Republic of the Philippines

Department of Education
Region 1
Schools Division Office
DAGUPAN CITY NATIONAL HIGH SCHOOL
Tapuac, Dagupan City

FOURTH QUARTER ACTIVITY SHEET NO. 1 in SCIENCE 9

S.Y. 2023-2024
I. Topic/Lesson: The Horizontal and Vertical Motions of Projectile
II. MELC & L.C. Code: Describe the horizontal and vertical motions of projectile (S9FE-Iva-34)
III. Objectives:
 Define concepts involving projectile and projectile motion
 Describe the horizontal and vertical motions of a projectile
 Cite examples and explain the horizontal and vertical motions of a projectile under various cases.

IV. Discussion:
Uniform acceleration is when the speed of an object changes at the same rate. This leads to the study of motion using
equations and known as kinematics. Knowing details such as how fast an object is going after a given time interval rather than just the
fact that the object is moving is our primary interest. To describe the properties, characteristics and behavior of motion with greater
detail the following equations were discussed.

Table1: Kinematic Equations (horizontal motion)

The four kinematic equations can be utilized to predict the unknown information about an object’s motion if other information is present.
These equations can only be utilized if the motion undergoes constant velocity (a = 0) or a motion having a constant acceleration. The
motion of objects acted solely by gravity is also an example of uniform acceleration having a constant value of g = −9.8 m/s 2. (“-”
means downward). It is associated with free-falling objects and objects thrown vertically straight to the air. With this, we also transform
our Kinematic Equations along the horizontal to Kinematic Equations along the vertical by changing variable x to y and a to g.

Table2: Kinematic Equation (vertical motion)

There are few conceptual characteristics of free fall motion that you need to recall in applying the equations from the above table:
 An object in free-fall experiences an acceleration of -9.8m/s2. (The negative sign indicates a downward acceleration) Whether
explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s2 for any freely falling object.
 If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s.
 If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it
reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic
equations
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 If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and
opposite in sign to the velocity that it has when it returns to the same height.

Projectile motion is a form of motion where an object given an initial velocity is thrown or projected and is allowed to be acted
on by gravity in a curved-like path. These objects are called projectiles. The curved path followed by a projectile is called a trajectory. In
projectile motion, the physical principles and mathematical formulas that must be applied are those concepts that were recalled earlier.
Combining the two allows us to make predictions concerning projectile motion. As such the principles and formulas are well understood
in various types of projectile problems.

Type 1: Horizontally Launched Projectiles

Horizontally launched projectiles are projectiles that are launched with an initial velocity from an elevated position and follows
a curved-like path to the ground. Consider the figure below.

Figure 1.3: A man diving into the water

Illustrated by: Jumari S. Sapio

In Figure1.3, the motion of the man as it dives into the water is moving along a curved path downwards due to a natural force
called gravitational force of the earth or gravity. Gravity is the natural force that causes objects to fall towards the earth. Hence, the
acceleration due to gravity is always directed downwards and has a value of -9.8m/s 2. With this, the motion of the man undergoes
projectile motion.

Type 2: Angle-Launched Projectiles

Angle-launched projectiles are projectiles launched at an angle with respect to the horizontal and rises to a peak while moving
horizontally. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. Consider the
situation below.
Figure 1.4: A sepak takraw player kicking a rattan ball over the net

What is the projectile in Figure 1.4? If you think that the rattan ball is the projectile, then you are right! How do you
describe its trajectory? The rattan ball is travelling on a curved path. In mathematical terms, what do you call this
pattern? Try to rearrange the following letters for you to answer the question.

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 Activity 1: SKETCH ME QUICK

Situation1: Free Kick! Situation 2: Throwing of Garbage!

Sam was given a free kick. Illustrate the Mat wants to shoot a crumpled paper inside the
trajectory of the ball in order for Sam to get a goal. On trash bin. Help him shoot his garbage right at the trash
your answer sheet, explain how you came up with that can by illustrating the trajectory. Explain below how you
trajectory. ended up with that trajectory.

The Horizontal and Vertical Motion of a Projectile

Type I: Horizontally Launched Projectiles

Suppose you roll a marble on a frictionless table, observe the motion of the marble as it goes down the floor. The
following illustration is a strobe of the falling marble.
Figure 2.2: Motion diagram of a marble falling from a table.

From Figure 2.2 the vertical velocity of the marble is gradually increasing from points A to D (as illustrated by the increasing
downward arrows). Due to the presence of gravity accelerating at the marble -9.8 m/s2 this causes the vertical velocity (𝑣𝑦) to increase.
For the horizontal velocity (𝑣𝑥), there is no external net force acting along the horizontal direction which means that there is
no acceleration along this direction (ax=0), resulting to a constant horizontal velocity (𝑣𝑥) as illustrated by a consistent set of horizontal
rays to the right for each of the location of the marble in the strobe.

Type II: Angle-Launched Projectiles

From the illustration below, discuss the motion of

the baseball as it was hit by a bat.

Figure 2.3: Motion diagram of a baseball as it was

hit by a bat

For angle-launched projectiles, horizontal velocity

(𝑣𝑥) is still constant while the vertical velocity can be
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described in three parts. From Figure 2.3, it is observed that as the projectile ascends (point A to B) the upward vertical velocity (𝑣𝑦) is
decreasing, this is because the direction of gravity is opposite to the projectile motion. As the projectile reaches the maximum height
(point B) it momentarily stops causing a vertical velocity equal to zero (𝑣y = 0). When the projectile descends (point B to C) the direction
of its motion is in the direction of the gravitational force hence the magnitude of its vertical velocity is increasing.
So, in Figure 2.3 the vertical velocity of the baseball as it rises to the air decreases due to the opposing direction of gravity
compared to its motion. When the baseball reaches the maximum height, its vertical velocity becomes zero. When it descends its
vertical velocity increases since the direction of the baseball’s motion is the same with gravity.

Enrichment Activity
Fill in the table below if the quantities are present in either horizontal or vertical motion. Assume air resistance to be zero.

ASSESSMENT A. Changes continuously C. Gradually

Multiple Choice: Read the following items carefully. On your increases
answer sheet, write the letter of the BEST ANSWER from the B. Gradually decreases D. Remains the
given options. same
1. What force enables objects to reach the ground? 7. What happens to the horizontal velocity of an object as it
A. Frictional Force C. Gravitational Force travels through the air?
B. Magnetic Force D. Tension Force A. Changes continuously C. Gradually
2. What is the shape of the trajectory of a projectile? increases
A. Circular C. Hyperbolic B. Gradually decreases D. Remains the
B. Elliptical D. Parabolic same
3. Which of the following composed the two linear motions of a 8. If you throw a baseball straight up, what is its vertical
projectile? velocity at the highest point?
A. Horizontal and Circular Motion C. Horizontal and Vertical A.0m/s C.0m/s2
Motion B.9.8m/s D.-9.8 m/s2
B. Vertical and Circular Motion D. Vertical and Curvilinear 9. If a stone is horizontally launched at a certain height, how do
Motion you describe the magnitude of its vertical velocity as it
4. What is referred to as an object that is given an initial approaches the
velocity and is then acted solely upon by gravitational force? ground?
A. Project C. Target A. Changes continuously C. Gradually
B. Projectile D. Trajectory increasing
5. What do you call the path followed by an object under B. Gradually decreasing D. Remains the
projectile motion? same
A. Project C. Target 10. What is the acceleration of a baseball thrown to the air at
B. Projectile D. Trajectory an angle of 45 degrees with respect to the horizontal as it
6. What happens to the vertical velocity of an object as it returns to the ground?
travels through the air? A.0m/s C.0m/s2
B.9.8m/s D.-9.8 m/s2
KEY ANSWER

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