Projectile Motion
Projectile- object that is launched, thrown, or fired in the
air that is in a state of free fall
Trajectory- the path the projectile follows.
- projectile motion is described in terms of position,
velocity, and accelertation.
- The horizontal and vertical components of
velocities are independent of each other.
Range – the horizontal distance from the point of release.
R = range
http://phet.colorado.edu/en/simulation/projecti
le-motion
Examples of projectiles
Projectile Motion
• Two-dimensional motion of an object
– Vertical
– Horizontal
We use a t-chart to represent the two motions:
X (horizontal)
Y (vertical)
Types of Projectile Motion
• Horizontal
– Motion of a ball rolling freely along a level
surface
– Horizontal velocity is ALWAYS constant
• Vertical
– Motion of a freely falling object
– Force due to gravity
– Vertical component of velocity changes with
time
• Parabolic
– Path traced by an object accelerating only
in the vertical direction while moving at
constant horizontal velocity
Projectile motion
• What velocity will horizontal projectiles have?
• What acceleration will projectiles have vertically?
What will the velocity look like?
Examples of Projectile Motion
• Launching a Cannon ball
Projectile motion
Projectile motion
• Compare the horizontal motion of the
gravity free path and the projectile motion.
• Compare the vertical motion and the
projectile motion.
https://docs.google.com/a/neisd.net/file/d/0Bxu8wXh_OF7WT2J1
LUhxYjZaZ0U/edit
https://docs.google.com/a/neisd.net/file/d/0Bxu8wXh_OF7WQU90
RUN0c2JMdDQ/edit
https://docs.google.com/a/neisd.net/file/d/0Bxu8wXh_OF7WR0Zr
QklYZEZMM2M/edit
https://docs.google.com/a/neisd.net/file/d/0Bxu8wXh_OF7WNDln
VUZBRGRiYms/edit
https://docs.google.com/a/neisd.net/file/d/0Bxu8wXh_OF7Wd01P
NG1oOXJsd0k/edit
http://www.pbs.org/opb/circus/classroom/circ
us-physics/projectile-motion/
Horizontal Components
dx = horizontal displacement
vx = horizontal velocity
t = time
dx =vxt  notice that there is no acceleration. Why?
Vertical Components
g = gravity
dy = vertical displacement
vy = vertical velocity
t = time
What is the common variable in the horizontal
and vertical components?
Example
A stone is thrown horizontally at a speed of 5.0 m/s
from the top of a cliff 78.4 m high. How long does it
take the stone to reach the bottom of the cliff?
T= ?
Example
A steel ball rolls with a constant velocity across a tabletop 0.950 m high. It
rolls off the table and hits the ground 0.352 m from the edge of the table.
How fast was the ball rolling just as it left the table?
Example
Divers at Acapulco dive horizontally from a cliff that is 65 meters high. If the rocks
below the cliff protrude 27 meters beyond the edge of the cliff, what is the minimum
horizontal velocity needed to safely clear the rocks below?
Example of a horizontally
launched projectile
• A cannon is fired horizontally at 20 m/s on a 10 m
tall cliff. How long will the cannon ball be in the
air? How far from the base of the cliff will the
cannon ball fall?
Example problem
• An airplane is flying horizontally with a velocity of
250 m/s.
• If the pilot drops a water balloon out of the window
and it lands a horizontal distance of 500m from the
launch point.
• From what height was it dropped?