Projectile motion refers to the two-dimensional motion of an object under the influence of gravity. A projectile has both horizontal and vertical motion, with the horizontal motion being constant and the vertical motion accelerating due to gravity. The path of a projectile through the air is a parabolic curve. Examples of projectile motion include throwing a ball, kicking a field goal, or launching a rocket.

1. PROJECTILE MOTION
• What happens when you launch the bird at a large angle with respect to the
ground? Why would you want to do this?
• What happens when you launch the bird at a smaller angle with respect to the
ground? Why would you want to do this?

2. PROJECTILE MOTION
• Definition: Two-dimensional motion of an object
• Free-fall with an initial horizontal velocity
• Projectile follows a parabolic path
• There is both horizontal and vertical motion
• Vertical motion is influenced by gravity
• Horizontal motion is constant
• Examples: golf, soccer, archery, football, etc.

3. PROJECTILE MOTION
• The path (trajectory) of a projectile is a parabola
• Projectile: Any object which projected by some
means and continues to move due to its own inertia
(mass).
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4. EXPERIMENT
What do you think? Which ball will hit the ground first?
a) The left ball will hit first
b) The right ball will hit first
c) They will hit the ground at the same time.

5. PROJECTILES

6. PROJECTILE MOTION
• Recall that velocity is a vector!
• There are two components for the vectors velocity – horizontal (vx)
and vertical (vy)
• Horizontal and vertical are perpendicular to one another and are
independent of each other.
Vx is CONSTANT
Vy is influenced by gravity
(Free-fall motion!)

7. PROJECTILE MOTION
• What do you notice here about the displacement of the projectile in the x & y
directions? • X: direction: displacement is the SAME every second!
• Y: displacement INCREASES every second

8. PACKAGE DROP
• The package follows a parabolic path and remains directly below the plane
at all times
• The vertical velocity changes (faster, faster)
• The horizontal velocity is constant!

9. HORIZONTALLY LAUNCHED PROJECTILES
Projectiles which have NO upward trajectory and NO initial VERTICAL
velocity.
vox vx constant
voy 0m/ s

10. HORIZONTALLY LAUNCHED PROJECTILES
To find the horizontal and vertical displacements:
• Need two equations: One for the “x” direction and one for the “y” direction.
• use our kinematic equations
xf = xi + vit + 0.5at2
x
X-direction: x =oxtxit
vv y-direction: y = 0.5ayt2
Remember, the velocity is Remember that since the projectile
CONSTANT horizontally, so that is launched horizontally, the INITIAL
means the acceleration is ZERO! VERTICAL VELOCITY is equal to
ZERO.

11. HORIZONTALLY LAUNCHED PROJECTILES
To find the horizontal and vertical velocities:
• Need two equations: One for the “x” direction and one for the “y” direction.
• use our kinematic equations
vf = vi + at
X-direction: vxfv= t xi
x ox v y-direction: vyf = vyi + ayt
OR vyf2 = vyi2 – 2ayΔy

12. HORIZONTALLY LAUNCHED PROJECTILES
Example: A plane traveling with a What do I What I want to
horizontal velocity of 100 m/s is know? know?
500 m above the ground. At some
point the pilot decides to drop vox=100 m/s t=?
some supplies to designated
target below. y = 500 m x=?
(a) How long are the supplies in the
air? voy= 0 m/s
(b) How far away from point where it g = -9.8 m/s/s
was launched will it land?
(a) y = 0.5ayt2  -500 = 0.5(-9.80)t2
t2= 102.04  t = 10.1 seconds (b) x = vxit = (100)(10.1) = 1010 m

13. PROJECTILES: LET’S REVISIT THIS VIDEO…
• Why did they land at the same time?
• As soon as both balls are released, they are in “free fall”
• Even if a marble is given an initial horizontal velocity, its initial vertical velocity is still zero
and only gravity is influencing it in the y-direction…just like it is for a marble in free-fall
motion!