9 . 2 S PA C E
Year 12 Physics
9.2.B – Projectile Motion
Galileo’s Analysis
•  There are two components to a
projectile’s motion
•  Horizontal – constant velocity
•  Vertical – changing velocity
accelerated by gravity
•  The resulting motion follows
the path of a parabola
•  Galileo was the first to analyse
and propose this idea
Horizontal and Vertical Motion
v
uy
θ
ux
Vertical Motion
•  All objects fall to the Earth at
the same rate
•  Vertical motion is accelerated
by gravity
•  v = u + at
•  v2 – u2 = 2as
•  s = ut + ½at2
Horizontal Motion
•  Constant velocity as there is no
acceleration
•  Occurs simultaneously with the
vertical motion
•  v = s/t or range, s = vt
•  A projectile dropped vertically
takes the same time to hit the
ground as one projected
horizontally
Motions Combined
Types of Projectile Motion Projected at an Angle to the
Horizontal
Types of Projectile Motion Projected Horizontally
Types of Projectile Motion Projected at an Angle to the
Horizontal with a Negative or
Positive Vertical Displacement
Negative displacement
Positive displacement
Projectile Motion Problems
1. 
Resolve the initial velocity into the
horizontal and vertical components
using trigonometry.
2. 
Work with the vertical component
to calculate time and the vertical
component of velocity at that time.
The horizontal component of
velocity will stay the same.
3. 
Use vector addition to combine the
horizontal and vertical vectors into
a velocity vector with magnitude
and direction.
4. 
If necessary, calculate the range
from the time of flight.
Example 1
A canon is fired at 30° to the horizontal with an initial velocity of
30 ms-1. Determine:
(a)  the maximum height reached by the canon ball.
(b)  the range of the canon ball.
Example 2
A car travelling at 30 ms-1 drives over the edge of a cliff and into the
water 58.8 m below. Calculate:
(a)  the time it takes for the car to hit the water.
(b)  the distance from the cliff that the car hits the water.
(c)  the speed of the car as it hits the water.
Example 3
A player kicked a football from 30 m in front of the goal posts. The
ball only just cleared the crossbar with was 3.0 m above the ground
2.0 s later. Calculate:
(a)  the the angle at which the ball was kicked.
(b)  the ball’s initial speed.
Points to Note
•  The time of flight is dependant
on the initial vertical velocity of
the projectile and the vertical
motion only.
•  The range of a projectile is
determined by the initial
horizontal velocity and time of
flight.
•  For a fixed initial velocity
(magnitude), maximum range
occurs at 45° while maximum
height occurs at 90°.