Senior High School Department

Academic Year 2024-2025

ADAPTIVE TEACHING GUIDE

Teacher: Dandy C. Dumayao, LPT Learning Area: General Physics I
Teaching September 2-6, 2024
Quarter: 1
Date/s: Day 1/2
Most Essential Topic #5: Projectile Motion
Topic to Teach: Projectile Motion
Prerequisite Content-knowledge:

A. Basic Kinematic Concepts:

1. Velocity and Speed:
o Understanding the difference between velocity (a vector quantity with both magnitude and direction)
and speed (a scalar quantity with only magnitude).
o Ability to calculate average velocity and speed using basic formulas.
2. Acceleration:
o Knowledge of acceleration as a change in velocity over time.
o Understanding constant acceleration and its effects on the motion of objects.
3. Displacement and Distance:
o Differentiating between displacement (a vector quantity indicating the change in position) and distance
(a scalar quantity representing the total path traveled).
4. Equations of Motion:
o Familiarity with the kinematic equations that relate displacement, velocity, acceleration, and time under
constant acceleration.
o Understanding these equations for both vertical and horizontal motion.
B. Vector Components:
1. Resolution of Vectors:
o Ability to resolve a vector into horizontal and vertical components using trigonometric functions.
o Understanding the concept of vector addition to find resultant velocities or displacements.

Prerequisite Skill:
A. Problem-Solving Skills:
1. Application of Kinematic Equations:
o Ability to apply kinematic equations to solve problems involving constant acceleration, both in vertical
and horizontal motions.
o Proficiency in manipulating equations to solve for unknown variables such as time, velocity,
displacement, and acceleration.
2. Mathematical Calculation:
o Competence in performing arithmetic operations and algebraic manipulations.
o Skills in solving quadratic equations and handling equations with multiple variables.
B. Vector Analysis:
1. Vector Decomposition:
o Ability to decompose vectors into their horizontal and vertical components using trigonometric
functions (sine and cosine).
o Skills in combining these components to find resultant vectors or to solve problems involving two-
dimensional motion.
2. Vector Addition and Subtraction:
o Proficiency in adding and subtracting vectors graphically or algebraically.
o Understanding how to resolve vectors into components and recombine them to determine overall
motion.
C. Trigonometric Application:
1. Use of Trigonometric Functions:
o Ability to use sine, cosine, and tangent functions to resolve vectors and solve for components in
projectile motion problems.
o Skills in calculating angles and understanding their impact on the trajectory of a projectile.
D. Graphical Interpretation:
1. Understanding Motion Graphs:
o Skills in interpreting and creating graphs of motion, such as displacement vs. time and velocity vs.
time.
o Ability to analyze the shape of these graphs to extract information about motion, such as acceleration
or velocity.
Prerequisite Assessment:

1. What the SI unit of measure for speed?

2. What the SI unit of measure for velocity?

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 3. What the unit of measure for distance?
4. What the SI unit of measure for displacement?
5. What the SI unit of measure for time?
6. What the SI unit of measure for mass?
7. What the unit of measure for weight?
8. This quantity has magnitude and doesn’t have direction.
9. This quantity has both magnitude and direction.
10. Is weight a scalar or vector quantity?
Constant Speed Motion
11. What is the equation of displacement?
Constant Acceleration Motion
12. What is the equation of average speed?
13. What is the equation of average velocity?
Constant Acceleration Motion
14. What is the equation of adjacent?
15. What is the equation of opposite?
16. What is the equation of hypotenuse?

Pre-Lesson Remediation Activity:

The title of this game is “Complete Me”.

In this game you need to find out the word of the day. To be able to do that you will answer the unfinished
statement in Column A. The answers are provided in Column B. You will be choosing the letter of the correct
answer, after that, you will be pasting it on the space provided by each number. If you got all the correct
answer the word of the day will appear.
P. 1. A change in the position of the object is ______.
R. 2. The rate of motion refers to ______.
O. 3. Speed that does not change is _______.
J. 4. When there is a change in the speed of an object in every given time the speed is called _______.
E. 5. The measurement of the distance of an object from the base to the top is called _______.
C. 6. The length of path of a moving object travelled is _____.
T. 7. The shortest distance between two points is _______.
I. 8. Is the ratio of displacement and Time of travel is _____.
L. 9. The quantity that has magnitude only is ______.
E. 10. The quantity that has both magnitude and direction.

E. Vector Quantity
P. Motion
R. Speed
J. Average Speed
O. Constant Speed
T. Displacement
C. Distance
L. Scalar Quantity
I. Velocity
E. Height
Introduction

1. Time Frame: 2 hours (1 session)

2. Gain the following thinking skills from learning the lesson (RUA):
A. Remembering
- Students should be able to remember and state the key kinematic equations relevant to projectile
motion, including equations for calculating the range, time of flight, maximum height, and the
components of velocity.
B. Understanding
- Students should be able to describe projectile motion as the motion of an object that is projected
into the air and influenced only by gravity (and air resistance, if considered).
C. Applying
- Solve projectile motion problems using appropriate kinematic equations.
3. Context: The lesson on projectile motion is situated within the broader study of mechanics in physics, focusing on
the motion of objects under the influence of gravity. Understanding projectile motion is crucial for analyzing and
solving real-world problems in various fields, including sports, engineering, and space exploration. The lesson
builds on foundational concepts of kinematics and dynamics, emphasizing the practical application of physics
principles to predict and analyze the behavior of projectiles.
4. 21st Century Skills: Critical Thinking involves analyzing complex problems and thinking logically to solve them. In
the context of projectile motion, students will engage in critical thinking by: Evaluating and interpreting the results
of their calculations. Considering how changes in initial conditions (e.g., angle, speed) affect the projectile’s
trajectory and range. Solving real-world problems that require integrating multiple aspects of physics.
5. Overview of the Lesson:
The lesson introduces students to the concept of projectile motion, focusing on the equations and principles
that govern the trajectory of objects projected into the air. Through a combination of theoretical instruction and
practical experiments, students will learn to calculate the range, time of flight, and maximum height of projectiles.

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 The lesson will include discussions, hands-on activities, and problem-solving exercises designed to deepen
students' understanding and application of kinematic equations. By the end of the lesson, students will be able to
analyze projectile motion scenarios and apply their knowledge to real-life situations..
Students’ Experiential Learning:

I. Chunk 1: Introduction to Projectile Motion

1. Activity (15 minutes)

Experiment: Basic Projectile Motion and Free-Fall

Materials Needed:
1. A small ball or projectile
2. A meter stick or measuring tape
3. A stopwatch
4. A calculator

Part 1: Object Falling from a Height

Procedure:
1. Measure the Height:
 Choose a vertical drop height (e.g., 1.5 meters). Measure this height using a meter stick or measuring
tape.
2. Drop the Object:
 Drop the ball from the measured height and use the stopwatch to time how long it takes to hit the
ground. Make sure to release the ball without pushing it to avoid adding any horizontal velocity.
3. Calculate the Height
4. Compare Results:
 Compare the calculated height with the measured height to check the accuracy of your time
measurements and the formula.

Part 2: Object Launched at an Angle

(PhET simulation)

Procedure:
1. Set Up the simulator:
 Set up the launcher or canon to launch the projectile at a known angle 45 degrees. Use the mouse to
adjust the position of your canon.
2. Launch the Projectile:
 Launch the projectile by clicking the fire button. You are also provided with the initial velocity of the
canon ball with 20 m/s.

 Measure the horizontal distance (range) 𝑅 traveled by the projectile.

3. Measure the Range:

4. Calculate Time of Flight and Range

5. Verify Results:
Compare the measured range with the calculated range using your values for initial velocity and angle.

Discussion #1: First and Second Law

Example Calculations:

For Part 1:

If the measured time of fall is 0.55 seconds:

For Part 2:

Initial velocity 𝑣 = 20 m/s and launch angle 𝜃 = 4 5 ∘

 Horizontal velocity component

 Vertical velocity component

 Time of Flight

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  Range

Question No. 1:
A projectile is launched with an initial velocity at an angle. If the launch angle is increased while keeping the
initial speed the same, what happens to the shape of the trajectory and the range of the projectile?

Question No. 2:
A projectile is launched with a certain speed and angle. If you were to double the initial speed while keeping
the launch angle the same, how would the maximum height and range of the projectile be affected?

In question number 1, it was asking what would be the shape of the trajectory and the range of the projectile
after the angle is increased. The trajectory of a projectile is a parabola. As the angle increases, the horizontal
component of the initial velocity decreases, leading to a smaller range. The time of flight increases, but since
the horizontal distance covered is reduced, the overall range is less.

speed while keeping the launch angle. The same the maximum height 𝐻 is given by 𝑣2 sin(θ)2 / 2 𝑔, and the
In question number 2, how would the maximum height and range of the projectile if we are to double the initial

range 𝑅 is given by 𝑣2 sin(2θ) / 𝑔 . Since 𝑣 0 𝑦 and 𝑣 0 𝑥 are both proportional to the initial speed 𝑣 0,
doubling 𝑣 0 results in quadrupling both the maximum height and the range.

For better understanding of projectile motion, let’s talk about each equation and focus on understanding the
concept and formulas, then, after a while you will answer some questions.

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 Senior High School Department
Academic Year 2024-2025

ADAPTIVE TEACHING GUIDE

Teacher: Dandy C. Dumayao, LPT Learning Area: General Physics 1
Teaching September 2-6, 2024
Quarter: 1
Date/s: Day 2/2
Most Essential Topic #2: Projectile Motion
Topic to Teach: Projectile Motion
II. Chunk 2: Projectile Motion Equation and Derivation

Object Falling from a Height

1. Equation: H = ½ × a × t²
•H: Height of the cliff
•a: Acceleration due to gravity
•t: Time to hit the ground
2. Horizontal displacement: D = v × t
•v: Horizontal velocity (constant)
•t: Time of fall
Object Launched at an Angle
Initial velocity (v) at an angle θ to the horizontal
1. Decompose velocity into horizontal (vx) and vertical (vy) components:
•vx = v × cos(θ)
•vy = v × sin(θ)
2. Time of flight (from launch to landing): T = 2 × v sin(θ) / g
•g: Acceleration due to gravity (-9.8m/s2)
3. Range (horizontal distance traveled): R = vx × T
•Substitute T with the equation from point 2
Effective Steps for Problems
1. Identify the type of projectile motion (falling object or launched at an angle).
2. List known variables and identify the unknown(s).
3. Choose appropriate equation(s) based on the given information and what you need to find.
4. Solve the equation(s) for the unknown variable(s).
5. Check your answer for reasonableness.

On what sports can we apply the concept of projectile motion?

Basketball
When shooting a basketball, the ball follows a curved path towards the hoop. Players need to
understand the angles and force required to make the ball go through the hoop.

Football (Soccer)
Kicking a soccer ball involves projectile motion. Whether it’s a pass, a shot on goal, or a free kick,
the trajectory of the ball is influenced by the angle and speed of the kick.

Golf
Hitting a golf ball involves projectile motion as the ball is struck and follows a parabolic path.
Understanding this helps golfers optimize their shots for distance and accuracy.

Volleyball
Serving and spiking the volleyball involve projectile motion. Players aim to control the trajectory of
the ball to make effective plays.

Tennis
The serve and groundstrokes in tennis involve understanding the projectile path of the ball to
place it effectively over the net and within the court boundaries.

Javelin Throw
The javelin follows a projectile path after being thrown, and athletes need to calculate the right
angle and force for maximum distance.

Synthesis
Review Questions:
1. How is the time t it takes for an object to fall freely from a height H to the ground related to the
acceleration due to gravity g?
2. What is the relationship between the horizontal displacement D of an object falling with a constant
horizontal velocity v and the time t it takes to reach the ground?

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 3. The total time of flight 𝑇, which is the duration from launch to when the object returns to the same

4. What is the horizontal range 𝑅 of a projectile, and how is it calculated using the time of flight and
vertical level (or ground level), is expressed into what equation?

horizontal velocity?

Answer:
1. The time t it takes for an object to fall freely from a height H is related to the acceleration due to gravity
g by the equation:

2. The horizontal displacement 𝐷 of an object with constant horizontal velocity 𝑣 while falling is given by:

3.

4. The horizontal range 𝑅 of a projectile, which is the horizontal distance traveled during the time of flight,
is given by:

Evaluation:

A ball is launched horizontally from the edge of a cliff with a horizontal velocity of 15 m/s. The cliff is 50m
high.

Calculate the following:

1. The time it takes for the ball to hit the ground.

3. If the ball was instead launched with an initial velocity of 25 m/s at an angle of 4 5 ∘ to the horizontal
2. The horizontal distance traveled by the ball before it hits the ground.

from the same cliff, calculate:

 The time of flight.
 The range of the projectile.

Solution:

Time to Hit the Ground (for Horizontal Launch)

For an object falling from a height 𝐻 H with no initial vertical velocity (horizontal launch), use the
equation:

No. 1

where 𝐻 = 50 m and 𝑎 = 9.8 m/s 2.

Rearrange to solve for 𝑡:

No. 2
Horizontal Distance Traveled (for Horizontal Launch)

The horizontal displacement 𝐷 is given by:

where 𝑣 = 15 m/s and 𝑡 = 3.19 s.

No. 3.1
Projectile Motion with Angle of 45∘

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 Time of Flight

First, decompose the initial velocity 𝑣:

The time of flight 𝑇 is given by:

No. 3.2
Range

The horizontal range 𝑅 is given by:

To summarize;

1. Time to Hit the Ground (Horizontal Launch): 3.19 s

Time of Flight (Angle 4 5 ∘): 3.61 s

2. Horizontal Distance Traveled (Horizontal Launch): 47.85 m

Range (Angle 4 5 ∘): 63.8 m

3.
4.

This problem demonstrates the application of both falling and projectile motion equations, providing insights into how
horizontal and angled launches interact with vertical motion.

Values Integration
The teacher will ask:
1. Why do you think it is important for you to have faith in solving problems that involves projectile motion?
2. How about in real-life scenarios, how important is the concept of projectile motion in creating and innovating?

RUA of a Student’s Learning:

Directions: Answer the following word problems.

1. What equation will use if we are to solve for the total time traveled by the projectile?
2. How about when we are to look for the total range of the projectile?
3. How about the height of a free falling object?
4. A basketball player shoots the ball with an initial velocity of 10 m/s at an angle of 30∘ above the horizontal.
Assume the height of the basket is 2.5 m above the ground.
a. Calculate the time of flight until the ball reaches the basket.
b. Determine the horizontal distance traveled by the ball when it reaches the height of the basket.
c. Find the maximum height reached by the ball above the launch point.
Assume the acceleration due to gravity, g, is 9.8 m/s2

Post-lesson Remediation Activity:

Answer the following word problems.
In a one whole sheet of paper calculate the problems below using the appropriate kinematic equations.

1. Calculate the Height of the Cliff

Acceleration due to gravity, 𝑎 = 9.8 m/s 2

Given:

Time to hit the ground, 𝑡 = 2.0 s

2. Calculate the Horizontal Displacement

Horizontal velocity, 𝑣 = 5.0 m/s

Given:

Time of fall, 𝑡 = 2.0 s t=2.0s

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