REVIEW
Teaching Resources
• TeacherEXPRESS
• Virtual Physics Lab 7
• Conceptual Physics Alive!
   DVDs Vectors and Projectiles
5 REVIEW
Concept Summary
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think! Answers
5.2
A crosswind would increase the speed of
the airplane and blow it off course by a
predictable amount.
Both cannonballs fall the same vertical
distance with the same acceleration g and
therefore strike the ground at the same
time. Do you see that this is consistent
with our analysis of Figure 5.9? Ask which
cannonball strikes the ground first when
the cannon is pointed at an upward angle.
In this case, the cannonball that is simply
dropped hits the ground first. Now con-
sider the case when the cannon is pointed
downward. The fired cannonball hits first.
So upward, the dropped cannonball hits
first; downward, the fired cannonball hits
first. There must be some angle where both
hit at the same time. Do you see it would
be when the cannon is pointing neither
upward nor downward, that is, when it is
pointing horizontally?
Its vertical acceleration is g because the
force of gravity is downward. Its horizontal
acceleration is zero because no horizontal
force acts on it.
The minimum speed of a projectile occurs
at the top of its path. If it is launched verti-
cally, its speed at the top is zero. If it is pro-
jected at an angle, the vertical component
of velocity is still zero at the top, leaving
only the horizontal component. So the
speed at the top is equal to the horizontal
component of the projectile’s velocity at
any point. How about that?
•
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•
•
•
•
A vector quantity includes both magni-
tude and direction, but a scalar quantity
includes only magnitude.
The resultant of two perpendicular vec-
tors is the diagonal of a rectangle con-
structed with the two vectors as sides.
The perpendicular components of a vec-
tor are independent of each other.
The horizontal component of motion
for a projectile is just like the horizontal
motion of a ball rolling freely along a
level surface without friction. The vertical
component of a projectile’s velocity is like
the motion for a freely falling object.
The downward motion of a horizontally
launched projectile is the same as that of
free fall.
The vertical distance a projectile falls
below an imaginary straight-line path in-
creases continually with time and is equal
to 5t2 meters.
••••••
5.5
5.6.1
Key Terms
components (p. 72)
resolution (p. 72)
projectile (p. 73)
5.6.2
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5 ASSESS
Check Concepts
Section 5.1
••••••
ASSESS
Check Concepts
Section 5.5
1. How does a vector quantity differ from a
   scalar quantity?
2. Why is speed classified as a scalar quantity
   and velocity classified as a vector quantity?
Section 5.2
9. At the instant a ball is thrown horizontally
   over a level range, a ball held at the side of
   the first is released and drops to the ground.
   If air resistance is neglected, which ball
   strikes the ground first?
Section 5.6
3. If a vector that is 1 cm long represents a
   velocity of 10 km/h, what velocity does a
   vector 2 cm long drawn to the same scale
   represent?
4. When a rectangle is constructed in
   order to add perpendicular velocities,
   what part of the rectangle represents the
   resultant vector?
Section 5.3
10. a. How far below an initial straight-line path
       will a projectile fall in one second?
    b. Does your answer depend on the angle
       of launch or on the initial speed of the
       projectile? Defend your answer.
5. Will a vector at 45° to the horizontal be
   larger or smaller than its horizontal and
   vertical components? By how much?
Section 5.4
6. Why does a bowling ball move without
   acceleration when it rolls along a bowl-
   ing alley?
7. In the absence of air resistance, why does
   the horizontal component of velocity for
   a projectile remain constant while the
   vertical component changes?
8. How does the downward component of
   the motion of a projectile compare with
   the motion of free fall?
11. Neglecting air resistance, if you throw a ball
    straight up with a speed of 20 m/s, how fast
    will it be moving when you catch it?
12. a. Neglecting air resistance, if you throw a
       baseball at 20 m/s to your friend who is
       on first base, will the catching speed be
       greater than, equal to, or less than 20 m/s?
    b. Does the speed change if air resistance is a
       factor?
13. What do we call a projectile that continually
    “falls” around Earth?
CHAPTER 5
PROJECTILE MOTION
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Think and Rank
5 ASSESS
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Think and Rank ••••••Concept Summary ••••••
Rank each of the following sets of scenarios in
order of the quantity or property involved. List
them from left to right. If scenarios have equal
rankings, then separate them with an equal sign.
(e.g., A B)
14. The vectors represent initial velocities of
    projectiles launched at ground level.
16. Water balloons of different masses are
    launched by slingshots at different launch-
    ing velocities v. All have the same vertical
    component of launching velocities.
a. Rank them by their vertical components
   of velocity from greatest to least.
b. Rank them by their horizontal compo-
   nents of velocity from greatest to least.
15. A toy car rolls off tables of various heights at
    different speeds as shown.
a. Rank by the time in the air, from longest
   to shortest.
b. Rank by the maximum height reached,
   from highest to lowest.
c. Rank by the maximum range, from great-
   est to least.
17. The airplane is blown off course by wind in
    the directions shown. Use the parallelogram
    rule and rank from highest to lowest the
    resulting speed across the ground.
a. Rank them for the time in the air, from
   greatest to least.
b. Rank them for horizontal range, from
   greatest to least.
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Plug and Chug
5 ASSESS
Plug and Chug
••••••
For Questions 18–19, recall that when two vec-
tors in the same or exactly opposite directions
are added, the magnitude of their resultant is the
sum or difference of their original magnitudes.
18. Calculate the resultant velocity of an air-
    plane that Summary ••••••Conceptnormally flies at 200 km/h if
    it encounters a 50-km/h tailwind. If it
    encounters a 50-km/h headwind.
19. Calculate the magnitude of the resultant
    of a pair of 100-km/h velocity vectors that
    are at right angles to each other.
25. The speed of falling rain is the same
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    about whether or not the rain encounters
    air resistance?
26. Marshall says that when a pair of vectors are
    at right angles to each other, the magnitude
    of their resultant is greaterthink! Answersthan the mag-henitude of either vector alone. Renee says
    is speaking in generalities and that what he
    says isn’t always true. With whom do you
    agree?
27. How is the horizontal component of veloc-
    ity for a projectile affected by the vertical
    component?
28. Rain falling vertically will make vertical
    streaks on a car’s side window. However, if the
    car is moving, the streaks are slanted. If the
    streaks from a vertically falling rain make 45°
    streaks, how fast is the car moving compared
    with the speed of the falling rain?
29. An airplane encounters a wind that blows in
    a perpendicular direction to the direction its
    nose is pointing. Does the effect of this wind
    increase or decrease speed across the ground
    below? Or does it have no effect on ground
    speed?
30. A projectile is launched vertically at 50 m/s.
    If air resistance can be neglected, at what
    speed will it return to its initial level? Where
    in its trajectory will it have minimum speed?
31. A batted baseball follows a parabolic path
    on a day when the sun is directly overhead.
    How does the speed of the ball’s shadow
    across the field compare with the ball’s hori-
    zontal component of velocity?
32. When air resistance acts on a projectile, does
    it affect the horizontal component of veloc-
    ity, the vertical component of velocity, or
    both? Defend your answer.
19.
Think and Explain
For questions 20–21, recall that the resultant V of
two vectors A and B at right angles to each other
is found using the Pythagorean theorem:
V
A2
B2
20. Calculate the resulting speed of an airplane
    with an airspeed of 120 km/h pointing due
    north when it encounters a wind of 90 km/h
    directed from the west. (Recall, speed is the
    magnitude of velocity.)
21. Calculate the speed of raindrops hitting
    your face when they fall vertically at 3 m/s
    while you’re running horizontally at 4 m/s.
Think and Explain
••••••
22. Whenever you add 3 and 4, the result is 7.
    This is true if the quantities being added are
    scalar quantities. If 3 and 4 are the mag-
    nitudes of vector quantities, when will the
    magnitude of their sum be 5?
23. Christopher can paddle a canoe in still water
    at 8 km/h. How successful will he be at canoe-
    ing upstream in a river that flows at 8 km/h?
24. How does the vertical distance a projectile
    falls below an otherwise straight-line path
    compare with the vertical distance it would
    fall from rest in the same time?
CHAPTER 5
PROJECTILE MOTION
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33
5 ASSESS
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33. You’re driving behind a car and wish toConcept Summary ••••••
pass, so you turn to the left and pull into the
passing lane without changing speed. Why
does the distance increase between you and
the car you’re following?
Think and Solve
••••••
37. Sneezlee flies at a speed of 10 m/s in still air.
Think and Solve
34. Brandon launches a projectile at an angle
    of 75° above the horizontal, which strikes
    the ground a certain distance down range.
    For what other angle of launch at the same
    speed would the projectile land just as far
    away?
35. When you jump up, your hang time is the
    time your feet are off the ground. Does hang
    time depend on your vertical component
    of velocity when you jump, your horizontal
    component of velocity, or both? Defend
    your answer.
36. The hang time of a basketball player who
    jumps a vertical distance of 2 feet (0.6 m)
    is 2/3 second. What will be the hang time
    if the player reaches the same height while
    jumping a horizontal distance of 4 feet
    (1.2 m)?
a. If he flies into a 2-m/s headwind, how fast
   will he be traveling relative to the ground
   below?
b. Relative to the ground below, how fast
   will he travel when he experiences a 2-m/s
   tailwind?
c. While flying at 10 m/s, suppose that he
   encounters a 10-m/s cross wind (coming
   at a right angle to his heading). What is
   his speed relative to the ground below?
38. A boat is rowed at 8 km/h directly across a
    river that flows at 6 km/h, as shown in the
    figure.
a. What is the resultant speed of the boat?
b. How fast and in what direction can the boat
   be rowed to reach a destination directly
   across the river?
39. If a 14-unit vector makes an angle of 45°
    with the horizontal, what are its horizontal
    and vertical components?
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5 ASSESS
40. Harry accidentally falls out of a helicopter
    that is traveling at 15 m/s. He plunges into
    a swimming pool 2 seconds later. Assuming
    no air resistance, what was the horizontal
    distance between Harry and the swimming
    pool when he fell from the helicopter?
41. Refer to the previous problem.
46. Joshua throws a stone horizontally from a
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Concept Summary ••••••
  a. What are the horizontal and vertical com-
   ponents of Harry’s velocity just as he hits
   the water?
b. Show that Harry hits the water at a speed
   of 25 m/s.
42. Harry and Angela look from their balcony
    to a swimming pool below that is 15 m from
    the bottom of their building. They estimate
    the balcony is 45 m high and wonder how
    fast they would have to jump horizontally to
    succeed in reaching the pool. What is your
    answer?
43. A girl throws a slingshot pellet directly at a
    target that is far enough away to take one-
    half second to reach. How far below the
    target does the pellet hit? How high above
    the target should she aim?
44. The boy on the tower in the figure below
    throws a ball a distance of 60 m, as shown.
    At what speed, in m/s, is the ball thrown?
think! Answers
a. Use your knowledge of vectors and show
   that the stone strikes the ground at a
   speed of about 28 m/s.
b. At what angle does the ball strike the
   ground?
47. On a bowling alley, Isabella rolls a bowling
    ball that covers a distance of 10 meters in
    1 second. The speed of the ball is 10 m/s. If
    the ball were instead dropped from rest off
    the edge of a building, what would be its
    speed at the end of 1 second?
48. A bowling ball is moving at 10 m/s when
    it rolls off the edge of a tall building. What
    is the ball’s speed one second later? (Hint:
    think vectors!)
49. Calculate Hotshot Harry’s hang time if he
    moves horizontally 3 m during a 1.25-m
    high jump. What is his hang time if he
    moves 6 m horizontally during this jump?
50. Megan rolls a ball across a lab bench y
    meters high and the ball rolls off the edge of
    the bench with horizontal speed v.
a. From the equation y = 1 gt2, which gives
                            2
   the vertical distance y an object falls from
   rest, derive an equation that shows the
   time t taken for the ball to reach the floor.
b. Write an equation showing how far the
   ball will land from a point on the floor
   directly below the edge of the bench.
c. Calculate the time in the air and the land-
   ing location for v 1.5 m/s and a bench
   height of 1.2 m.
45. A cannonball launched with an initial veloc-
    ity of 141 m/s at an angle of 45° follows a
    parabolic path and hits a balloon at the top
    of its trajectory. Neglecting air resistance,
    how fast is it going when it hits the balloon?
    What is the acceleration of the cannonball
    just before it hits the balloon?
Teaching Resources
More Problem-Solving Practice
Appendix F
CHAPTER 5
PROJECTILE MOTION
• Computer Test Bank
• Chapter and Unit Tests
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