DEPARTMENT OF EDUCATION

DIVISION OF LAPU-LAPU CITY

MARIGONDON NATIONAL HIGH SCHOOL
Marigondon, Lapu-Lapu City, Cebu, Philippines 6015
Telephone Number: 254 -4295

Name of Learner: Score:

Teacher: Grade and Section: Date:
SCIENCE 9_QUARTER 4_Learning Activity Sheet 1: Projectile Motion
Most Essential Learning Competency:
• Describe the horizontal and vertical motions of a projectile S9FEIVa-34
• Investigate the relationship between the angle of release and the height and range of the projectile S9FEIVa-35
CONCEPT NOTES:
Kinematics is about the range of movement or change a system can undergo, or the state space in which it acts.
Dynamics is about the movement it undergoes according to the laws of motion.
Projectile Motion is the motion of a body
projected horizontally or at an angle other
than 90⁰ with the horizontal. It examples
includes a soccer ball being kicked, a
basketball that was thrown, a bullet fired, and
a water out of a fountain. There are two
components of projectile motion: the
Horizontal component is uniform motion;
and the Vertical component is free fall.
- in projectile motion it change occurs only in
the vertical velocity because of the influence
of gravity while the horizontal velocity does
not alter. Thus, if air resistance is neglected, a
projectile moves horizontally at constant
speed and simultaneously travels vertically
with acceleration equal to gravity of 9.8 m/s2.
- the direction of velocity always to the right
and the direction of the acceleration changes from up and down.
- the path of a projectile is called trajectory, which follows a parabola. This results from the combined motions in the horizontal
and vertical directions. At the highest points of trajectory, only the vertical velocity is zero, and the acceleration is 9.8 m/s2.
- The horizontal distance traveled by a projectile is range while the vertical distance is height.
- a projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the
downward force of gravity.
CHARACTERISTICS OF A PROJECTILE TRAJECTORY:
• There are no horizontal forces acting upon projectiles and
thus no horizontal acceleration,
• The horizontal velocity of a projectile is constant (a never
changing in value),
• There is a vertical acceleration caused by gravity; its value
is 9.8 m/s2, down,
• The vertical velocity of a projectile changes by 9.8 m/s
each second,
• The horizontal motion of a projectile is independent of its
vertical motion.
TYPES OF PROJECTILE MOTION
A. Projectile launched horizontally (zero angle) B. Projectile launched at an angle

A projectile launched horizontally has no initial vertical When a projectile is launched upward at an angle, its
velocity. Thus, its vertical motion is identical to that of a velocity has two components:
dropped object. The downward velocity increases uniformly 1. a constant horizontal velocity that moves in the same
 due to gravity as shown by the vector arrows of increasing direction as the launch, the acceleration of which is zero; and
lengths. The horizontal velocity is uniform as shown by the 2. an upward positive vertical velocity component that is
identical horizontal vector arrows. decreasing in magnitude until it becomes zero at the top of
The dashed black line represents the path of the object. The the trajectory (therefore it no longer goes up any further).
velocity vector v at each point is in the direction of motion But because gravity makes it accelerates downward at a rate
and thus is tangent to the path. The velocity vectors are of 9.8 m/s per second or 9.8 m/s2, (therefore it stays at rest
solid arrows, and velocity components are dashed. (A only for an instant) it will start to descend with an increasing
vertically falling object starting at the same point is shown at negative
the left for comparison; vy is the same for the falling object vertical velocity until it is stopped by something.
and the projectile.) So as the projectile moves forward horizontally with uniform
For a projectile beginning and ending at the same height, velocity, its vertical velocity is also accelerated creating a
the time it takes a projectile to rise to its highest point trajectory that is a parabola. The trajectory is shown in black
equals the time it takes to fall from the highest point back to dash, the velocity vectors are in solid arrows, and velocity
its original position. components are dashed.
Sample problem: If a bullet is fired with a speed of 600 Sample problem: A soccer ball is kicked 35º above with an
m/s horizontally from a height of 48 m, how long will it take initial velocity of 23.0 m/s and reaches a maximum height of
to hit the ground? What is the range of the projectile? 1.27 m at 0.10 second. Determine the horizontal
Assume that there is no air resistance. displacement (range) of the ball.
Given: 𝑣𝑖𝑥= 600 m/s
𝑣𝑖𝑦= 0 (bullet was fired horizontally)
𝑑𝑦 = - 48 m (negative sign indicates height of fall)
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 Given: 𝑣𝑜 = 23 m/s sin θ = 0.574
ax = 0 ay = -9.8 m/s2 θ = 35º cos θ = 0.819 t = 0.10 s
Find: 𝑡 and 𝑑𝑥 Find: Range (𝑑𝑥) = ?
Solution: The original equation that we need to use is: Solution:
𝑑𝑥 = 𝑣𝑜 cos θ t
𝑑𝑥 = (23 m/s) (0.819) (0.20 s)
𝑑𝑥 = 3.77 m
Solve for t:
t = 2t
t = 2 (0.10 s)
t = 0.20 s

Learning Task 1: True or False (10 points)

Identify if the following statement is TRUE or FALSE. Write T if the statement is correct and F if it is incorrect.
___ 1. A projectile motion has a constant velocity in the horizontal direction.
___ 2. The velocity at the maximum height of a projectile motion is not equal to zero.
___ 3. The path of the projectile motion is called a trajectory.
___ 4. A force acting on a projectile is gravity.
___ 5. The gravity at the maximum height of a projectile motion is zero.
___ 6. At 90⁰ angle, the object experience projectile motion.
___ 7. The highest range the object reach is at 45⁰ angle.
___ 8. Range is the highest vertical distance in projectile.
___ 9. Projectile motion has two component the vertical and horizontal.
___ 10. The acceleration in vertical component of projectile motion is constant at 9.8 m/s2.
Learning Task 2: Figure analysis (15 points)
The motion of a projectile may be described in terms of range and the maximum height it reaches. But what affects these
kinematic quantities? Below is a figure of the height reached and range covered by a projectile launched at the same initial
velocity but at different angles. Study it carefully and answer the questions that follow. Use separate paper to answer this.
1. How do you describe the height reached by the projectile at different
projection angles? (1pt)
2. At what angle does it reach the highest? (1pt)
3. At what angle does it reach the lowest? (1pt)
4. Does the projection angle affect the maximum height reached? Why do
you say so? (3pts)
5. How do you describe the range covered by the projectile at different
projection angles? (2pts)
6. At what angle/s does it reach the farthest? (1pt)
7. At what angle/s does it reach the nearest? (1pt)
8. What angles cover the same range? (2pts)
Height and range of a projectile launched at different angles 9. Does the projection angle affect the range covered? Explain. (3pts)
Learning Task 3: Picture analysis (5 points)
Choose the letter that correctly describes the motion of the basketball at different positions as indicated in the diagram below.
A. vertical velocity is zero; horizontal velocity is constant
B. final velocity is maximum
C. initial velocity is maximum
D. vertical velocity decreases; horizontal velocity is constant
E. vertical velocity increases; horizontal velocity is constant
F. vertical velocity increases; horizontal velocity decreases
G. vertical velocity decreases; horizontal velocity increases

1. _______ 2. _______ 3. _______ 4. _______ 5. _______

WRITTEN WORKS (50%): 20 POINTS

I. MULTIPLE CHOICE: (20 POINTS) Read and analyze its questions and choose the correct answer from the given
choices. Write the CAPITAL LETTER of your answer before the number.
1. A sepak takraw that is kicked from a height of two meters. What do you call to the path it follows?
A. Circular B. Hyperbolic C. Linear D. Parabolic
2. A Batang Pinoy athlete from you school throws a javelin, always at the same speed, at four different angles (30⁰,
40⁰, 60⁰, and 80⁰) above horizontal. Which two throws cause the javelin to land the same distance away?
A. 30⁰ and 80⁰ B. 30⁰ and 40⁰ C. 30⁰ and 60⁰ D. 40⁰ and 60⁰
3. A soccer ball is hit vertically upward by a player. What is its acceleration after 1 second?
A. 0 m/s B. 1 m/s C. 9.8 m/s D. -9.8 m/s
4. If a water hose is aimed in order for the water to land with the greatest horizontal range, what would be the angle
of projection?
A. 0⁰ B. 30⁰ C. 45⁰ D. 60⁰
5. At what angle of projectile is the horizontal range minimum?
A. 45⁰ B. 60⁰ C. 75⁰ D. 90⁰
6. Suppose a ping pong ball is tossed. When the ball reaches the highest point, which statement about the ball’s
velocity and acceleration is true?
A. Both its velocity and its acceleration are zero. C. Its velocity is not zero and its acceleration is zero.
B. Its velocity is zero and its acceleration is not zero. D. Neither its velocity nor its acceleration is zero.
7. A ball is hit at an angle of 30⁰. At what point in its trajectory does this projectile have the least speed?
A. Just after it was launched C. Just before it hits the ground
B. At the highest point in its flight D. Halfway between the ground and the highest point
8. A ball is hit at an angle of 30⁰ and it reaches a distance of 50 m. Given the same initial velocity, at what other
angle should a ball be hit to reach the same distance?
A. 15⁰ B. 45⁰ C. 60⁰ D. 75⁰
9. A bomb is dropped from an aeroplane moving horizontally at a constant speed. When air resistance is taken into
consideration, what happen to the bomb?
A. It flies with the aeroplane. C. It falls to earth ahead of the plane.
B. It falls to earth behind the aeroplane. D. It falls to earth exactly below the aeroplane.
10. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown?
A. Its vertical speed increases, and its horizontal speed increases.
B. Its vertical speed increases, and its horizontal speed remains the same.
C. Its vertical speed remains the same, and its horizontal speed increases.
D. Its vertical speed remains the same, and its horizontal speed remains the same.
Item 11 – 15. Based your answer from the following information.
A cannonball is fired and follows the parabolic path shown
below. Air resistance is negligible.
Point B is the highest point on the path and points A and C
are at the same height.
11. Which of the following best describes the direction of the net force on the ball at point A?
A. up and to the right B. to the right C. down D. no net force
12. Which of the following best describes the direction of the velocity of the cannonball at point B?
A. up and to the right B. to the right C. down and to the right D. down
13. Which of the following best describes the direction of the acceleration of the ball at point C?
A. up and to the right B. to the right C. down and to the right D. down
14. How do the acceleration of the ball at the three points compare?
A. aA < aB < aC B. aB < aA < aC C. aA = aB = aC D. aB < aA = aC
15. How do the speeds of the cannonball at the three points compare?
A. vA < vB < vC B. vB < vA < vC C. vA = vB = vC D. vB < vA = vC
 II. ESSAY: (5 POINTS)
1. Suppose you are a javelin throw athlete; how will you apply your knowledge of
projectile motion in order to win the event? (5 pts)

PERFORMANCE TASK (50%): 50 POINTS

Performance task 1: What is my Sport?
Objective: Relate projectile motion to sports.
Materials: pen, coloring materials, picture, long bond paper.
Procedure: Draw or cut out pictures of your sport/s which observe projectile motion and explain it in a long bond paper.
Closure: What are the examples of sports that exhibits projectile motion aside from the chosen sport?
Rubric:
Picture: 10 points
Content/explanation: 25 points
Creativity/design: 15 points
Total: 50 points
REFLECTION:
What I have learned? I learned …

NOTE: DO AND ANSWER ALL THE LEARNING TASK, WRITTEN WORKS AND PERFORMANCE TASK.
Sources: Learning modules from DIVISION OF PASIG CITY and DIVISION OF LAPU – LAPU CITY

ANSWER SHEET
Learning Learning Written
Task 1 Learning Task 2 (15 points) Task 3 Works 1
(10pts) (5 pts) (20 pts)
1. 1. 1. 1.
2. 2. 2. 2.
3. 3. 3. 3.
4. 4. 4. 4.
5. 5. 5. 5.
6. 6. 6.
7. 7. 7.
8. 8. 8.
9. 9. 9.
10. 10
Written works essay answer: (5points) 11.
12.
13.
14.
15.
Reflection: (10 points) What I have learned? I learned …