Transcript Ch 3.4 Projectile motion PPT projectile_motion_2d

Introduction to 2D
Projectile Motion
Projectile Motion
An example of 2-dimensional motion.
 An object dropped from rest.
 An object that is thrown vertically
upward.
 an object which is thrown upward at an
angle to the horizontal
 Something is fired, thrown, shot, or
hurled near the earth’s surface.
Projectile Motion
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A projectile is any object that once
projected or dropped continues in
motion by its own inertia and is
influenced only by the downward
force of gravity.
Horizontal velocity is constant.
Vertical velocity is accelerated.
Air resistance is ignored.
Trajectory of
Projectile
y
x
This projectile is launched an angle
and rises to a peak before falling
back down.
Trajectory of
Projectile
y
The trajectory of such a
projectile is defined by a
parabola.
x
Trajectory of
Projectile
y
Range
The RANGE of the
projectile is how far it
travels horizontally.
x
Trajectory of
Projectile
y
Maximum
Height
Range
x
The MAXIMUM HEIGHT of
the projectile occurs
halfway through its range.
Trajectory of
Projectile
y
g
g
g
g
g
x
Acceleration points down at 9.8
m/s2 for the entire
trajectory.
To work projectile
problems…
…you must
first resolve the initial
velocity into components.
Vo

Vo,x = Vo cos 
Vo,y = Vo sin 
Trajectory of Projectile
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The velocity -components
all along its path.
Notice how the vertical
velocity changes while the
horizontal velocity
remains constant.
Where is there no vertical
velocity?
Where is the total
velocity maximum?
2D Motion
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Resolve vector into components.
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Position, velocity or acceleration
Work as two one-dimensional
problems.
Each dimension can obey
different equations of motion.
Horizontal Component
of Velocity
Horizontal and Vertical
2D motion
Horizontal
Motion
Forces
(Present? - Yes or No)
(If present, what
direction?)
Acceleration
(Present? - Yes or No)
(If present, what
direction?)
Velocity
(Constant or
Changing?)
Vertical
Motion
NO
Yes
The force of gravity
acts downward
NO
Yes
"g" is downward at 9.8
m/s/s
Constant
Changing
(by 9.8 m/s each
second)
Vertical Component of
Velocity
Undergoes accelerated motion
 Accelerated by gravity (9.8
m/s2 down)

Vy = Vo,y - gt
1
2
 y = yo + Vo,yt - /2gt
2
2
 Vy = Vo,y - 2g(y – yo)

Launch angle
vo
Zero launch angle
Launch angle
vo

Positive launch angle
Symmetry in Projectile
Motion

Launch
and
Landing
Velocity
Negligible
air
resistance
Projectile
fired
over
level
ground
-
vo
vo
Symmetry in Projectile
Motion
t
to = 0
Time of flight
Symmetry in Projectile
Motion
t
to = 0
Time of
Projectile
fired
over level ground
Negligible
airflight
resistance
2t