Vectors and

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Vectors and Two-Dimensional Motion
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Vectors Two-Dimensional Motion
Topics
3-01 Vectors and Their Properties
3-02 Components of a Vector
3-04 Motion in Two Dimensions
3-05 Relative Velocity
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Vectors ad Their Properties
Magnitude and Direction
Magnitude Only
Scalars
Vectors
Displacement
Distance
Time
Velocity
Mass
Acceleration
Speed
Force
Energy
Momentum
Work
Torque
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Vectors ad Their Properties
Vectors have magnitude and direction, but no place
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Vectors ad Their Properties
Two vectors are equal if they have the same
magnitude and the same direction
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Vectors ad Their Properties s
Scaling Vectors
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Vectors ad Their Properties
Scaling a Displacement Vector
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Vectors ad Their Properties
Scaling a Change in Velocity Vector
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Vectors ad Their Properties
Vector Addition (Graphical)
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Vectors ad Their Properties
Vector Subtraction (Graphical) (A - B)
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Components of a Vector
y
x
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Components of a Vector
Vector Components
y
x
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Components of a Vector
Vector Components
y
x
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Components of a Vector
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Components of a Vector
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Components of a Vector
Adding Vectors
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Components of a Vector
q2
F2
F1
q1
q3
q4
F4
F3
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Components of a Vector
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Components of a Vector
Add the following vectors
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Motion in Two Dimensions
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Motion in Two Dimensions
ax 0
ay -g
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Motion in Two Dimensions
Ignoring air resistance, the horizontal component
of a projectile's acceleration A) is zero. B)
remains a non-zero constant. C) continuously
increases. D) continuously decreases.
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Motion in Two Dimensions
If an object is launched at an initial angle of ?
with the horizontal, the analysis is similar
except that the initial velocity has a vertical
component.
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Motion in Two Dimensions
Ignoring air resistance, the horizontal component
of a projectile's velocity A) is zero. B)
remains constant. C) continuously increases. D)
continuously decreases.
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Motion in Two Dimensions
y
At t 0
vo
Constant acceleration
q
x
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Motion in Two Dimensions
A ball is thrown with a velocity of 20 m/s at an
angle of 60 above the horizontal. What is the
horizontal component of its instantaneous
velocity at the exact top of its trajectory? A)
10 m/s B) 20 m/s C) 5.0 m/s D) zero
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Motion in Two Dimensions
Horizontal Position
y
Constant velocity
vo
q
x
Sub Eq 1
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EOC Problem 03-04
Vx
If Vx 6.80 units and Vy -7.40 units, a)
determine the magnitude of V.
q
Vy
V
b) determine the direction of V
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Motion in Two Dimensions
Vertical Position
y
Constant acceleration
vo
q
x
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Motion in Two Dimensions
A soccer ball is kicked with a velocity of 25 m/s
at an angle of 45 above the horizontal. What
is the vertical component of its acceleration as
it travels along its trajectory? A) 9.80 m/s2
downward B) (9.80 m/s2) sin (45) downward C)
(9.80 m/s2) sin (45) upward D) (9.80 m/s2)
upward
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EOC Problem 03-18
A diver running 1.8 m/s dives out horizontally
from the edge of a vertical cliff and 3.0 s later
reaches the water below. a) How high was the
cliff?
b) How far from its base did the diver hit the
water?
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Motion in Two Dimensions
Vertical Position as a Function of Horizontal
Displacement
y
vo
h
q
Solve Eq 3 for t
x
Sub into Eq 4
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Motion in Two Dimensions
y
Maximum Height
vo
h
q
Sub into Eq 4
x
At the maximum height (vy 0)
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Motion in Two Dimensions
When a football in a field goal attempt reaches
its maximum height, how does its speed compare
to its initial speed? A) It is zero. B) It is
equal to its initial speed. C) It is greater
than its initial speed. D) It is less than its
initial speed.
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EOC Problem 03-22
A football is kicked at ground level with a speed
of 18.0 m/s at an angle of 35.0º to the
horizontal. How much later does it hit the ground?
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Motion in Two Dimensions
Range
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Motion in Two Dimensions
At what angle should a water-gun be aimed in
order for the water to land with the greatest
horizontal range? A) 0 B) 30 C) 45 D) 60
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EOC Problem 03-30
A projectile is fired with an initial speed of
65.2 m/s at an angle of 34.5º above the
horizontal on a long flat firing range. Determine
(a) the maximum height reached by the projectile.
(b) the total time in the air
(c) the total horizontal distance covered (that
is, the range).
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Equations
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Equations
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Relative Velocity
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Relative Velocity
Time required to go directly across.
q
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Motion in Two Dimensions
You are trying to cross a river that flows due
south with a strong current. You start out in
your motorboat on the east bank desiring to
reach the west bank directly west from your
starting point. You should head your
motorboat A) due west. B) due north. C) in a
southwesterly direction. D) in a northwesterly
direction.
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