Projectile Motion
 A projectile is an object moving through the air (both horizontally and vertically)
that has only the force of gravity Fg acting on it. It has uniform motion (constant
velocity) occurs in x-axis, and accelerated motion (due to gravity) in the y-axis.
 Horizontally:
Uniform Motion
(Constant Speed)
vx  x
t
Vertically: The “Big 5” Eq'ns for
Accelerated Motion
(with a = – 9.8 m/s2)
 Since we will be analyzing the object’s motion in the x-axis and in the y-axis
independently, to avoid confusion we will not use ∆d to represent the object’s
displacement anymore. Our variables will now look like this:
In x-axis: vx  constant horizontal
(Little 3)
speed
∆x  horizontal displ./
“range”
∆t  time in air*
In y-axis: v1  initial vertical speed
(Big 5)
v2  final vertical speed
a  gravitational accel
(9.8 m/s2 [down])
∆y  vertical displ.
∆t  time in air*
* Note: The time that the projectile spends in the air is the only variable that is
the same in the x-axis and the y-axis.
Analyzing the Motion of Objects Projected Horizontally: when viy  0
 IMPORTANT: The vertical motion of an object that is dropped is identical to the
vertical motion of an object that is launched horizontally.
 Ex.1: A child leaves a waterslide at 4.2 m/s [hor], then lands in pool 3.2m below.
a) how long is he airborne? b) what is his horizontal displacement?
c) with what velocity does he hit the water?
 Ex.2: A helicopter moving horizontally 82m above ground drops a package so
that it lands 96 m ahead. Find the package's initial velocity.
More Complex Projectile Motion: when viy  0 and we need to use components
 When a projectile is launched at an angle to the horizontal we need to break the
angled initial velocity vector, v, into horizontal and vertical components.
OR
 As the projectile travels through the air, the horizontal component of the velocity
vector is always changing, while the vertical component remains constant.
 When a projectile is launched at a 45˚ angle it will achieve its max range (∆x).
For angles greater or less than 45˚ the range will decrease by the same amount.
 Ex.3: A golfer hits ball at 42 m/s [32˚above horizon]. Find: a) horizontal range,
b) maximum height of ball, c) horizontal displacement when 15 m high.
 Ex.4: A medieval prince locked in a castle attaches a note to a rock and throws it
at 12 m/s from atop the castle’s outer wall at a height of 9.5 m so it just
clears the surrounding moat. Determine: a) the rock’s time of flight,
b) the width of the moat, c) the rock’s velocity at impact.