Kinematics

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Kinematics 2D Motion

• Kinematics
• and
• 2D Motion
• Updated 9/25/06

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Kinematics 2D Motion

• In 2D (and 3D) motion we combine what we learned
  in basic kinematics with vector concepts. This
  will help us
• cross a river or ocean current
• shoot artillery
• fly in a crosswind

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Kinematics 2D Motion

• Shooting artillery is a special kind of 2D motion
  called projectile motion. In dealing with this
  kind of motion, we will make a few basic
  assumptions.
• air friction and the rotation of the earth will
  be ignored
• the object will follow a parabolic path

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Kinematics 2D Motion

• The x- and y-directions of motion are completely
  independent of each other
• The x-direction is uniform motion ( ax 0 )
• The y-direction is free fall ( ay g )
• The initial velocity can be broken down into its
  x and y components

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Kinematics 2D Motion
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Kinematics 2D Motion

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

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Kinematics 2D Motion

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

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Kinematics 2D Motion

• Projectile Motion Problem Solving
• 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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Kinematics 2D Motion

• Problem Solving (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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Kinematics 2D 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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Kinematics 2D Motion

• Follow the 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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Kinematics 2D Motion

• Relative Velocity
• Relative velocity is about relating the
  measurements of two different observers
• It may be useful to use a moving frame of
  reference instead of a stationary one
• It is important to specify the frame of
  reference, since the motion may be different in
  different frames of reference
• There are no specific equations to learn to solve
  relative velocity problems

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Kinematics Linear Motion

• End of
• 2D Motion