/s2

11. Which of the following would NOT be considered a projectile?

A. a cannonball thrown straight C. a cannonball rolling off a
up table
B. a cannonball resting on a D. a cannonball thrown in the
table air

12. What is the direction of the acceleration for any projectile?

A. Same direction as the C. up
projectile’s path
B. down D. sideways

13. At which of the following points in its path does a projectile have the
greatest acceleration?
A. at the peak of its trajectory C. at the instant it is launched
B. halfway to the peak D. all points have the same
acceleration

14. Ignoring air resistance, an object falling toward the surface of the earth
has a velocity that is___?
A. accelerating C. decreasing
B. constant D. increasing

15. Which component of projectile motion is constant?

A. horizontal velocity C. both vertical and horizontal
B. vertical velocity D. none

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 Let Us Enhance
Activity 3: Find me

Read the problem below and find the answer.

1. The diagram below shows the trajectory of a horizontally launched

projectile. Positions of the projectile at 1-second intervals are shown.
Demonstrate your understanding of the components of the
displacement by determining the horizontal displacement (y) and the
vertical displacement (x) after 4 seconds.
2. If the ball in the diagram above strikes the ground after 4 seconds,
then, (please use the information you have written on Figure 6)
a. How high was the cliff?
b. How far from the base of the cliff will the ball land?

Y component 0 50 100 150 200 250 m

t = 0s
sec
t = 1s

t = 2s

t = 3s
t = 4s

X = _____ meters Y = _____meters X component

Redraw the diagram in a separate sheet of graphing paper. Show its

horizontal and vertical displacements at every second of its fall.

Activity notes/ Hints

Write and show your solution on a separate sheet of paper. Equation to
𝒗𝟐𝒇
use for letter A problem 𝒗𝒇 𝟐 = 𝒗𝒊 𝟐 + 𝟐𝒂𝒅 ---𝒅𝒚 = 𝒗𝟐 .
𝒊
For letter B problem; 𝒅𝒙 = 𝒗𝒙 . 𝒕

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 Let Us Reflect

Several crimes happen in our country which are related to stray

bullets. We usually hear this over the media mostly in December during
the holiday revelry when in the excitement of lighting firecrackers, those
who own guns resort to using them instead of firecrackers . When we hear
of stray bullets, policemen relate this to ballistics which is the study of
gunfire patterns for the purposes of crime-solving. It is in this application,
ballistics become a significant part of police science. It allows law–
enforcement investigators to determine when, where and how a firearm was
used.
We do have ballistic experts here in our country. The government
has spent large amount of money for the training of these expert. Does it
really help the speedy solution for the stray bullet cases happened in the
country?
Follow up questions:
1. Do research on the stray bullet’s cases reported in your own
barangay?
2. How many of these cases are are solved? Cases that are NOT solved?
3. How does irresponsible use of firearms affects the lives of the people
in the neighborhood?

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 15
Problem 1
𝑥 = 200 𝑚𝑒𝑡𝑒𝑟𝑠 𝑦 = 100 𝑚𝑒𝑡𝑒𝑟𝑠
Problem 2
Given for Question A
Given for Question B
a) 𝑎 = 9.8 𝑚/𝑠𝑒𝑐 #
a) vx = 25 m/sec
b) vi = 0
b) t = 4 seconds
c) vf = 39.2 m/sec2
𝒗𝒙 = 𝒅𝒙 /𝒕
vf 2 = vi 2 + 2ad
25 m/sec = d x / 4 sec
(39.2 m/sec)2 = 0 + 2(9.8 m/s2 ) d
dx = vx (t )
1537m/s2 = 19.6 m/s2 (d)
𝟏𝟓𝟑𝟕 = 25m/s(4sec)
dy = 𝟏𝟗.𝟔
----- 78.4 met ers = 100 met ers
Activity 2: Compare Me
1. The two plastic bottle caps will reach the floor at the same time, though the projectile
has traveled some horizontal distance from the point of release. It suggests that
projectile motion is a combination of horizontal and vertical motion that are
independent of each other.
.
2. t = 1sec; 𝑣, = -9.8 m/s2 𝑣- = 25 constant or same
/01
t = 2sec; 𝑣, = -19.6 m/s2
t = 3sec; 𝑣, = -29.4 m/s2
t = 4sec; 𝑣, = -39.4 m/s2
t = 5sec; 𝑣, = -49.0 m/s2
Activity 1: Know Me More
Possible answers:
1. Playing almost every sports (basketball, volleyball, skateboarding, etc)
2. Plotting an airplane flight
3. Launching a rocket
4. Gymnastics
5. Throwing a fishing rod
Let Us Assess
Let Us Try
1. C 6. B 11. B
1. B
2. B 7. A 12. B 2. C
3. D
3. C 8. D 13. D 4. A
5. A
4. A 9. C 14. B
5. D 10. B 15. A
Answer Key
 References

(n.d.). Retrieved January 25, 2021, from http://www.scienceclarified.com

Alumaga, M. B., Antero, E., Joaquin, C. C., Lagunzad, C. B., Crisostomo, R.
M., Padua, A. L., & Mingoa, T. R. (2014). Science and Technology.
Quezon: Vibal Group, INC.
Angeles, D. C., Crisostomo, L. M., Quinsaat, D. T., & Toledo, S. B. (2018).
Science Vistas 9 Updated Edition. Makati City: Salesians Books by Don
Bosco Press, Inc.
Aquino, M. D., Madriaga, E. A., Valdoz, M. P., & Biong, J. A. (2017).
SCIENCE Link: Worktext for Scientific and Technological Literacy.
Manila: Rex Bookstore.
Binene, J. L., Maglaya, R. B., & Tolentino, T. S. (2016). Experiencing
SCIENCE: An Activity - Based Worktext for Grade 9. Manila:
Innovative Educational Material, INC.
Padua, A. L., & Crisostomo, R. M. (2003). Practical and Explorational
Physics: Modular Approach. Vibal Publishing House.
Singh, K. S. (2013, September 13). (OpenStax CNX) Retrieved January 31,
2021, from https://courses.lumenlearning.com/boundless-
physics/chapter/projectile-motion/
Urone, P., & Hinrichs, R. (2020, March 26).
https://openstax.org/books/physics@13.9/pages/1-introduction.
Retrieved January 30, 2021, from Openstax.
Varon, S. (2021, January 25). Retrieved from quizizz.

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For inquiries or feedback, please write or call:

Department of Education – Davao City Division

E. Quirino Avenue, Davao City

Telephone: (082) 227 4762

Email Address: lrms.davaocity@deped.gov.ph