Projectile Motion

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Projectile Motion

• Unit 8
• POE Ballistic Device

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• What is a Projectile?

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Projectile Motion

• A projectile is an object upon which the only
  force is gravity.

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• A projectile is an object which once projected
  continues in motion by its own inertia and is
  influenced only by the downward force of gravity.

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• With gravity, a projectile will fall below its
  inertial path. Gravity acts downward to cause a
  downward acceleration.

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• There are two components of a projectiles
  motion
• Vertical and Horizontal

Perpendicular components of motion are
independent of each other.
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• In the absence of gravity a projectile would
  continue its horizontal motion at a constant
  velocity.

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• If dropped from rest in the presence of gravity,
  the canon ball would accelerate downward gaining
  speed at a rate of 32.15ft/sec2.

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• The presence of gravity does not affect the
  horizontal motion of the projectile.

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• The projectile travels with a constant
  horizontal velocity and a downward vertical
  acceleration.

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Projectile Motion Notion
Imagine a pickup truck moving with a constant
speed along a city street. In the course of its
motion, a ball is projected straight upwards by a
launcher located in the bed of the truck. Imagine
as well that the ball does not encounter a
significant amount of air resistance.
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Projectile Motion Notion
What will be the path of the ball and where will
it be located with respect to the pickup
truck? How can the motion of the ball be
described? Where will the ball land with respect
to the truck?
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Projectile Motion Notion
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What is Kinematics?
Kinematics analyzes the positions and motion of
objects as a function of time, without regard to
the causes of motion.
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What is Kinematics?
Kinematics involves the relationships between the
quantities displacement (s), velocity (v),
acceleration (a), and time (t). The first three
of these quantities are vectors
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The Language of Kinematics
Vector Quantities Quantities that are fully
described by BOTH a magnitude and a
direction. ex 15 degrees Northeast, 75 miles
South
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The Language of Kinematics
Scalar Quantities Quantities that are fully
described by magnitude alone. ex 30? F, 1500
calories, 12 hours
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The Language of Kinematics
Distance (d) Scalar Quantity How far an object
has traveled during its time in motion. Ex A
person walks ½ mile to the end of a trail and
then returns on the same route. The distance
walked is 1 mile. d 1 mile
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The Language of Kinematics
Displacement (s) Vector Quantity How far an
object is from where it started, or the change in
position of an object. Ex A person walks ½ mile
to the end of a trail and then returns along the
same route. The displacement is 0 miles. s 0
miles
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The Language of Kinematics
Speed Scalar Quantity The rate an object is
moving without regard to direction. A ratio of
the total distance (d) traveled divided by the
time. Ex A car traveled 400 miles for 8-hours.
What was its average speed? Speed 50 mph
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The Language of Kinematics
Velocity (v) Vector Quantity The rate that an
object is changing position with respect to
time. Average Velocity is the ratio of the total
displacement (s) divided by the time. The
direction can be indicated by a () or a (-) sign.
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The Language of Kinematics
Velocity (v) Vector Quantity Ex What would be
the average velocity of a car that traveled
3-miles north and then returned on the same route
traveling 3-miles south in a total of 22 minutes?
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The Language of Kinematics
Acceleration (a) Vector Quantity The rate at
which an object is changing its velocity with
respect to time. Average Acceleration is the
ratio of change in velocity divided by the
elapsed time.
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The Language of Kinematics
Acceleration (a) Vector Quantity Ex What is the
average acceleration of a car that starts from
rest and is traveling at 50m/s (meters per
second) after 5-seconds?
a 50m/s 0m/s a 10 m/s2 5 sec
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Projectile Motion Motion in a plane
Motion in 2 directions Horizontal and
Vertical Horizontal motion is INDEPENDENT of
vertical motion Path is always parabolic in
shape and is called a Trajectory Graph of the
Trajectory starts at the origin
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Projectile Motion Assumptions
Curvature of the earth is ignored, as if the
earth were flat over the horizontal range of the
projectile. Effects of wind resistance on the
object are ignored
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Projectile Motion Assumptions

• The variations of gravity (g) with respect to
  differing altitudes is negligible and can be
  ignored.
• Gravity is constant

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Projectile Motion Assumptions
To start To analyze projectile motion, separate
the two-dimensional motion into vertical and
horizontal components.
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Projectile Motion Assumptions
To start Horizontal Direction x the range,
or distance the projectile travels Vertical
Direction y the altitude, or height, the
projectile reaches
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Projectile Motion Formulas
Initial Velocity (vi) can be broken down into its
x and y components
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Projectile Motion Formulas
Initial Velocity in the x direction (vix)
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Projectile Motion Formulas
Initial Velocity in the y direction (viy)
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Projectile Motion Assumptions

• Horizontal Direction
• No acceleration therefore ax 0
• velocity is constant
• Vertical Direction
• Gravity affects the acceleration. It is
  constant and directed downward, therefore ay
  -g.

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Projectile Motion Formulas
Horizontal Motion The x position (range) is
defined as
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Projectile Motion Formulas
Horizontal Motion Since the horizontal motion
has a constant velocity and the acceleration in
the x direction equals 0 (ax 0), the equation
simplifies to
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Projectile Motion Assumptions
At the maximum height
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Projectile Motion Formulas
Vertical Motion The y position (height) is
defined as
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Projectile Motion Formulas
Vertical Motion Since vertical motion is
accelerated due to gravity, ay g, the equation
simplifies to
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Projectile Motion Formulas

• Horizontal Motion
• Combine the two equations

and
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Projectile Motion Formulas

• Vertical Motion
• Combine the two equations

and
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Projectile Motion Problem
A ball is fired from a device, at a rate of 160
ft/sec, with an angle of 53 degrees to the ground.
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Projectile Motion Problem

• Find the x and y components of Vi.
• At the highest point (the vertex) what is the
  altitude (h) and how much time has elapsed?
• What is the balls range (the distance traveled
  horizontally)?

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Projectile Motion Problem
1. Find the x and y components of Vi.
Vi initial velocity 160 ft/sec
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Projectile Motion Problem

• Find the x and y components of Vi.

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Projectile Motion Problem

• Find the x and y components of Vi.

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Projectile Motion Problem
At the highest point (the vertex) what is the
altitude (ymax) and how much time has elapsed?
Start by solving for time.
128 ft/sec 32 ft/sec2t1
t1 128 ft/sec 32 ft/sec2
0 128 ft/sec 32 ft/sec2t1
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Projectile Motion Problem
At the highest point (the vertex) what is the
altitude (h) ? Now using time, find h (ymax).
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Projectile Motion Problem
What is the balls range (the distance traveled
horizontally)?
It takes the ball the same amount of time to
reach its maximum height as it does to fall to
the ground, so ttotal 8 sec. Using the formula
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Citations

• http//www.physicsclassroom.com