Learning Area Science Grade Level 9

W1 Quarter 4th Date

I. LESSON TITLE Forces and Motion
II. MOST ESSENTIAL LEARNING
Describe the horizontal and vertical motions of a projectile.
COMPETENCIES (MELCs)
III. CONTENT/CORE CONTENT Projectile Motion
IV. LEARNING PHASES AND LEARNING ACTIVITIES
I. Introduction (Time Frame: Day 1)

Uniformly Accelerated Motion

A body is said to have uniform acceleration if it maintains a constant change in its velocity in each time interval along a straight
line. This can be along the horizontal (rectilinear) or along the vertical (free fall). For rectilinear motion, let us take a track and
field runner competing in the 100-m run as an example. If the runner’s positions are taken at equal time intervals and the
change in position for each time interval is increasing, then, the runner is moving faster and faster. This means that the runner is
accelerating.

The pull of gravity acts on all objects. So, when you drop something or even when you throw something up, it will go down.
Things thrown upward always fall at a constant acceleration which has a magnitude of 9.8 m/s 2. This means that the velocity
of an object changes by 9.8 m/s every second of fall. Consider a ball thrown upward. As the ball goes up, it decelerates until
it stops momentarily and changes direction. That means, it reaches its maximum height before it starts to fall back to the point
where it was thrown, and its speed will be equal to the speed at which it was thrown. Note that the magnitudes of the two
velocities are equal, but they have opposite directions – velocity is upward when it was thrown, but downward when it returns.
Free-fall is an example of uniformly accelerated motion, with its acceleration being -9.8 m/s2, negative because it is downward.

The equations for Uniformly Accelerated Motion (UAM) are:

𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 where: 𝑣𝑓 = final velocity/speed
1
𝑑 = 𝑣𝑖 𝑡 + 𝑎𝑡 2 𝑣𝑖 = initial velocity/speed
2
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎𝑑 𝑎 = constant acceleration
𝑣𝑖 + 𝑣𝑓
𝑑= ( ) 𝑡 or 𝑑 = 𝑣̅ 𝑡 𝑡 = time
2
𝑑 = distance/displacement
𝑣̅ = average speed/velocity

D. Development (Time Frame: Day 2)

Motion in Two Dimensions

Many of the games you play and sporting events you join/officiate in during PE classes involve flying objects or balls. Have you
noticed the curved paths they make in mid-air? This curve is what naturally happens when an object, called a projectile, moves
in two dimensions –having both horizontal and vertical motion components, acted by gravity only. In physics this is called
projectile motion. Not only balls fly when in projectile motion. Have you noticed that in many sports and games, players come
“flying” too? Understanding motion in two-dimensions will help you apply the physics of sports and enhance game events
experiences.

Projectile motion is a combination of uniform motion along the horizontal and the motion of a freely falling body along the
vertical. It is an instance of uniformly accelerated motion in two-dimensions. The moving body is called a projectile, the curved
path it travels is known as the trajectory and the horizontal distance it covers is called range. The horizontal and vertical motions
of a projectile are completely independent of each other.

Therefore, horizontal and vertical motion can be treated separately.

IV. LEARNING PHASES AND LEARNING ACTIVITIES

Types of Projectile Motion

I. Projectile Launched Horizontally II. Projectile Launched at an Angle

Learning Task 1: JUMBLED LETTERS: Rearrange the letters to form the word described in each statement.

1. It is a combination of uniform horizontal motion and free fall. CEEIJLOPRT IMNOOT

2. It is the curved path traveled by a projectile. ACEJORRTTY
3. It is a body traveling in projectile motion. CEEIJLOPRT
4. It is the horizontal distance traveled by a projectile. AEGNR
5. It is the vertical distance traveled by a projectile. EGHHIT

E. Engagement (Time Frame: Day 3)

Kinematic Equations for Projectile Motion

Horizontal Motion Vertical Motion
𝑑𝑥 = 𝑣𝑖𝑥 𝑡 1
𝑑𝑦 = 𝑣𝑖𝑦 𝑡 + 𝑔𝑡 2
2 2
𝑣𝑖 sin(2𝜃)
𝑑𝑥 = 𝑣𝑓𝑦 − 𝑣𝑖𝑦
𝑔 𝑑𝑦 = ( )𝑡
2
𝑣𝑖𝑥 = 𝑣𝑓𝑥
𝑣𝑖2 𝑠𝑖𝑛2 𝜃
𝑑𝑦 =
𝑣𝑖𝑥 = 𝑣𝑖 cos 𝜃 2𝑔
2𝑣𝑖 sin 𝜃 𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑔𝑡
𝑡𝑇 =
𝑔 2 2
𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 2𝑔𝑑𝑦
𝑣𝑖𝑦 = 𝑣𝑖 sin 𝜃

where:
𝑑𝑥 = range 𝑑𝑦 = height
𝑣𝑖 = initial velocity/speed 𝑣𝑖𝑦 = initial vertical velocity
𝑣𝑖𝑥 = initial horizontal velocity 𝑣𝑓𝑦 = final vertical velocity
𝑣𝑓𝑥 = final horizontal velocity 𝑔 = acceleration due to gravity (9.8 m/s2)
𝑡𝑇 = total time of flight 𝑡 = time of flight
𝜃 = angle of projection

Note: You will use the equations with sin or cos when the angle is given.

Sample Problem: If a bullet is fired with a speed of 600 m/s horizontally from a height of 48 m, how long will it take to hit the
ground? What is the range of the projectile? Assume that there is no air resistance.

Given: 𝑣𝑖𝑥 = 600 m/s

𝑣𝑖𝑦 = 0 (bullet was fired horizontally)
𝑑𝑦 = - 48 m (negative sign indicates height of fall)
IV. LEARNING PHASES AND LEARNING ACTIVITIES
Analyzing the situation given, we can see the available information in the horizontal and vertical axes, respectively.
Horizontal information Vertical information
dx = ? (range) dy = -48 m
vix = 600 m/s viy = 0
ax = 0 ay = -9.8 m/s2

Find: 𝑡 and 𝑑𝑥

Solution: The original equation that we need to use is:

𝑑𝑥 = 𝑣𝑖𝑥 𝑡
1
𝑑𝑦 = 𝑣𝑖𝑦 𝑡 + 𝑔𝑡 2
2 𝑚
𝑑𝑥 = (600 ) (3.1 𝑠)
It is simplified to: 𝑠
2𝑑𝑦
𝑡 = √−
𝑔 𝑑𝑥 = 𝟏 𝟖𝟔𝟎 𝒎
then substitute the values
2 (−48 𝑚)
𝑡 = √−
9.8 𝑚/𝑠2

𝑡 = 𝟑. 𝟏 𝒔

Learning Task 2: PROBLEM-SOLVING: A marble is thrown horizontally from a tabletop with a velocity of 1.50 m/s. The marble
falls 0.70 m away from the table’s edge. How high is the lab table? What is the marble’s velocity just before it hits the floor?

A. Assimilation (Time Frame: Day 4)

The Newbie Archer

A school introduced the sports of archery so they can send players to Division and Regional Sports competition in the
future. A student tries out. He was taught how to handle the equipment. Then, he sets a bow and arrow and directs it to the
target, so the arrow is almost in direct line with the bull’s eye target 30 m away. Will the boy hit a bullseye? Why?

Image sources:
https://classroomclipart.com/images/gallery/Clipart/Black_and_White_Clipart/Sports/TN_black-white-boy-aiming-with-bow-and-arrow-archery-clipart.jpg
https://cdn.britannica.com/26/91526-050-C4C7B73A/Archer-recurve-bow-target.jpg

V. ASSESSMENT (Time Frame: Day 5)

(Learning Activity Sheets for Enrichment, Remediation, or Assessment to be given on Weeks 3 and 6)

Directions. Choose the letter of the best answer.

*For questions 1-5, consider the given situation.
Maria throws a ball straight up with an initial velocity of 10 m/s.

1. What is its velocity at the highest point?

2. What is its velocity when it returned to the elevation from where it was thrown?
3. What is its acceleration at the highest point?
4. What is its acceleration just before it hits the ground?
5. After 1 second what is the acceleration of the ball?
A. 0 m/s
B. 0 m/s2
C. 9.8 m/s2
D. - 9.8 m/s2
E. 10 m/s2
F. -10 m/s SOURCE: GRADE 9 SCIENCE LM

G. cannot be determined
IV. LEARNING PHASES AND LEARNING ACTIVITIES
6. If a freely falling ball is somehow equipped with a speedometer, by how much would its speed-reading increase for every
second?
A. 0 m/s
B. 9.8 m/s
C. 10 m/s
D. 20 m/s
7. A sepak takraw ball is hit vertically upward by a player. What is its acceleration after 1 second?
A. 0
B. 1 m/s2
C. 9.8 m/s2
D. -9.8 m/s2
8. A volleyball is tossed vertically upward, with an initial velocity of 5 m/s and caught back at the same level as when it was
thrown. What is the velocity of the ball at that point?
A. 0 m/s
B. -5 m/s
C. -9.8 m/s
D. 9.8 m/s2
9. The motion of an object with constant acceleration is also known as
A. Motion
B. Uniform Motion
C. Constant Motion
D. Uniformly Accelerated Motion
10. A ball is thrown vertically upward. What is its instantaneous speed at its maximum height?
A. 0
B. 5 m/s
C. 9.8 m/s
D. 9.8 m/s2

VI. REFLECTION (Time Frame: Day 5)

• Communicate your personal assessment as indicated in the Learner’s Assessment Card.
Personal Assessment on Learner’s Level of Performance
Using the symbols below, choose one which best describes your experience in working on each given task. Draw it in the column
for Level of Performance (LP). Be guided by the descriptions below:
 - I was able to do/perform the task without any difficulty. The task helped me in understanding the target content/ lesson.
✓ - I was able to do/perform the task. It was quite challenging, but it still helped me in understanding the target content/lesson.
? – I was not able to do/perform the task. It was extremely difficult. I need additional enrichment activities to be able to do/perform this
task.
Learning Task LP Learning Task LP Learning Task LP Learning Task LP
Number 1 Number 3 Number 5 Number 7
Number 2 Number 4 Number 6 Number 8

VII. REFERENCES 1. Science – Grade 9 Learner’s Material, First Edition 2015. Pasig City: REX Book Store and DepEd-
IMCS, 2015.
2. Science – Grade 9 Teacher’s Guide, First Edition 2015. Pasig City: REX Book Store and DepEd-
IMCS, 2015.
3. https://www.basic-mathematics.com/projectile-launched-horizontally.html
4. http://www.studyphysics.ca/newnotes/20/unit02_circulargravitation/chp07_2d/lesson27.htm
5. https://sites.google.com/site/fradleyphysics/mechanics/projectile-
motion?tmpl=%2Fsystem%2Fapp%2Ftemplates%2Fprint%2F&showPrintDialog=1
6. https://classroomclipart.com/images/gallery/Clipart/Black_and_White_Clipart/Sports/TN_black-
white-boy-aiming-with-bow-and-arrow-archery-clipart.jpg
7. https://cdn.britannica.com/26/91526-050-C4C7B73A/Archer-recurve-bow-target.jpg

Prepared by: Anthony F. Batuto Checked by: Edna B. Gabriel

Rizalito A. Licos
Mary Ann L. Castro
Rosziel S. Rosales