Projectile Motion
Notes
Projectile Motion

Definition

2 models
• Movement in 2 dimensions rather than 1
• Horizontal launch
• Kicking a stone off a bridge
• Angled launch
• Golf/base/football
• Artillery shell
• In both models, the only effect on the
projectile, after leaving the launch, is g↓
Horizontal Launch

Basic premise
• In the absence of air
•
•
resistance…
The objects are in
free fall!
Both objects reach
the ground at the
same time
vx
Horizontal Launch
dy
dx

Analysis technique
• Break the model down into vertical (y) and
horizontal (x) component columns
• Vertical (y) ↓
• vo = 0 (drop model)
• g = 9.8 (always on Earth!)
• dy = height
• t = time to fall
• Horizontal (x) →
• dx = range
• vx = initial velocity in horizontal direction
• t = time to fall
vx
Projectile Motion
dy
dx
Vertical (y)
Horizontal (x)
g = 9.8
dx = range
vo = 0
vx = initial velocity in x direction
dy = height
t=
t=
TOOL: dy = vot + ½ g t2 (iii)
TOOL: dx = vx*t
Identify the target parameter, and start in the opposite column.
ex. If vx (horizontal column) is requested, start solving in the
vertical column
Use the time (t) value as common to both axes – the time taken to
follow the parabolic path is the same as a simple drop!
vx
Ex. Horizontal
dy
dx


A baseball rolls off a 0.7 m high desk and
strikes the floor 0.25 m away from the base
of the desk.
How fast was it rolling?
vx
Solution
dy
dx

1) vertical

2) horizontal
• dy = vot + ½ g t2
• 0.7 = 0 + ½ (9.8) t2
• t = 0.38 seconds (use in the “other” column)
• dx = vx*t
• 0.25 = vx* 0.38
• vx = 0.66 m/s
Practice

Your turn!
What if the projectile is launched
at an angle to the horizontal?
Angled Launch Projectile Motion

Definition
• The motion of the projectile is uniquely
defined by:
• Its launch angle (Ө) and
• its initial velocity (vo)
Angled Launch Parameters
Angled Launch
Angled Launch – refer to sheet




Max Height:
• dymax = (V0 sin
)2/2g
Range:
• d xmax= V02 sin (2
)/g
Time to max height:
• t = (V0 sin
)/g
Total time in air (hang time)
• (time up=time down)
• ttotal = 2 (V0 sin )/g
Comparing Trajectories
Max range angle
Which angle provides the maximum down range (x) distance?
Practice time

Your turn!