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Physics Chapter 3: Kinematics in 2-Dimensions

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Title: Physics Chapter 3: Kinematics in 2-Dimensions


1
Physics Chapter 3 Kinematics in 2-Dimensions
  • Christopher Chui

2
Kinematics in Two Dimensions
  • A quantity having both magnitude and direction is
    a vector
  • A quantity having magnitude only is a scalar
  • Two vectors can be added graphically, giving a
    resultant displacement
  • A vector can move without altering its direction
  • Use tail-to-tip method to add vectors
  • Subtraction of vectors is similar to adding
    vectors
  • Vectors can be multiplied by a scalar
  • Vectors can be resolved into its components

3
Components of Vectors
  • Horizontal component vx v cos q
  • Vertical component vy v sin q
  • Resultant, v sqrt (vx2 vy2 )
  • Direction, tan q vy / vx

4
Projectile Motion
  • Analyze horizontal and vertical components
    separately
  • Horizontal component does not change
  • Vertical component changes continuously

5
Solving Problems Involving Projectiles
  • X component velocity vx vx0 ax t
  • X component distance x x0 vx0t ½ ax t2
  • vx2 vx02 2 ax (x x0)
  • y component velocity vy vy0 ay t
  • y component distance x x0 vy0t ½ ay t2
  • vy2 vy02 2 ay (x x0)
  • Vertical projectile ax 0, ay -g -9.8 m/s2

6
Problem Solving Techniques for Projectile Motion
  • Read carefully and draw a careful diagram
  • Choose an origin and an xy coordinate system
  • Analyze the horizontal motion and the vertical
    motion separately
  • List the known and unknown quantities, choosing
    ax 0 and ay -g or g depending on y up ve or
    down ve
  • vx never changes, and vy 0 at highest point
  • For final magnitude and direction, x and y
    components must be combined as a vector
  • Firing projectile for maximum range must be at
    45o
  • Projectile motion is parabolic
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