Questions and Problems 111
Questions and Problems
In a few problems, you are given more data than you actually need;
in a few other problems, you are required to supply data from
your general knowledge, outside sources, or informed estimate.
Interpret as significant all digits in numerical values that
have trailing zeros and no decimal points. For all problems, use
g = 9.80 m>s2 for the free-fall acceleration due to gravity.
• Basic, single-concept problem
•• Intermediate-level problem, may require synthesis of concepts
and multiple steps
••• Challenging problem
SSM Solution is in Student Solutions Manual
Conceptual Questions
1. •(a) Can the sum of two vectors that have different magnitudes ever be equal to zero? If so, give an example. If not,
explain why the sum of two vectors cannot be equal to zero.
(b) Can the sum of three vectors that have different magnitudes
ever be equal to zero? SSM
2. •What is the difference between a scalar and a vector? Give
an example of a scalar and an example of a vector.
3. •Describe a situation in which the average velocity and the
instantaneous velocity vectors are identical. Describe a situation in which these two velocity vectors are different.
4. •(a) Explain the difference between an object undergoing
uniform circular motion and an object experiencing projectile
motion. (b) In what ways are these kinds of motion similar?
5. •Consider the effects of air resistance on a projectile. Describe
qualitatively how the projectile’s velocities and accelerations in
the vertical and horizontal directions differ when the effects of air
resistance are ignored and when the effects are considered. SSM
6. •Astronomy If you were playing tennis on the Moon, what
adjustments would you need to make in order for your shots to
stay within the boundaries of the court? Would the trajectories
of the balls look different on the Moon compared to on Earth?
7. •Explain what is meant by the magnitude of a vector.
8. •During the motion of a projectile, which of the following
quantities are constant during the flight: x, y, vx, vy, ax, ay?
(Neglect any effects due to air resistance.)
9. •For a given, fixed launch speed, at what angle should you
launch a projectile to achieve (a) the longest range, (b) the longest time of flight, and (c) the greatest height? (Neglect any
effects due to air resistance.) SSM
10. •A rock is thrown from a bridge at an angle 20° below
horizontal. At the instant of impact, is the rock’s speed greater
than, less than, or equal to the speed with which it was thrown?
Explain your answer. (Neglect any effects due to air resistance.)
11. •Sports A soccer player kicks a ball at an angle 60° from the
ground. The soccer ball hits the ground some distance away. Is
there any point at which the velocity and acceleration vectors
are perpendicular to each other? Explain your answer. (Neglect
any effects due to air resistance.)
12. •Sports Suppose you are the coach of a champion long
jumper. Would you suggest that she take off at an angle less
than 45°? Why or why not?
Freed_c03_067-116_st_hr1.indd 111
13. •An ape swings through the jungle by hanging from a vine.
At the lowest point of its motion, is the ape accelerating? If so,
what is the direction of its acceleration? SSM
14. •A cyclist rides around a flat, circular track at constant
speed. Is his acceleration vector zero? Explain your answer.
15. •You are driving your car in a circular path on flat ground
with a constant speed. At the instant you are driving north and
turning right, are you accelerating? If so, what is the direction
of your acceleration at that moment? If not, why not?
Multiple-Choice Questions
16. •Which of the following is not a vector?
A. average velocity
B. instantaneous velocity
C. distance
D. displacement
E. acceleration
s has an x component and a y component that
17. •Vector A
are equal in magnitude. Which of the following is the angle
s makes with respect to the x axis in the same
that vector A
x–y coordinate system?
A. 0°
B. 45°
C. 60°
D. 90°
E. 120° SSM
18. •The vector in Figure 3-35
has a length of 4.00 units and
makes a 30.0° angle with respect
to the y axis as shown. What are
the x and y components of the
vector?
A. 3.46, 2.00
B. 22.00, 3.46
C. 23.46, 2.00
D. 2.00, 23.46
E. 23.46, 22.00
y
30°
x
Figure 3-35 Problem 18
19. •The acceleration of a particle in projectile motion
A. points along the parabolic path of the particle.
B. is directed horizontally.
C. vanishes at the particle’s highest point.
D. is vertically downward.
E. is zero.
20. •Adam drops a ball from rest from the top floor of a building at the same time that Bob throws a ball horizontally from
the same location. Which ball hits the ground first? (Neglect any
effects due to air resistance.)
A. Adam’s ball
B. Bob’s ball
C. They both hit the ground at the same time.
D. It depends on how fast Bob throws the ball.
E. It depends on how fast the ball falls when Adam
drops it.
3/12/13 10:01 AM
112 Chapter 3 Motion in Two or Three Dimensions
22. •A zookeeper is trying to shoot a monkey sitting at the top
of a tree with a tranquilizer gun. If the monkey drops from the
tree at the same instant that the zookeeper fires, where should
the zookeeper aim if he wants to hit the monkey? (Neglect any
effects due to air resistance.)
A. Aim straight at the monkey.
B. Aim lower than the monkey.
C. Aim higher than the monkey.
D. Aim to the right of the monkey.
E. It’s impossible to determine.
23. •The acceleration vector of a particle in uniform circular
motion
A. points along the circular path of the particle and in
the direction of motion.
B. points along the circular path of the particle and
opposite the direction of motion.
C. is zero.
D. points toward the center of the circle.
E. points outward from the center of the circle.
24. •If the speed of an object in uniform circular motion is constant and the radial distance is doubled, the magnitude of the
radial acceleration decreases by what factor?
A. 2
B. 3
C. 4
D. 6
E. 1
25. •You toss a ball into the air at an initial angle 40° from the
horizontal. At what point in the ball’s trajectory does the ball have
the smallest speed? (Neglect any effects due to air resistance.)
A. just after it is tossed
B. at the highest point in its flight
C. just before it hits the ground
D. halfway between the ground and the highest point on
the rise portion of the trajectory
E. halfway between the ground and the highest point on
the fall portion of the trajectory
Estimation/Numerical Analysis
26. •If sr has a magnitude of 24 and points in a direction 36°
south of west, find the vector components of sr . Use a protractor
and some graph paper to verify your answer by drawing sr and
measuring the length of the lines representing its components.
27. •A vector sr has a magnitude of 18 units and makes a 30°
angle with respect to the x axis. Find the vector components
of sr using a protractor and some graph paper to verify your
answer by drawing sr and measuring the length of the lines
representing its components.
28. •Sports In the 1970 National Basketball Association championship, Jerry West made a 60-ft shot from beyond half court
to lead the Los Angeles Lakers to an improbable tie at the
Freed_c03_067-116_st_hr1.indd 112
­ uzzer with the New York Knicks. West threw the ball at an
b
angle of 50.0° above the horizontal. The basket is 10 ft from
the court floor. Neglecting air resistance, estimate the initial
speed of the ball. (The Knicks won the game in overtime.)
29. •Sports In Detroit in 1971, Reggie Jackson hit one of the
most memorable home runs in the history of the Major League
Baseball All-Star Game. The approximate trajectory is plotted
in Figure 3-36. (The asymmetry is due to air resistance.) Using
the information in the graph, estimate the initial speed of the
ball as it left Reggie’s bat. SSM
Vertical distance (ft.)
21. •Sports Two golf balls are hit from the same point on a flat
field. Both are hit at an angle of 30° above the horizontal. Ball 2
has twice the initial speed of ball 1. If ball 1 lands a distance d1
from the initial point, at what distance d2 does ball 2 land from
the initial point? (Neglect any effects due to air resistance.)
A. d2 = 0.5d1
B. d2 = d1
C. d2 = 2d1
D. d2 = 4d1
E. d2 = 8d1 SSM
150
100
50
0
0
50
100 150 200 250 300 350 400 450 500
Horizontal distance (ft.)
Figure 3-36 Problem 29
30. •Use a spreadsheet program or a graphing calculator to make
(a) a graph of vx versus time, (b) a graph of vy versus time, (c)
a graph of ax versus time, and (d) a graph of ay versus time for
an object that undergoes parabolic motion. Identify the points
where the object reaches its highest point and where it hits the
ground at the end of its flight.
Problems
3-2 A vector quantity has both a magnitude and a direction
3-3 Vectors can be described in terms of components
3-4 Using components greatly simplifies vector calculations
s has components Ax = 6 and Ay = 9. Vector B
s
31. •Vector A
s has compohas components Bx = 7, By = 23, and vector C
nents Cx = 0, Cy = 26. Determine the components of the fols + B
s, (b) A
s - 2C
s , (c) A
s + B
s - C
s , and
lowing vectors: (a) A
1s
s
s
(d) A + 2B - 3C.
32. •Calculate the magnitude and direction
of the vector sr using Figure 3-37.
y
r
2.5
x
θ
5.0
Figure 3-37 Problem 32
s in the
33. •What are the components Ax and Ay of vector A
three coordinate systems shown in Figure 3-38? SSM
(1)
(2)
y
(3)
y
y
A
5
A
30°
5
x
120°
x
x
A
30°
Ax =
Ax =
Ax =
Ay =
Ay =
Ay =
5
Figure 3-38 Problem 33
3/12/13 10:02 AM
Questions and Problems 113
34. •Each of the following vectors is given in terms of its x and
y components. Find the magnitude of each vector and the angle
it makes with respect to the +x axis.
A. Ax = 3, Ay = 22
B. Ax = 22, Ay = 2
C. Ax = 0, Ay = 22
s is 66.0 m long at a 28° angle with respect to the +x axis.
35. •A
s is 40.0 m long at a 56° angle above the 2x axis. What is
B
s and B
s (magnitude and angle with the
the sum of vectors A
+x axis)?
s with components Ax = 2.00 and Ay =
36. •Given the vector A
s with components Bx = 3.00 and By =
6.00, and the vector B
22.00, calculate the magnitude and angle with respect to the
s = A
s + B
s.
+x axis of the vector sum C
s with components Ax = 2.00, Ay = 6.00,
37. •Given the vector A
s with components Bx = 2.00, By = 22.00, and the
the vector B
s = A
s - B
s, calculate the magnitude and angle with the
vector D
s . SSM
+x axis of the vector D
s = 30 m>s,
38. •Two velocity vectors are given as follows: A
s = 40 m>s, due north. Calculate each of
45° north of east and B
s + B
s, (b) A
s - B
s, (c) 2A
s + B
s.
the resultant velocity vectors: (a) A
39. •What are the magnitude and direction of the change in velocity if the initial velocity is 30 m>s south and the final velocity
is 40 m>s west?
40. •Consider the set of vectors in
Figure 3-39. Nathan says the magnitude of the resultant vector is 7, and
the resultant vector points in a direction 37° in the northeasterly direction.
What, if anything, is wrong with his
statement? If something is wrong,
­explain the error(s) and how to correct
it (them).
y
3
Figure 3-39 Problem 40
15 m/s
30°
x
45°
vi
y
vf
Figure 3-42 Problem 45
46. •An object undergoing parabolic motion travels 100 m in
the horizontal direction before returning to its initial height. If
the object is thrown initially at a 30° angle from the horizontal,
determine the x component and the y component of the initial
velocity. (Neglect any effects due to air resistance.)
47. •Five balls are thrown off
a cliff at the angles shown in
Figure 3-43. Each has the same
initial velocity. Rank (a) the horizontal distance traveled, (b) the
time required for each to hit the
ground, and (c) the magnitude
of the velocity when each hits
the ground. (Neglect any effects
due to air resistance.) SSM
1
30°
2
30°
3
30°
30°
4
5
Figure 3-43 Problem 47
48. •Biology A Chinook salmon can jump out of water with a
speed of 6.30 m>s. How far horizontally can a Chinook salmon
travel through the air if it leaves the water with an initial angle
of 40°? (Neglect any effects due to air resistance.)
Figure 3-40 Problem 41
20 m/s
30°
30° vi
20 m/s
Figure 3-41 Problem 42
Freed_c03_067-116_st_hr2.indd 113
45. •An object is undergoing parabolic motion as shown from
the side in Figure 3-42. Assume the object starts its motion at
ground level. For the five positions shown, draw to scale vectors representing the magnitudes of (a) the x components of
the velocity, (b) the y components of the velocity, and (c) the
accelerations. (Neglect any effects due to air resistance.)
x
x
vf
42. ••An object travels with a
constant acceleration for 10 s.
The vectors in Figure 3-41 represent the final and initial velocities.
Carefully graph the x component
of the velocity versus time, the y
component of the velocity versus
time, and the y component of the
acceleration versus time.
3-6 A projectile moves in a plane and has a constant
acceleration
3-7 You can solve projectile motion problems using
techniques learned for straight-line motion
4
y
30 m/s
44. ••Cody starts at a point 6.00 km to the east and 4.00
km to the south of a location that represents the origin of a
coordinate system for a map. He ends up at a point 10.0 km
to the west and 6.00 km to the north of the map origin. (a)
What was his average velocity if the trip took him 4.00 h to
complete? (b) Cody walks to his destination at a constant
rate. His friend Marcus covers the distance with a combination of jogging, walking, running, and resting so that the
total trip time is also 4.00 h. How do their average velocities
compare?
y
3-5 For motion in a plane, velocity and acceleration are
vector quantities
41. ••The two vectors
shown in Figure 3-40 represent the initial and final
velocities of an object during
a trip that took 5 s. Calculate the average acceleration
during this trip. Is it possible
to determine whether the acceleration was uniform from
the information given in the
problem? SSM
43. ••An object experiences a constant acceleration of
2.00 m>s 2 along the 2x axis for 2.70 s, attaining a velocity
of 16.0 m>s in a direction 45° from the +x axis. Calculate the
initial velocity vector of the object.
x
49. •Biology A tiger leaps horizontally out of a tree that is 4.00 m
high. If he lands 5.00 m from the base of the tree, calculate his
initial speed. (Neglect any effects due to air resistance.) SSM
50. •A football is punted at 25.0 m>s at an angle of 30.0°
above the horizon. What is the velocity vector of the ball when
it is 5.00 m above ground level? Assume it starts 1.00 m above
ground level. (Neglect any effects due to air resistance.)
51. •• A dart is thrown at a dartboard 2.37 m away. When
the dart is released at the same height as the center of the
4/2/13 3:12 PM
114 Chapter 3 Motion in Two or Three Dimensions
­ artboard, it hits the center in 0.447 s. At what angle relative
d
to the floor was the dart thrown? (Neglect any effects due to
air resistance.)
from the rotation axis of the sample chamber in such a ­device.
What is the speed of an object traveling under the given
­conditions?
3-8 An object moving in a circle is accelerating even if its
speed is constant
General Problems
3-9 Any problem that involves uniform circular motion uses
the idea of centripetal acceleration
52. •A ball attached to a string is twirled in a circle of radius
1.25 m. If the constant speed of the ball is 2.25 m>s, what is the
period of the circular motion?
53. •A ball spins on a 0.870-m-long string with a constant
speed of 3.36 m>s. Calculate the acceleration of the ball. Be
sure to specify the direction of the acceleration. SSM
54. •A washing machine drum 80.0 cm in diameter starts from
rest and achieves 1200 rev>min in 22.0 s. Assuming the acceleration of the drum is constant, calculate the net acceleration
(magnitude and direction) of a point on the drum after 1.00 s
has elapsed.
55. •A 14.0-cm-diameter drill bit accelerates from rest up to
800 rev>min in 4.33 s. Calculate the acceleration of a point
on the edge of the bit once it has achieved its operating speed.
56. •Riders on a Ferris wheel of diameter 16.0 m move in a
circle with a radial acceleration of 2.00 m>s 2. What is the speed
of the Ferris wheel?
57. •In 1892 George W. G. Ferris designed a carnival ride in the
shape of a large wheel. This Ferris wheel had a diameter of
76 m and rotated one revolution every 20 min. What was the
magnitude of the acceleration that riders experienced? SSM
58. •A car races at a constant speed of 330 km>h around a
flat, circular track 1.00 km in diameter. What is the car’s radial
­acceleration in m>s 2?
59. ••Mary and Kelly decide they want to run side by side
around a circular track. Mary runs in the inside lane of the track
while Kelly runs in one of the outer lanes. What is the ratio of
their accelerations?
60. •Astronomy We know that the Moon revolves around
Earth ­during a period of 27.3 days. The average distance from
the center of Earth to the center of the Moon is 3.84  108 m.
What is the acceleration of the Moon due to its motion around
Earth?
61. •Astronomy The space shuttle is in orbit about 300 km
above the surface of Earth. The period of the orbit is about 5.43
 103 s. What is the acceleration of the shuttle? (The radius of
Earth is 6.38  106 m.) SSM
62. ••Calculate the accelerations of (a) Earth as it orbits the
Sun, and (b) a car traveling along a circular path that has a
radius of 50 m at a speed of 20 m>s.
63. •Biology In a vertical dive, a peregrine falcon can accelerate
at 0.6 times the free-fall acceleration (that is, at 0.6g) in reaching a speed of about 100 m>s. If a falcon pulls out of a dive into
a circular arc at this speed and can sustain a radial acceleration
of 0.6g, what is the radius of the turn? SSM
64. •Commercial ultracentrifuges can rotate at rates of
100,000 rpm (revolutions per minute). As a consequence, they
can create accelerations on the order of 800,000g. (A “g”
­represents an acceleration of 9.80 m>s 2.) Calculate the distance
Freed_c03_067-116hr2.indd 114
65. ••You observe two cars traveling in the same direction on
a long, straight section of Highway 5. The red car is moving
at a constant vR equal to 34 m>s and the blue car is moving at
constant vB equal to 28 m>s. At the moment you first see them,
the blue car is 24 m ahead of the red car. (a) How long after
you first see the cars does the red car catch up to the blue car?
(b) How far did the red car travel between when you first saw
it and when it caught up to the blue car? (c) Suppose the red car
started to accelerate at a rate of a equal to 43 m>s 2 just at the
moment you saw the cars. How long after that would the red
car catch up to the blue car?
66. ••An experiment to measure the value of g is constructed
using a tall tower outfitted with two sensing devices, one a distance H above the other. A small ball is fired straight up in the
tower so that it rises to near the top and then falls back down;
each sensing device reads out the time that elapses between the
ball going up past the sensor and back down past the sensor.
(a) It takes a time 2t1 for the ball to rise past and then come
back down past the lower sensor, and a time 2t2 for the ball
to rise past and then come back down past the upper sensor.
Find an expression for g using these times and the height H.
(b) Determine the value of g if H equals 25.0 m, t1 equals 3.00 s,
and t2 equals 2.00 s.
67. ••Sports Steve Young stands on the 20-yard line, poised to
throw long. He throws the ball at initial velocity v0 equal to
15.0 m>s and releases it at an angle u equal to 45.0°. (a) Having
faked an end around, Jerry Rice comes racing past Steve at a
constant velocity VJ equal to 8.00 m>s, heading straight down
the field. Assuming that Jerry catches the ball at the same height
above the ground that Steve throws it, how long must Steve
wait to throw, after Jerry goes past, so that the ball falls directly
into Jerry’s hands? (b) As in part (a), Jerry is coming straight
past Steve at VJ equal to 8.00 m>s. But just as Jerry goes past,
Steve starts to run in the same direction as Jerry with VS equal
to 1.50 m>s. How long must Steve wait to release the ball so
that it falls directly into Jerry’s hands? SSM
68. ••You drop a rock from rest from the top of a tall building.
(a) How far has the rock fallen in 2.50 s? (b) What is the velocity of the rock after it has fallen 11.0 m? (c) It takes 0.117 s for
the rock to pass by a 2.00-m high window. How far from the
top of the building is the top of the window?
69. ••You throw a ball from the balcony onto the court in the
basketball arena. You release the ball at a height of 7.00 m
above the court, with an initial velocity equal to 9.00 m>s at
33° above the horizontal. A friend of yours, standing on the
court 11.0 m from the point directly beneath you, waits for
a period of time after you release the ball and then begins to
move directly away from you at an acceleration of 1.80 m>s 2.
(She can only do this for a short period of time!) If you throw
the ball in a line with her, how long after you release the ball
should she wait to start running directly away from you so that
she’ll catch the ball exactly 1.00 m above the floor of the court?
70. ••Marcus and Cody want to hike to a destination 12.0 km
north of their starting point. Before heading directly to the
9/13/12 5:07 PM
Questions and Problems 115
­destination, Marcus walks 10.0 km in a direction that is 30.0°
north of east and Cody walks 15.0 km in a direction that is
45.0° north of west. How much farther must each hike on the
second part of the trip?
71. •Nathan walks due east a certain distance and then walks
due south twice that distance. He finds himself 15.0 km from
his starting position. How far east and how far south does
­Nathan walk?
72. •••A group of campers must decide the quickest way to
reach their next campsite. Figure 3-44 is a map of the area.
One option is to walk directly to the site along a straight path
10.6 mi in length. Another option is to take a canoe down a
river and then walk uphill 6.60 mi from the beach to the campsite. The campers estimate a hiking pace of 2.00 mi>h on the
straight path and 0.500 mi>h walking up the hill. How fast
would the canoe need to travel (assume a constant speed) in
order for the second route to take less time than the first?
Camp
6 mi
255 m
Figure 3-45 ​Problem 75
76. ••An airplane flying upward at 35.3 m>s and an angle of
30.0° relative to the horizontal releases a ball when it is 255
m above the ground. Calculate (a) the time it takes the ball to
hit the ground, (b) the maximum height of the ball, and (c) the
horizontal distance the ball travels from the release point to the
ground. (Neglect any effects due to air resistance.)
77. ••Sports In 1993, Javier Sotomayor set a world record of
2.45 m in the men’s outdoor high jump. He is 193 cm (6 ft
4 in) tall. By treating his body as a point located at half his
height, and given that he left the ground a horizontal distance
from the bar of 1.5 m at a takeoff angle of 65°, determine Javier Sotomayor’s takeoff speed. (Neglect any effects due to air
resistance.)
78. ••Sports A boy runs straight off the end of a diving platform at a speed of 5.00 m>s. The platform is 10.0 m above the
surface of the water. (a) Calculate the boy’s speed when he hits
the water. (b) How much time is required for the boy to reach
the water? (c) How far horizontally will the boy travel before
he hits the water? (Neglect any effects due to air resistance.)
70°
30°
10 mi
Starting point
Figure 3-44 Problem 72
73. ••A water balloon is thrown horizontally at a speed of
2.00 m>s from the roof of a building that is 6.00 m above the
ground. At the same instant the balloon is released, a second
balloon is thrown straight down at 2.00 m>s from the same
height. Determine which balloon hits the ground first and how
much sooner it hits the ground than the other balloon. Which
balloon is moving with the greatest speed at impact? (Neglect
any effects due to air resistance.) SSM
74. •You throw a rock from the upper edge of a 75.0-m vertical dam with a speed of 25.0 m>s at 65.0° above the horizon.
How long after throwing the rock will you (a) see it and (b)
hear it hit the water flowing out at the base of the dam? The
speed of sound in the air is 344 m>s. (Neglect any effects due
to air resistance.)
75. •An airplane releases a ball as it flies parallel to the ground
at a height of 255 m (Figure 3-45). If the ball lands on the
ground at a horizontal displacement of exactly 255 m from the
release point, calculate the airspeed of the plane. (Neglect any
effects due to air resistance.)
Freed_c03_067-116hr2.indd 115
255 m
79. •Sports Gabriele Reinsch threw a discus 76.80 m on
July 9, 1988, to set the women’s world record. Assume that
she launched the discus with an elevation angle of 45° and that
her hand was 2.0 m above the ground at the instant of launch.
What was the initial speed of the discus required to achieve that
range? (Neglect any effects due to air resistance.) SSM
80. •Astronomy The froghopper, a tiny insect, is a remarkable
jumper. Suppose you raised a colony of the little critters on the
Moon, where the acceleration due to gravity is only 1.62 m>s 2.
If on Earth a froghopper’s maximum jump height is h and
­maximum horizontal range is R, what would its maximum
height and range be on the Moon in terms of h and R? Assume
a froghopper’s takeoff speed is the same on the Moon and on
Earth.
81. ••Sports In 1998, Jason Elam kicked a record field goal.
The football started on the ground 63.0 yards from the base of
the goal posts and just barely cleared the 10-ft-high bar. If the
initial trajectory of the football was 40.0° above the horizontal,
(a) what was its initial speed and (b) how long after the ball
was struck did it pass through the goal posts? (Neglect any
­effects due to air resistance.)
82. •••Sports In the hope that the Moon and Mars will one day
become tourist attractions, a golf course is built on each. An average golfer on Earth can drive a ball from the tee about 63%
of the distance to the hole. If this is to be true on the Moon
and on Mars, by what factor should the dimensions of the golf
courses on the Moon and Mars be changed relative to a course
on Earth? (Neglect any effects due to air resistance.)
9/13/12 5:07 PM
116 Chapter 3 Motion in Two or Three Dimensions
the diameter of the circle, by what percent must you change the
time for the pilot to make one spin?
83. ••Biology Anne is working on a research project that
­involves the use of a centrifuge. Her samples must first experience an acceleration of 100g, but then the acceleration must
increase by a factor of 8. By how much will the rotation speed
have to increase? Express your answer as a fraction of the initial rotation rate. SSM
85. •Medical Modern pilots can survive radial accelerations up
to 9g (88 m>s 2). Can a fighter pilot flying at a constant speed of
500 m>s and in a circle that has a diameter of 8800 m survive
to tell about his experience?
84. •Medical In a laboratory test of tolerance for high ­angular
acceleration, pilots were swung in a circle 13.4 m in ­diameter.
It was found that they blacked out when they were spun at
30.6 rpm (rev>min). (a) At what acceleration (in SI units and
in multiples of g) did the pilots black out? (b) If you want
to decrease the acceleration by 25.0% without changing
86. •Sports A girl’s fast-pitch softball player does a windmill
pitch, moving her hand through a circular arc with her arm
straight. She releases the ball at a speed of 24.6 m>s. Just
­before the ball leaves her hand, the ball’s radial acceleration is
1960 m>s 2. What is the length of her arm from the pivot point
at her shoulder?
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