Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
eSolutionsManual-PoweredbyCogneroPage1
Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
eSolutionsManual-PoweredbyCogneroPage2
Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
eSolutionsManual-PoweredbyCogneroPage3
Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
eSolutionsManual-PoweredbyCogneroPage4
Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
eSolutionsManual-PoweredbyCogneroPage5
Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
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Chapter 3 Practice Problems, Review, and Assessment
Section 3 Free Fall: Practice Problems
41.
A construction worker accidentally drops a brick from a high scaffold.
a.
Whatisthevelocityofthebrickafter4.0s?
b.
How far does the brick fall during this time?
SOLUTION:
a. Let upward be the positive direction.
b.
The brick falls 78 m.
ANSWER:
a. Let upward be the positive direction.

v
f
= 39 m/s downward
b. x =
–78m

Thebrickfalls78m.
44.Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Itiscaughtatthesamedistanceabovethe
ground.
a.
How high does the ball rise?
b.
How long does the ball remain in the air? Hint: The time it takes the ball to rise equals the time it takes to fall.
SOLUTION:
a.

b.

ANSWER:
a. x = 26 m
b. t = 4.6 s
45.
You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a.
What is the velocity of the coin at the top of its trajectory?
b.
Ifthecoinreachesahighpointof0.25mabovewhereyoureleasedit,whatwasitsinitialspeed?
c.
If you catch it at the same height as you released it, how much time did it spend in the air?
SOLUTION:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b.

c.

ANSWER:
a. v
top
= 0 m/s; a
top
= 9.8 m/s downward
b. v
i
= 2.2 m/s
c. t = 0.45 s
Section 3 Free Fall: Review
47.
MAIN IDEA
Suppose you hold a book in one hand and a flat sheet of paper in another hand. You drop them both,
and they fall to the ground. Explain why the falling book is a good example of free fall, but the paper is not.
SOLUTION:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
ANSWER:
Free fall is the motion of an object when gravity is the only significant force on it. The paper is
significantly affected by the air, but the book is not.
49.
Free-Fall Ride
Suppose a free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity
oftherideafter2.3s?Howfardopeopleontheridefallduringthe2.3
-s time period?
SOLUTION:
Let upward be the positive direction.

ANSWER:
Let upward be the positive direction.

v
f
= 23 m/s downward

x
f
=
−
26 m
The people fall 26 m during the 2.3-s time period.
51.
Velocity and Acceleration
Suppose you throw a ball straight up into the air. Describe the changes in the velocity of
the ball. Describe the changes in the acceleration of the ball.
SOLUTION:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
ANSWER:
Velocity is reduced at a constant rate as the ball travels upward. At its highest point, velocity is zero. As
the ball begins to drop, the velocity begins to increase in the negative direction. When it reaches the
height from which it was initially released, the ball has the same speed it had upon release. The
acceleration is constant throughout the ball
’sflight.
Chapter Assessment
Section 3 Free Fall: Mastering Problems
72.Astonethatstartsatrestisinfreefallfor8.0s.(Level1)
a.
Calculate the stone
’svelocityafter8.0s.
b.
What is the stone
’
s displacement during this time?
SOLUTION:
a. v
f
= v
i
+ at
f
where a =
−
9.8 m/s
2
= 0.0 m/s + (
−
9.8 m/s
2
)(8.0 s)
=
−
78 m/s
= 78 m/s downward
b. Choose the coordinate system to have the origin where the stone is at rest and positive to be upward.


=3.1×10
2
m downward
ANSWER:
a. 78 m/s downward
b. 310 m downward
74.Youthrowaballdownwardfromawindowataspeedof2.0m/s.Howfastwillitbemovingwhenithitsthe
sidewalk2.5mbelow?(Level2)
SOLUTION:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

ANSWER:
Choose a coordinate system with the positive direction downward and the origin at the point where the
ball leaves your hand.

76.
Beanbag
Youthrowabeanbagintheairandcatchit2.2slateratthesameplaceatwhichyouthrewit.(Level3)
a.
How high did it go?
b.
What was its initial velocity?
SOLUTION:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
is half of the time in the air.

b.

v
i
= 11 m/s upward
ANSWER:
a. Choose a coordinate system with the upward direction positive. The time to reach the maximum height
ishalfofthetimeintheair.

v
i
=10.78m/s

x
f
= 5.9 m
b.

v
i
= 11 m/s upward
Chapter Assessment: Mixed Review
88.
Bicycle
Abicycleacceleratesfrom0.0m/sto4.0m/sin4.0s.Whatdistancedoesittravel?(Level1)
SOLUTION:
ANSWER:
8.0 m
89.AweatherballoonisfloatingataconstantheightaboveEarthwhenitreleasesapackofinstruments.(Level1)
a.
If the pack hits the ground with a downward velocity of
−73.5m/s,howfardidthepackfall?
b.
Calculatethedistancetheballhasrolledattheendof2.2s.
SOLUTION:
a.


b.

ANSWER:
a. x
f
=2.8×10
2
m downward

b. t
f
= 7.5 s
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Chapter 3 Practice Problems, Review, and Assessment