Physic 110 Lecture 06 from Chapter 3'''Sections 4

1
Physic 110 Lecture 06 from Chapter
3...Sections 4

• Projectile Motion

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e-learn site for Physics 110
Where to get these slides
or

• My website at
• myweb.loras.edu/cm418218

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Homework Assignment 06

• Conceptual questions
• Chapter 3 10 and 17 on page 73

• Problems
• Chapter 3, Problem 24 on page 75
• Chapter 3, Problem 30 on page 76

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Projectile Motion

• An object may move in both the x and y directions
  simultaneously
• It moves in two dimensions
• The form of two dimensional motion we will deal
  with is called projectile motion

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Assumptions of Projectile Motion

• We may ignore air friction
• We may ignore the rotation of the earth
• With these assumptions, an object in projectile
  motion will follow a parabolic path

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Rules of Projectile Motion

• The x- and y-directions of motion are completely
  independent of each other
• The x-direction is uniform motion
• vx constant and ax 0
• The y-direction is uniformly accelerated motion
• ay constant -g -9.81 m/s2
• The initial velocity can be broken down into its
  x- and y-components

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Rules of Projectile Motion

• In x direction In y direction

where
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Projectile Motion
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Projectile Motion at Various Initial Angles

• Complementary values of the initial angle result
  in the same range
• The heights will be different
• The maximum range occurs at a projection angle of
  45o

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Some Details About the Rules

• x-direction
• ax 0
• x vxot
• This is the only operative equation in the
  x-direction since there is uniform velocity in
  that direction

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More Details About the Rules

• y-direction
• free fall problem
• a -g
• take the positive direction as upward
• uniformly accelerated motion, so the motion
  equations all hold

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Velocity of the Projectile

• The velocity of the projectile at any point of
  its motion is the vector sum of its x and y
  components at that point
• Remember to be careful about the angles quadrant

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Problem-Solving Strategy

• Select a coordinate system and sketch the path of
  the projectile
• Include initial and final positions, velocities,
  and accelerations
• Resolve the initial velocity into x- and
  y-components
• Treat the horizontal and vertical motions
  independently

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Problem-Solving Strategy, cont

• Follow the techniques for solving problems with
  constant velocity to analyze the horizontal
  motion of the projectile
• Follow the techniques for solving problems with
  constant acceleration to analyze the vertical
  motion of the projectile

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Some Variations of Projectile Motion

• An object may be fired horizontally
• The initial velocity is all in the x-direction
• vo vx and vy 0
• All the general rules of projectile motion apply

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Projectile comparisons
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Example 1

• Find our projectile velocity from measuring
  initial height and distance traveled.
• Height h distance d
• Along y-direction yo h
• yf 0
• voy 0.0
• a -9.81 m/s2
• Start by finding t

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Projectile example
Use
then
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Projectile example
Once the time has been found, you may use it to
find the horizontal velocity.
then, solve fore velocity
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Projectile comparisons
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Non-Symmetrical Projectile Motion

• Follow the general rules for projectile motion
• Break the y-direction into parts
• up and down
• symmetrical back to initial height and then the
  rest of the height

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Non-Symmetrical Projectile Motion

• Known
• xo 0 t tx ty ?
• xf ?
• vox20 cos30o 17.3m/s
• yo 0 voy20 sin30o 10 m/s
• yf -45 m ay -9.81m/s2

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Non-Symmetrical Projectile Motion

• Use Uniform Accelerated Motion

then
fits quadratic equation form
?
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Non-Symmetrical Projectile Motion

• Solving for t

What does the -2.16 s answer mean?
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Non-Symmetrical Projectile Motion

• Using t 4.21 s
• Along the horizontal direction
• use uniform motion

Giving