Demonstration:

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Physics 1710 Chapter 4 2-D MotionI
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• Demonstration
• Stuntman Lead

REVIEW
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Physics 1710 Chapter 4 2-D MotionI
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• Demonstration Stuntman Lead

No lead
REVIEW
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Physics 1710 Chapter 4 2-D MotionI
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• Demonstration Stuntman Lead

Proper lead d vtruck v(2h/g) d (15 m/s)v2
(3.15 m)/9.8 m/s2) d 12.0 m
REVIEW
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Physics 1710 Chapter 4 2-D MotionI
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• 1' Lecture
• Displacement, velocity and acceleration are
  vector quantities in two or more dimensions.
• Each component of the kinematic variables
• is separate and independent.
• In projectile motion the x-motion is
  unaccelerated while the y-motion experiences a
  constant acceleration equal to -g.

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Physics 1710 Chapter 4 2-D MotionI
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• Position r is a vector.
• r x i y j
• Or rx x ry y
• Thus, one can represent a vector by a position
  vector, ie an arrow.

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Physics 1710 Chapter 4 2-D MotionI
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• Displacement in 2-D is a vector
• ? r r final - r initial
• ? rx x final - x initial ?x
• ? ry yfinal - y initial ?y
• ? r ?? r?
• ?? r? v(x final - x initial ) 2 (yfinal - y
  initial) 2
• Tan ? (yfinal - y initial)/ (x final - x
  initial )

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Physics 1710 Chapter 4 2-D MotionI
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• Average velocity is a vector
• vave ? r / ?t
• This means the following
• vx, ave ? x / ?t
• vy, ave ? y / ?t .

y(x) trajectory
y(t)
y
x
x(t)
t
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Physics 1710 Chapter 4 2-D MotionI
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• Average velocity is a vector

vy, ave ? y / ?t
y(x) trajectory
y(t)
y
x
x(t)
vx, ave ? x / ?t
t
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Physics 1710 Chapter 4 2-D MotionI
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• Instantaneous velocity is a vector
• v lim ?t ? 0 ? r / ?t
• This means the following
• vx lim ?t ? 0 ? x / ?t dx /dt
• vy lim ?t ? 0 ? y / ?t dy/dt

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Physics 1710 Chapter 4 2-D MotionI
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• Instantaneous velocity is a vector

y
x
t
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Physics 1710 Chapter 4 2-D MotionI
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• Average acceleration is a vector
• aave ? v / ?t
• This means the following
• ax, ave ?vx / ?t
• ay, ave ?vy / ?t .

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Physics 1710 Chapter 4 2-D MotionI
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• Instantaneous acceleration is a vector
• a lim ?t ? 0 ? v / ?t
• This means the following
• ax lim ?t ? 0 ? vx / ?t dvx /dt
• ay lim ?t ? 0 ? vy / ?t dvy /dt
• N.B.
• The components are strictly segregated!

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Physics 1710 Chapter 4 2-D MotionI
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• Motion in Two Dimensions
• All the one dimensional kinematic equations can
  be generalized to two (or more) dimensions.
• All the component equations obey the one
  dimensional kinematics separately.

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Physics 1710 Chapter 4 3-D MotionI
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• Two two balls are simultaneously shot
  horizontally and dropped,which will the ground
  first? Why?

REVIEW
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Physics 1710 Chapter 4 2-D MotionI
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• Vector kinematic equations (uniform a)
• rfinal rinitial vinitial t ½ a t 2
• vfinal vinitial a t

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Physics 1710 Chapter 4 2-D MotionI
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• Projectile Motion
• Horizontal acceleration
• ax 0
• ? vx, final vx, initial
• xfinal x initial vx, initial t .
• Vertical acceleration
• ay -g
• ? vy, final vy, initial - g t
• yfinal y initial vy, initial t - ½ g t 2

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Physics 1710 Chapter 4 2-D MotionII
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• Summary
• Kinematics in two (or more) dimensions obeys the
  same 1- D equations in each component
  independently.
• rfinal rinitial vinitial t ½ a t 2
• vfinal vinitial a t
• vx,final2 vx,initial 2 2 ax /?x
• vy,final2 vy,initial 2 2 ay /?y
• Projectiles follow a parabola y(x) A Bx
  Cx2