The document discusses projectile motion, which refers to the motion of an object thrown or projected into the air at an angle, noting that the motion is determined by the object's initial velocity and gravity and follows a parabolic trajectory. It explores the independent horizontal and vertical components of a projectile's motion, with the horizontal motion at constant velocity and the vertical motion undergoing gravitational acceleration, and examines how changing the launch angle impacts the height, range, and time of the projectile's flight.

1. Projectile Motion
Motion In Two Dimensions
We restrict ourselves to objects thrown near the Earth’s surface so that gravity
can be considered constant.

2. Objective
At the end of the lesson the
learners will be able to :
•Investigate the relationship
between the projection angle,
the height and range of the
projectile

3. Projectile motion refers to the motion of an
object that is thrown, or projected into the air
at an angle.
The motion of a projectile is determined only
by the object’s initial velocity and gravity.

4. Projectile motion applies to sports.

5. Projectile motion applies to destructive
projectiles.

6. Projectile motion is a combination of horizontal motion and
vertical motion.
The horizontal motion of a projectile is constant because no
gravitational force acts horizontally

7. The vertical motion of a projectile is nothing more than free fall
with a constant downward acceleration due to gravity.

8. The vertical motion of a projected object is
independent of its horizontal motion.

10. A projectile moves horizontally with constant velocity
while being accelerated vertically. The result is a motion
in a curved path.

12. The path of a projectile is called its
trajectory.
The trajectory of a projectile in free fall
is a parabola.

13. A projectile, once projected, continues in
motion by its own inertia and is influenced
only by the downward force of gravity.

14. An object projected
horizontally will
reach the ground in
the same time as
an object dropped
vertically.
No matter how
large the horizontal
velocity is, the
downward pull of
gravity is always
the same.

16. The cannonball falls the same amount of distance as it did when it was merely
dropped from rest

18. Horizontally launched projectile
Horizontal velocity is constant. Vertical velocity is changing
due to gravitational acceleration..

19. Vertically launched projectile
The horizontal velocity component remains the same size
throughout the entire motion of the cannonball.

20. Projectiles launched at different angles.

21. Sports Trivia
Maximum range is achieved if the projectile is
fired at an angle of 45 degrees with respect to
the horizontal.

25. In Conclusion
A projectile is any object thrown horizontally or vertically upon
which the only force acting is gravity.
Projectiles travel with a parabolic trajectory due to
the influence of gravity.
There are no horizontal forces acting upon projectiles
and thus no horizontal acceleration.
The horizontal velocity of a projectile is constant.
there is a vertical acceleration caused by gravity
(9.8 m/s).
The horizontal motion of a projectile is independent
of its vertical motion.

26. Relationship between angles and the height:
•As the angle increases, the height also increases.
Relationship between the angle and the
range:
•If the angle is less than 45 degrees, the range is
increasing. if the angle is greater than 45 degrees the
range is decreasing.
Relationship between the angle and the time:
•As the angle increases, the time also increases.
Maximum range is achieved if the projectile is
fired at an angle of 45 degrees with respect to

27. In the diagram below, two different possible trajectories are shown for a
ball thrown by a center fielder to home plate in a baseball game. Which
of the two trajectories, the higher on or the lower one, will result in a
longer time for the ball to reach home plate? Explain

28. Test your knowledge
Suppose a snowmobile is equipped with a
flare launcher which is capable of launching
a sphere vertically. If the snowmobile is in
motion and launches the flare and maintains a
constant horizontal velocity after the launch,
then where will the flare land (neglect air
resistance)?
A.On the snowmobile.
b. Ahead the snowmobile.
C. Behind the snowmobile.

29. Test your knowledge
Suppose an airplane drops a flare while it
is moving at constant horizontal speed at
an elevated height. Assuming that air
resistance is negligible, where will the flare
land relative to the plane?
A. Directly below the plane.
B. Below the plane and ahead of it.
C. Below plane and behind it.

32. ASSIGNMENT.
1. Why does the horizontal component of a
projectile’s motion remain constant?
2. Why does the vertical component of a
projectile’s motion undergo change?
3. A projectile is launched vertically at 100 m/s. If
air resistance is neglected, at what speed does it
return to its initial level?
In a long bond paper, draw 2 situations in
which you can observe projectile motion and
explain each situation.