Introduction to
Projectile Motion
Mr. Chin-Sung Lin
Introduction to Projectile Motion
 What is Projectile Motion?
 Trajectory of a Projectile
 Calculation of Projectile Motion
Introduction to Projectile Motion
 What is Projectile Motion?
 Trajectory of a Projectile
 Calculation of Projectile Motion
What is Projectile Motion?
Features of Projectile Motion?
Thrown into the Air
2-D Motion
Parabolic Path
Affected by Gravity
Determined by Initial Velocity
Definition: Projectile Motion
Projectile motion refers to the 2-D motion of
an object that is given an initial velocity and
projected into the air at an angle.
The only force acting upon the object is
gravity. It follows a parabolic path
determined by the effect of the initial
velocity and gravitational acceleration.
Definition: Projectile Motion
Projectile motion refers to the 2-D motion of
an object that is given an initial velocity and
projected into the air at an angle.
The only force acting upon the object is
gravity. It follows a parabolic path
determined by the effect of the initial
velocity and gravitational acceleration.
Introduction to Projectile Motion
 What is Projectile Motion?
 Trajectory of a Projectile
 Calculation of Projectile Motion
Trajectory (Path) of a Projectile
Trajectory (Path) of a Projectile
y
v0
x
y
x
y
x
y
x
y
 Velocity is changing and
the motion is accelerated
 The horizontal
component of velocity (vx)
is constant
 Acceleration from the
vertical component of
velocity (vy)
g = 9.81m/s2
 Acceleration due to
gravity is constant, and
downward
 a = - g = - 9.81m/s2
x
y
 The horizontal and
vertical motions are
independent of each other
 Both motions share the
same time (t)
 The horizontal velocity
....vx = v0
 The horizontal distance
.... dx = vx t
g=
9.81m/s2
 The vertical velocity ....
.... vy = - g t
 The vertical distance ....
.... dy = 1/2 g t2
x
Trajectory (Path) of a Projectile
 The path of a projectile is the result of the
simultaneous effect of the H & V components of its
motion
 H component  constant velocity motion
 V component  accelerated downward motion
 H & V motions are independent
 H & V motions share the same time t
 The projectile flight time t is determined by the V
component of its motion
Trajectory (Path) of a Projectile
 H velocity is constant vx = v0
 V velocity is changing vy = - g t
 H range:
dx = v0 t
 V distance:
dy = 1/2 g t2
Introduction to Projectile Motion
 What is Projectile Motion?
 Trajectory of a Projectile
 Calculation of Projectile Motion
Calculation of Projectile Motion
 Example: A projectile was fired with initial
velocity v0 horizontally from a cliff d meters
above the ground. Calculate the horizontal
range R of the projectile.
v0
d
g
t
R
Strategies of Solving Projectile Problems
 H & V motions can be calculated independently
 H & V kinematics equations share the same
variable t
v0
d
g
t
R
Strategies of Solving Projectile Problems
H motion:
dx = vx t
R = v0 t
V motion:
dy = d = 1/2 g t2
t = sqrt(2d/g)
So,
R = v0 t = v0 * sqrt(2d/g)
v0
d
g
t
R
Numerical Example of Projectile Motion
H motion:
dx = vx t
R = v0 t = 10 t
V motion:
dy = d = 1/2 g t2
t = sqrt(2 *19.62/9.81) = 2 s
So,
R = v0 t = v0 * sqrt(2d/g) = 10 * 2 = 20 m
V0 = 10 m/s
19.62 m
g = 9.81 m/s2
t
R
Exercise 1: Projectile Problem
A projectile was fired with initial velocity 10 m/s
horizontally from a cliff. If the horizontal range of the
projectile is 20 m, calculate the height d of the cliff.
V0 = 10 m/s
d
g = 9.81 m/s2
t
20 m
Exercise 1: Projectile Problem
H motion:
dx = vx t
20 = v0 t = 10 t
V motion:
dy = d = 1/2 g t2 = 1/2 (9.81) 22 = 19.62 m
So,
d = 19.62 m
t=2s
V0 = 10 m/s
d
g = 9.81 m/s2
t
20 m
Exercise 2: Projectile Problem
A projectile was fired horizontally from a cliff 19.62 m
above the ground. If the horizontal range of the
projectile is 20 m, calculate the initial velocity v0 of the
projectile.
V0
19.62 m
g = 9.81 m/s2
t
20 m
Exercise 2: Projectile Problem
H motion:
dx = vx t
V motion:
dy = d = 1/2 g t2
So,
20 = v0 t
20 = v0 t = 2 v0
t = sqrt(2 *19.62/9.81) = 2 s
v0 = 20/2 = 10 m/s
V0
19.62 m
g = 9.81 m/s2
t
20 m
Summary of Projectile Motion
 What is Projectile Motion?
 Trajectory of a Projectile
 Calculation of Projectile Motion
Projectile Motion
with Angles
Mr. Chin-Sung Lin
Example: Projectile Problem – H & V
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. What’s the horizontal and
vertical components of the initial velocity?
g = 9.81 m/s2
20 m/s
vy
60o
vx
Example: Projectile Problem – At the Top
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. What’s the velocity of the
projectile at the top of its trajectory?
g = 9.81 m/s2
v
20 m/s
vy
t
60o
vx
R
Example: Projectile Problem – Height
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. What’s the maximum height
that the ball can reach?
g = 9.81 m/s2
20 m/s
vy
h
60o
vx
Example: Projectile Problem - Time
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. How long will the ball travel
before hitting the ground?
g = 9.81 m/s2
20 m/s
vy
60o
vx
t
Example: Projectile Problem – H Range
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. How far will the ball reach
horizontally?
g = 9.81 m/s2
20 m/s
vy
60o
vx
R
Example: Projectile Problem – Final V
A projectile was fired from ground with 20 m/s initial
velocity at 60-degree angle. What’s the final velocity of
the projectile right before hitting the ground?
g = 9.81 m/s2
20 m/s
vy
60o
vfx
vx
vfy
vf
Example: Projectile Problem – Max R
A projectile was fired from ground with 20 m/s initial
velocity. How can the projectile reach the maximum
horizontal range? What’s the maximum horizontal range
it can reach?
g = 9.81 m/s2
20 m/s
q
R