Chapter 01 ~ 04 review
&
Additional exercises
Chapter 01: Summary
Measurement
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Defined by relationships to
base quantities
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Each defined by a standard,
and given a unit
Changing Units
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SI Units
Use chain-link conversions
Write conversion factors as
unity
Manipulate units as algebraic
quantities
International System of Units
Each base unit has an
accessible standard of
measurement
Length
l 
Meter is defined by the
distance traveled by light in a
vacuum in a specified time
interval
Chapter 01: Summary
Time
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Mass
Second is defined in terms of
oscillations of light emitted by a
cesium-133 source
Atomic clocks are used as the
time standard
Density
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Mass/volume
Eq. (1-8)
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Kilogram is defined in terms of
a platinum-iridium standard
mass
Atomic-scale masses are
measured in u, defined as
mass of a carbon-12 atom
Chapter 02: Summary
Position
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Displacement
Relative to origin
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Positive and negative
directions
Average Velocity
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Change in position (vector)
Eq. (2-1)
Average Speed
Displacement / time (vector)
Eq. (2-2)
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Distance traveled / time
Eq. (2-3)
Chapter 02: Summary
Instantaneous Velocity
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At a moment in time
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Speed is its magnitude
Average Acceleration
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Eq. (2-7)
Eq. (2-4)
Instantaneous Acceleration
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First derivative of velocity
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Second derivative of position
Eq. (2-8)
Ratio of change in velocity to
change in time
Constant Acceleration
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Includes free-fall, where
a = -g along the vertical axis
Tab. (2-1)
Chapter 03: Summary
Scalars and Vectors
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Adding Geometrically
Scalars have magnitude only
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Vectors have magnitude and
direction
Eq. (3-2)
Eq. (3-3)
Both have units!
Vector Components
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Unit Vector Notation
Given by
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Eq. (3-5)
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Obeys commutative and
associative laws
We can write vectors in terms
of unit vectors
Eq. (3-7)
Related back by
Eq. (3-6)
Chapter 03: Summary
Adding by Components
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Add component-by-component
Scalar Times a Vector
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Eqs. (3-10) - (3-12)
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Scalar Product
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Product is a new vector
Magnitude is multiplied by
scalar
Direction is same or opposite
Cross Product
Dot product
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Eq. (3-20)
Eq. (3-22)
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Produces a new vector in
perpendicular direction
Direction determined by righthand rule
Eq. (3-24)
Chapter 04: Summary
Position Vector
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Displacement
Locates a particle in 3-space
Eq. (4-1)
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Change in position vector
Eq. (4-2)
Eq. (4-3)
Eq. (4-4)
Average and Instantaneous
Velocity
Average and Instantaneous
Accel.
Eq. (4-8)
Eq. (4-15)
Eq. (4-10)
Eq. (4-16)
Chapter 04: Summary
Projectile Motion
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Uniform Circular Motion
Flight of particle subject only
to free-fall acceleration (g)
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Magnitude of acceleration:
Eq. (4-34)
Eq. (4-22)
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Eq. (4-23)
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Trajectory is parabolic path
Eq. (4-25)
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Horizontal range:
Eq. (4-26)
Time to complete a circle:
Eq. (4-35)
Chapter 04: Summary
Relative Motion
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For non-accelerating reference
frames
Eq. (4-44)
Eq. (4-45)
More examples
•  Problems on concepts, basic pictures (self-study)
•  Previous exam problems
1.3.1. Complete the following statement: The ratio 1 milligram
1 kilogram
is equal to
a) 102
b) 103
c) 106
d) 10-3
e) 10-6
1.3.1. Complete the following statement: The ratio 1 milligram
1 kilogram
is equal to
a) 102
b) 103
c) 106
d) 10-3
e) 10-6
1.3.2. Which one of the following choices is equivalent to
8.0 m2?
a) 8.0 × 10–4 cm2
b) 8.0 × 102 cm2
c) 8.0 × 10–2 cm2
d) 8.0 × 104 cm2
e) 8.0 × 103 cm2
1.3.2. Which one of the following choices is equivalent to
8.0 m2?
a) 8.0 × 10–4 cm2
b) 8.0 × 102 cm2
c) 8.0 × 10–2 cm2
d) 8.0 × 104 cm2
e) 8.0 × 103 cm2
1.4.1. Express 61 mg in kilograms.
a) 6.1 kg
b) 0.061 kg
c) 0.00061 kg
d) 0.000061 kg
e) 0.0000061 kg
1.4.1. Express 61 mg in kilograms.
a) 6.1 kg
b) 0.061 kg
c) 0.00061 kg
d) 0.000061 kg
e) 0.0000061 kg
1.4.2. A section of a river can be approximated as a rectangle that is 48
m wide and 172 m long. Express the area of this river in square
kilometers.
a) 8.26 × 10-3 km2
b) 8.26 km2
c) 8.26 × 103 km2
d) 3.58 km2
e) 3.58 × 10-2 km2
1.4.2. A section of a river can be approximated as a rectangle that is 48
m wide and 172 m long. Express the area of this river in square
kilometers.
a) 8.26 × 10-3 km2
b) 8.26 km2
c) 8.26 × 103 km2
d) 3.58 km2
e) 3.58 × 10-2 km2
1.4.3. Express the following statement as an algebraic expression:
“There are 264 gallons in a one cubic meter container.” Let G
represent the number of gallons and M represent the number of one
cubic meter containers.
a) G = 264M
b) G = M/264
c) G = 0.00379M
d) M = G/264
e) M = G
1.4.3. Express the following statement as an algebraic expression:
“There are 264 gallons in a one cubic meter container.” Let G
represent the number of gallons and M represent the number of one
cubic meter containers.
a) G = 264M
b) G = M/264
c) G = 0.00379M
d) M = G/264
e) M = G
1.4.6. Approximately how many seconds are there in a century?
a) 86 400 s
b) 5.0 × 106 s
c) 3.3 × 1018 s
d) 3.2 × 109 s
e) 8.6 × 104 s
1.4.6. Approximately how many seconds are there in a century?
a) 86 400 s
b) 5.0 × 106 s
c) 3.3 × 1018 s
d) 3.2 × 109 s
e) 8.6 × 104 s
1.4.8. Which one of the following pairs of units may not be
added together, even after the appropriate unit
conversions have been made?
a) feet and centimeters
b) seconds and slugs
c) meters and miles
d) grams and kilograms
e) hours and years
1.4.8. Which one of the following pairs of units may not be
added together, even after the appropriate unit
conversions have been made?
a) feet and centimeters
b) seconds and slugs
c) meters and miles
d) grams and kilograms
e) hours and years
1.6.2. Consider each of the following comparisons between various
time units. Which one of these comparisons is false?
a) 84 600 s = 1 day
b) 1 h > 3000 s
c) 1 ns > 1000 µs
d) 1 s = 1000 ms
e) 1 y = 5.26 × 105 h
1.6.2. Consider each of the following comparisons between various
time units. Which one of these comparisons is false?
a) 84 600 s = 1 day
b) 1 h > 3000 s
c) 1 ns > 1000 µs
d) 1 s = 1000 ms
e) 1 y = 5.26 × 105 h
1.7.1. Gold can be compressed to a thickness of 1.0 micron to make
gold leaf. If each cubic centimeter of gold has a mass of 19.32 g,
what mass of gold leaf in grams is needed to cover a statue with a
total surface area of 12 m2? Note: a micrometer is sometimes
called a micron.
a) 1.2 × 10-5 g
b) 1.6 g
c) 0.62 g
d) 231.8 g
e) 2.3 × 10-3 g
1.7.1. Gold can be compressed to a thickness of 1.0 micron to make
gold leaf. If each cubic centimeter of gold has a mass of 19.32 g,
what mass of gold leaf in grams is needed to cover a statue with a
total surface area of 12 m2? Note: a micrometer is sometimes
called a micron.
a) 1.2 × 10-5 g
b) 1.6 g
c) 0.62 g
d) 231.8 g
e) 2.3 × 10-3 g
2.9.2. A child throws a ball vertically upward at the school playground.
Which one of the following quantities is (are) equal to zero at the
highest point of the ball’s trajectory? Assume that at the time of
release t = 0, the ball is at y = 0 m.
a) instantaneous velocity
b) displacement
c) instantaneous acceleration
d) average acceleration
e) both instantaneous velocity and instantaneous acceleration
2.9.2. A child throws a ball vertically upward at the school playground.
Which one of the following quantities is (are) equal to zero at the
highest point of the ball’s trajectory? Assume that at the time of
release t = 0, the ball is at y = 0 m.
a) instantaneous velocity
b) displacement
c) instantaneous acceleration
d) average acceleration
e) both instantaneous velocity and instantaneous acceleration
2.7.1. Consider the position versus time and velocity versus time graphs for an
object in motion. Which one of the following phrases best describes the motion
of the object?
a) constant position
b) constant speed
c) constant velocity
d) constant acceleration
e) none of the above
2.7.1. Consider the position versus time and velocity versus time graphs for an
object in motion. Which one of the following phrases best describes the motion
of the object?
a) constant position
b) constant speed
c) constant velocity
d) constant acceleration
e) none of the above
2.5.4. A dog is initially walking due east. He stops, noticing a cat behind him. He
runs due west and stops when the cat disappears into some bushes. He starts
walking due east again. Then, a motorcycle passes him and he runs due east
after it. The dog gets tired and stops running. Which of the following graphs
correctly represent the position versus time of the dog?
2.5.4. A dog is initially walking due east. He stops, noticing a cat behind him. He
runs due west and stops when the cat disappears into some bushes. He starts
walking due east again. Then, a motorcycle passes him and he runs due east
after it. The dog gets tired and stops running. Which of the following graphs
correctly represent the position versus time of the dog?
2.6.1. Which of the following velocity vs. time graphs represents an object with a
negative constant acceleration?
2.6.1. Which of the following velocity vs. time graphs represents an object with a
negative constant acceleration?
2.6.11. The graph below represents the speed of a car traveling due east for a portion of its travel
along a horizontal road. Which of the following statements concerning this graph is true?
a) The car initially increases its speed, but then the speed decreases at a constant rate until the car
stops.
b) The speed of the car is initially constant, but then it has a variable positive acceleration before it
stops.
c) The car initially has a positive acceleration, but then it has a variable negative acceleration
before it stops.
d) The car initially has a positive acceleration, but then it has a variable positive acceleration before
it stops.
e) No information about the acceleration of the car can be determined from this graph.
2.6.11. The graph below represents the speed of a car traveling due east for a portion of its travel
along a horizontal road. Which of the following statements concerning this graph is true?
a) The car initially increases its speed, but then the speed decreases at a constant rate until the car
stops.
b) The speed of the car is initially constant, but then it has a variable positive acceleration before it
stops.
c) The car initially has a positive acceleration, but then it has a variable negative acceleration
before it stops.
d) The car initially has a positive acceleration, but then it has a variable positive acceleration before
it stops.
e) No information about the acceleration of the car can be determined from this graph.
2.7.2. Complete the following statement: In dimensional analysis, the
dimensions for velocity are
L
a)
T
b) L
T2
L2
c) 2
T
L2
d)
T
e) LT
2.7.2. Complete the following statement: In dimensional analysis, the
dimensions for velocity are
L
a)
T
b) L
T2
L2
c) 2
T
L2
d)
T
e) LT
2.7.4. A fishing boat starts from rest and has a constant acceleration.
In a certain time interval, its displacement doubles. In the same
time interval, by what factor does its velocity increase?
a) 0.500
b) 0.707
c) 1.41
d) 2.00
e) 4.00
2.7.4. A fishing boat starts from rest and has a constant acceleration.
In a certain time interval, its displacement doubles. In the same
time interval, by what factor does its velocity increase?
a) 0.500
b) 0.707
c) 1.41
d) 2.00
e) 4.00
2.7.5. In the five equations of kinematics for constant acceleration
given in the text, there are five variables. What is the minimum
number of variables you must know in order to determine all five
variables by using the equations?
a) 1
b) 2
c) 3
d) 4
\
2.7.5. In the five equations of kinematics for constant acceleration
given in the text, there are five variables. What is the minimum
number of variables you must know in order to determine all five
variables by using the equations?
a) 1
b) 2
c) 3
d) 4
2.7.6. Starting from rest, a particle confined to move along a straight
line is accelerated at a rate of 2 m/s2. Which one of the following
statements accurately describes the motion of this particle?
a) The particle travels 2 m during each second.
b) The particle travels 2 m only during the first second.
c) The speed of the particle increases by 2 m/s during each second.
d) The acceleration of the particle increases by 2 m/s2 during each
second.
e) The final speed of the particle will be proportional to the distance
that the particle covers.
2.7.6. Starting from rest, a particle confined to move along a straight
line is accelerated at a rate of 2 m/s2. Which one of the following
statements accurately describes the motion of this particle?
a) The particle travels 2 m during each second.
b) The particle travels 2 m only during the first second.
c) The speed of the particle increases by 2 m/s during each second.
d) The acceleration of the particle increases by 2 m/s2 during each
second.
e) The final speed of the particle will be proportional to the distance
that the particle covers.
2.7.7. Which one of the following statements must be true if the
expression x - x0 = (½)(v - v0)t is to be used?
a) x is constant.
b) t is constant.
c) v is constant.
d) a is constant.
e) Both v0 and t are constant.
x - x0 = (½)(v)t
2.7.7. Which one of the following statements must be true if the
expression x - x0 = (½)(v - v0)t is to be used?
a) x is constant.
b) t is constant.
c) v is constant.
d) a is constant.
e) Both v0 and t are constant.
2.7.5. Consider the graph the
position versus time
graph shown. Which
curve on the graph best
represents a constantly
accelerating car?
a) A
b) B
c) C
d) D
e) None of the curves
represent a constantly
accelerating car.
2.7.5. Consider the graph the
position versus time
graph shown. Which
curve on the graph best
represents a constantly
accelerating car?
a) A
b) B
c) C
d) D
e) None of the curves
represent a constantly
accelerating car.
2.7.6. Consider the graph the
position versus time graph
shown. Which curve on
the graph best represents a
car that is initially moving
in one direction and then
reverses directions?
a) A
b) B
c) C
d) D
e) None of the curves represent
a car moving in one
direction then reversing its
direction.
2.7.6. Consider the graph the
position versus time graph
shown. Which curve on
the graph best represents a
car that is initially moving
in one direction and then
reverses directions?
a) A
b) B
c) C
d) D
e) None of the curves represent
a car moving in one
direction then reversing its
direction.
2.9.1. A heavy lead ball is dropped from rest from the top of a very
tall tower. Neglecting the effect due to air resistance, which one
of the following statements is false?
a)
b)
c)
d)
e)
The magnitude of the velocity of the ball increases by 9.8 m/s for each second that the
ball falls.
At time t = 2.0 s, the position of the ball is 19.6 m below its initial position.
At time t = 1.0 s, the instantaneous speed of the ball is 4.9 m/s.
The ball falls 4.9 m during the first second that it falls.
The magnitude of the acceleration of the ball is constant.
2.9.1. A heavy lead ball is dropped from rest from the top of a very tell
tower. Neglecting the effect due to air resistance, which one of the
following statements is false?
a) The magnitude of the velocity of the ball increases by 9.8 m/s for
each second that the ball falls.
b) At time t = 2.0 s, the position of the ball is 19.6 m below its initial
position.
c) At time t = 1.0 s, the instantaneous speed of the ball is 4.9 m/s.
d) The ball falls 4.9 m during the first second that it falls.
e) The magnitude of the acceleration of the ball is constant.
Stone-1:
Known: v0, a, x-x0
Unknown: v, t
Stone-2:
Known: t, a, x-x0
Unknown: v0, v
44.4=0*t+9.8*t2/2
44.4=v0*(t-1.86)+9.8*(t-1.86)2/2
àsqrt(44.4*2/9.8) = 3.01
à44.4=v0*(3.01-1.86)+9.8*(3.01-1.86)2/2
root [0] (44.4-9.8*(3.01-1.86)*(3.01-1.86)/2.0)/
(3.01-1.86)=3.29736956521739231e+01
3.2.1. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities must be represented by base units.
b) Scalar quantities have both magnitude and direction.
c) Scalar quantities can be added to vector quantities using rules of
trigonometry.
d) Scalar quantities can be added to other scalar quantities using rules
of trigonometry.
e) Scalar quantities can be added to other scalar quantities using rules
of ordinary addition.
3.2.1. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities must be represented by base units.
b) Scalar quantities have both magnitude and direction.
c) Scalar quantities can be added to vector quantities using rules of
trigonometry.
d) Scalar quantities can be added to other scalar quantities using rules
of trigonometry.
e) Scalar quantities can be added to other scalar quantities using rules
of ordinary addition.
3.2.2. Which one of the following situations involves a vector?
a) The submarine followed the coastline for 35 kilometers.
b) The air temperature in Northern Minnesota dropped to -4 °C.
c) The Hubble Telescope orbits 598 km above the surface of the earth.
d) The baseball flew into the dirt near home plate at 44 m/s.
e) The flock of Canadian Geese was spotted flying due south at 5 m/s.
3.2.2. Which one of the following situations involves a vector?
a) The submarine followed the coastline for 35 kilometers.
b) The air temperature in Northern Minnesota dropped to -4 °C.
c) The Hubble Telescope orbits 598 km above the surface of the earth.
d) The baseball flew into the dirt near home plate at 44 m/s.
e) The flock of Canadian Geese was spotted flying due south at 5 m/s.
3.3.1. Which expression is false concerning the vectors shown in the sketch?
! !
!
a) C + A = − B
! ! !
b) C = A + B
! ! !
c) A + B + C = 0
d) C < A + B
e) A2 + B2 = C2
3.3.1. Which expression is false concerning the vectors shown in the sketch?
! !
!
a) C + A = − B
! ! !
b) C = A + B
! ! !
c) A + B + C = 0
d) C < A + B
e) A2 + B2 = C2
3.3.5. What is the minimum number of vectors with unequal
magnitudes whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.3.5. What is the minimum number of vectors with unequal
magnitudes whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.4.2. The city of Denver is located approximately one mile (1.61 km)
above sea level. Assume you are standing on a beach in Los
Angeles, California, at sea level; estimate the angle of the resultant
vector with respect to the horizontal axis between your location in
California and Denver.
a) between 1° and 2°
b) between 0.5° and 0.9°
c) between 0.11° and 0.45°
d) between 0.06° and 0.10°
e) less than 0.05°
3.4.2. The city of Denver is located approximately one mile (1.61 km)
above sea level. Assume you are standing on a beach in Los
Angeles, California, at sea level; estimate the angle of the resultant
vector with respect to the horizontal axis between your location in
California and Denver.
a) between 1° and 2°
b) between 0.5° and 0.9°
c) between 0.11° and 0.45°
d) between 0.06° and 0.10°
e) less than 0.05°
3.4.4. Determine the length of the side of the right triangle labeled x.
a) 2.22 m
b) 1.73 m
c) 1.80 m
d) 2.14 m
e) 1.95 m
3.4.4. Determine the length of the side of the right triangle labeled x.
a) 2.22 m
b) 1.73 m
c) 1.80 m
d) 2.14 m
e) 1.95 m
3.4.7. In a two-dimensional coordinate
system, the angle between the
r
positive x axis and vector A is θ. Which one of the following
r
choices is the expression to determine the x-component of A ?
a) A sin θ
b) A tan θ
c) A cos θ
d) A cos-1 θ
e) A/sin θ
3.4.7. In a two-dimensional coordinate
system, the angle between the
r
positive x axis and vector A is θ. Which one of the following
r
choices is the expression to determine the x-component of A ?
a) A sin θ
b) A tan θ
c) A cos θ
d) A cos-1 θ
e) A/sin θ
3.8.1. Consider the various vectors given in the choices below. The
cross product of which pair of vectors is equal to zero?
3.8.1. Consider the various vectors given in the choices below. The
cross product of which pair of vectors is equal to zero?
3.8.5. The vector product of two vectors is equal to zero, but the
magnitudes of the two vectors are not equal to zero. Which one of
the following statements is true?
a) Based on the definition of the vector product, this situation can
never occur.
b) The two vectors must be perpendicular to each other.
c) The two vectors must be parallel to each other.
d) The two vectors must be unit vectors.
e) This can only be true if the scalar product is also equal to zero.
3.8.5. The vector product of two vectors is equal to zero, but the
magnitudes of the two vectors are not equal to zero. Which one of
the following statements is true?
a) Based on the definition of the vector product, this situation can
never occur.
b) The two vectors must be perpendicular to each other.
c) The two vectors must be parallel to each other.
d) The two vectors must be unit vectors.
e) This can only be true if the scalar product is also equal to zero.
3.8.6. Which of the following vector operations produces a vector as
the result if the magnitudes of all of the vectors are not equal to
zero?
! ! !
a) A i B × C
(
)
! !
b) A i B
!
!
!
c) C − B i D
(
)
(
(
)
! ! !
d) A i B C
!
! !
!
e) A × B i C × D
) (
)
3.8.6. Which of the following vector operations produces a vector as
the result if the magnitudes of all of the vectors are not equal to
zero?
! ! !
a) A i B × C
(
)
! !
b) A i B
!
!
!
c) C − B i D
(
)
(
(
)
! ! !
d) A i B C
!
! !
!
e) A × B i C × D
) (
)
4.3.3. An eagle takes off from a tree branch on the side of a mountain
and flies due west for 225 m in 19 s. Spying a mouse on the
ground to the west, the eagle dives 441 m at an angle of 65°
relative to the horizontal direction for 11 s to catch the mouse.
Determine the eagle’s average velocity for the thirty second
interval.
a) 19 m/s at 44° below the horizontal direction
b) 22 m/s at 65° below the horizontal direction
c) 19 m/s at 65° below the horizontal direction
d) 22 m/s at 44° below the horizontal direction
e) 25 m/s at 27° below the horizontal direction
4.3.3. An eagle takes off from a tree branch on the side of a mountain
and flies due west for 225 m in 19 s. Spying a mouse on the
ground to the west, the eagle dives 441 m at an angle of 65°
relative to the horizontal direction for 11 s to catch the mouse.
Determine the eagle’s average velocity for the thirty second
interval.
a) 19 m/s at 44° below the horizontal direction
b) 22 m/s at 65° below the horizontal direction
c) 19 m/s at 65° below the horizontal direction
d) 22 m/s at 44° below the horizontal direction
e) 25 m/s at 27° below the horizontal direction
4.4.2. A ball is rolling down one hill and up another as shown. Points A and B are at the same
height. How do the velocity and acceleration change as the ball rolls from point A to point B?
a) The velocity and acceleration are the same at both points.
b) The velocity and the magnitude of the acceleration are the same at both points, but the
direction of the acceleration is opposite at B to the direction it had at A.
c) The acceleration and the magnitude of the velocity are the same at both points, but the direction
of the velocity is opposite at B to the direction it had at A.
d) The horizontal component of the velocity is the same at points A and B, but the vertical
component of the velocity has the same magnitude, but the opposite sign at B. The acceleration at
points A and B is the same.
e) The vertical component of the velocity is the same at points A and B, but the horizontal
component of the velocity has the same magnitude, but the opposite sign at B. The
acceleration at points A and B has the same magnitude, but opposite direction.
4.4.2. A ball is rolling down one hill and up another as shown. Points A and B are at the same
height. How do the velocity and acceleration change as the ball rolls from point A to point B?
a) The velocity and acceleration are the same at both points.
b) The velocity and the magnitude of the acceleration are the same at both points, but the
direction of the acceleration is opposite at B to the direction it had at A.
c) The acceleration and the magnitude of the velocity are the same at both points, but the direction
of the velocity is opposite at B to the direction it had at A.
d) The horizontal component of the velocity is the same at points A and B, but the vertical
component of the velocity has the same magnitude, but the opposite sign at B. The acceleration at
points A and B is the same.
e) The vertical component of the velocity is the same at points A and B, but the horizontal
component of the velocity has the same magnitude, but the opposite sign at B. The
acceleration at points A and B has the same magnitude, but opposite direction.
4.5.1. A bullet is aimed at a target on the wall a distance L away from the firing position.
Because of gravity, the bullet strikes the wall a distance Δy below the mark as suggested
in the figure. Note: The drawing is not to scale. If the distance L was half as large, and
the bullet had the same initial velocity, how would Δy be affected?
a) Δy will double.
b) Δy will be half as large.
c) Δy will be one fourth as large.
d) Δy will be four times larger.
e) It is not possible to determine unless numerical values are given for the distances.
4.5.1. A bullet is aimed at a target on the wall a distance L away from the firing position.
Because of gravity, the bullet strikes the wall a distance Δy below the mark as suggested
in the figure. Note: The drawing is not to scale. If the distance L was half as large, and
the bullet had the same initial velocity, how would Δy be affected?
a) Δy will double.
b) Δy will be half as large.
c) Δy will be one fourth as large.
d) Δy will be four times larger.
e) It is not possible to determine unless numerical values are given for the distances.
4.6.6. Balls A, B, and C are identical. From the top of a tall building, ball A
is launched with a velocity of 20 m/s at an angle of 45° above the
horizontal direction, ball B is launched with a velocity of 20 m/s in the
horizontal direction, and ball C is launched with a velocity of 20 m/s at
an angle of 45° below the horizontal direction. Which of the following
choices correctly relates the magnitudes of the velocities of the balls just
before they hit the ground below? Ignore any effects of air resistance.
a) vA = vC > vB
b) vA = vC = vB
c) vA > vC > vB
d) vA < vC < vB
e) vA > vC < vB
4.6.6. Balls A, B, and C are identical. From the top of a tall building, ball A
is launched with a velocity of 20 m/s at an angle of 45° above the
horizontal direction, ball B is launched with a velocity of 20 m/s in the
horizontal direction, and ball C is launched with a velocity of 20 m/s at
an angle of 45° below the horizontal direction. Which of the following
choices correctly relates the magnitudes of the velocities of the balls just
before they hit the ground below? Ignore any effects of air resistance.
a) vA = vC > vB
b) vA = vC = vB
c) vA > vC > vB
d) vA < vC < vB
e) vA > vC < vB
4.6.8. At time t = 0 s, Ball A is thrown vertically upward with an initial speed
v0A. Ball B is thrown vertically upward shortly after Ball A at time t.
Ball B passes Ball A just as Ball A is reaching the top of its trajectory.
What is the initial speed v0B of Ball B in terms of the given parameters?
The acceleration due to gravity is g.
a) v0B = 2v0A - gt
b) v0B = v0A - (1/2)gt
c) v0B = v0A - (1/2)gt2
d) v0 B =
e)
v0 B =
v0 A + 12 g 2t 2
v0 A − gt
v02A + 12 g 2t 2 − v0 A gt
v0 A − gt
4.6.8. At time t = 0 s, Ball A is thrown vertically upward with an initial speed
v0A. Ball B is thrown vertically upward shortly after Ball A at time t.
Ball B passes Ball A just as Ball A is reaching the top of its trajectory.
What is the initial speed v0B of Ball B in terms of the given parameters?
The acceleration due to gravity is g.
a) v0B = 2v0A - gt
b) v0B = v0A - (1/2)gt
c) v0B = v0A - (1/2)gt2
d) v0 B =
e)
v0 B =
v0 A + 12 g 2t 2
v0 A − gt
v02A + 12 g 2t 2 − v0 A gt
v0 A − gt
4.9.2. A boat attempts to cross a river. The boat’s speed with respect
to the water is 12.0 m/s. The speed of the river current with
respect to the river bank is 6.0 m/s. At what angle should the boat
be directed so that it crosses the river to a point directly across
from its starting point?
a) 45.0°
b) 26.6°
c) 30.0°
d) 53.1°
e) 60.0°
4.9.2. A boat attempts to cross a river. The boat’s speed with respect
to the water is 12.0 m/s. The speed of the river current with
respect to the river bank is 6.0 m/s. At what angle should the boat
be directed so that it crosses the river to a point directly across
from its starting point?
a) 45.0°
b) 26.6°
c) 30.0°
d) 53.1°
e) 60.0°
Backup slides