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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