Physics

James S. Walker

Chapter 4

Two-Dimensional Kinematics - all with Video Answers

Educators

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Chapter Questions

Problem 1

$\cdot$ CE Predict/Explain As you walk briskly down the street, you toss
a small ball into the air. (a) If you want the ball to land in your hand
when it comes back down, should you toss the ball straight upward,
in a forward direction, or in a backward direction, relative to your
body? (b) Choose the best explanation from among the following:
$$
\begin{array}{l}{\text { If the ball is thrown straight up you will leave it behind. }} \\ {\text { II. You have to throw the ball in the direction you are walking. }} \\ {\text { III. The ball moves in the forward direction with your walking }} \\ {\text { speed at all times. }}\end{array}
$$

William Dunkerton

William Dunkerton

Numerade Educator

Problem 2

A sailboat runs before the wind with a constant speed of 4.2 $\mathrm{m} / \mathrm{s}$
in a direction $32^{\circ}$ north of west. How far (a) west and (b) north has
the sailboat traveled in 25 $\mathrm{min}$ ?

William Dunkerton

William Dunkerton

Numerade Educator

Problem 3

As you walk to class with a constant speed of $1.75 \mathrm{m} / \mathrm{s},$ you
are moving in a direction that is $18.0^{\circ}$ north of east. How much
time does it take to change your position by (a) 20.0 $\mathrm{m}$ east or
(b) 30.0 $\mathrm{m}$ north?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 4

Starting from rest, a car accelerates at 2.0 $\mathrm{m} / \mathrm{s}^{2}$ up a hill that is
inclined $5.5^{\circ}$ above the horizontal. How far (a) horizontally and
(b) vertically has the car traveled in 12 $\mathrm{s} ?$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 5

Predict/Calculate A particle passes through the origin with a
velocity of $(6.2 \mathrm{m} / \mathrm{s}) \hat{\mathbf{y}}$ . If the particle'sacceleration is $\left(-4.4 \mathrm{m} / \mathrm{s}^{2}\right) \hat{\mathbf{x}},$
(a) what are its $x$ and $y$ positions after 5.0 $\mathrm{s} ?$ (b) What are $v_{x}$ and $v_{y}$ at this time? (c) Does the speed of this particle increase with time,
decrease with time, or increase and then decrease? Explain.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 6

A skateboarder travels on a horizontal surface with an initial
velocity of 3.8 $\mathrm{m} / \mathrm{s}$ toward the south and a constant acceleration
of 2.2 $\mathrm{m} / \mathrm{s}^{2}$ toward the east. Let the $x$ direction be eastward and the $y$ direction be northward, and let the skateboarder be at the origin
at $t=0 .($ a) What are her $x$ and $y$ positions at $t=0.80$ s? (b) What
are her $x$ and $y$ velocity components at $t=0.80$ s?

Keshav Singh

Numerade Educator

Problem 7

A hot-air balloon is drifting in level flight due east at 2.5 $\mathrm{m} / \mathrm{s}$
due to a light wind. The pilot suddenly notices that the balloon
must gain 24 $\mathrm{m}$ of altitude in order to clear the top of a hill 120 $\mathrm{m}$ to the east. (a) How much time does the pilot have to make the altitude change without crashing into the hill? (b) What minimum,constant, upward acceleration is needed in order to clear the hill?
(c) What are the horizontal and vertical components of the balloon's velocity at the instant that it clears the top of the hill?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 8

An electron in a cathode-ray tube is traveling horizontally at
$2.10 \times 10^{9} \mathrm{cm} / \mathrm{s}$ when deflection plates give it an upward acceleration of $5.30 \times 10^{17} \mathrm{cm} / \mathrm{s}^{2}$ . (a) How much time does it take for
the electron to cover a horizontal distance of 6.20 $\mathrm{cm} ?$ (b) What is
its vertical displacement during this time?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 9

Two canoeists start paddling at the same time and head toward
a small island in a lake, as shown in FIGURE 4-18. Canoeist 1 paddles with a speed of 1.10 $\mathrm{m} / \mathrm{s}$ at an angle of $45^{\circ}$ north of east. Canoeist 2 starts on the opposite shore of the lake, a distance of 1.5 $\mathrm{km}$
due east of canoeist 1 (a) In what direction relative to north must canoeist 2 paddle to reach the island? (b) What speed must canoeist
2 have if the two canoes are to arrive at the island at the same time?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 10

CE Predict/Explain Two divers run horizontally off the edge of a
low cliff. Diver 2 runs with twice the speed of diver $1 .$ (a) When the
divers hit the water, is the horizontal distance covered by diver 2 twice as much as, four times as much as, or equal to the horizontal
distance covered by diver 1? (b) Choose the best explanation from
among the following:
$$
\begin{array}{l}{\text { 1. The drop time is the same for both divers. }} \\ {\text { II. Drop distance depends on } t^{2} \text { . }} \\ {\text { III. All divers in free fall cover the same distance. }}\end{array}
$$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 11

CE Predict/Explain Two youngsters dive off an overhang into
a lake. Diver 1 drops straight down, and diver 2 runs off the cliff
with an initial horizontal speed $v_{0} .$ (a) Is the splashdown speed of diver 2 greater than, less than, or equal to the splashdown speed of
diver 1$?($ b) Choose the bestexplanation from among the following:
$$
\begin{array}{l}{\text { I. Both divers are in free fall, and hence they will have the same }} \\ {\text { splashdown speed. }} \\ {\text { II. The divers have the same vertical speed at splashdown, but }} \\ {\text { diver } 2 \text { has the greater horizontal speed. }} \\ {\text { II. The diver who drops straight down gains more speed than the }} \\ {\text { one who moves horizontally. }}\end{array}
$$

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 12

An archer shoots an arrow horizontally at a target 15 $\mathrm{m}$ away. The
arrow is aimed directly at the center of the target, but it hits 52 $\mathrm{cm}$
lower. What was the initial speed of the arrow?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 13

Victoria Falls The great, gray-green, greasy Zambezi River flows
over Victoria Falls in south central Africa. The falls are approximately 108 $\mathrm{m}$ high. If the river is flowing horizontally at 3.60 $\mathrm{m} / \mathrm{s}$
just before going over the falls, what is the speed of the water when
it hits the bottom? Assume the water is in free fall as it drops.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 14

A diver runs horizontally off the end of a diving board with an
initial speed of 1.85 $\mathrm{m} / \mathrm{s}$ ' If the diving board is 3.00 $\mathrm{m}$ above the
water, what is the diver's speed just before she enters the water?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 15

An astronaut on the planet Zircon tosses a rock horizontally with
a speed of 6.95 $\mathrm{m} / \mathrm{s}$ . The rock falls through a vertical distance of
1.40 $\mathrm{m}$ and lands a horizontal distance of 8.75 $\mathrm{m}$ from the astronaut. What is the acceleration due to gravity on Zircon?

Hubert Agamasu

Numerade Educator

Problem 16

Predict/Calculate Pitcher's Mounds Pitcher's mounds are raised
to compensate for the vertical drop of the ball as it travels a horizontal distance of 18 $\mathrm{m}$ to the catcher. (a) If a pitch is thrown horizontally with an initial speed of 32 $\mathrm{m} / \mathrm{s}$ , how far does it drop by the time it reaches the catcher? (b) If the speed of the pitch is increased,
does the distance increase, decrease, or stay the same? Explain.
(c) If this baseball game were to be played on the Moon, would the
drop distance increase, decrease, or stay the same? Explain.

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 17

Playing shortstop, you pick upa ground ball and throw it to second base. The ball is thrown horizontally, with a speed of 18 $\mathrm{m} / \mathrm{s}$ , directly toward point A (FIGURE 4-19). When the ball reaches the second baseman 0.54 s later, it is caught at point B. (a) How far
were you from the second baseman? (b) What is the distance of
vertical drop, $A B ?$

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 18

Predict/Calculate A crow is flying horizontally with a constant speed of 2.70 $\mathrm{m} / \mathrm{s}$ when it releases a clam from its beak. The clam lands on the rocky beach 2.10 s later. Just before the clam lands, what are (a) its horizontal component
of velocity, and (b) its vertical component of velocity? (c) How
would your answers to parts (a) and (b) change if the speed of the
crow were increased? Explain.

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 19

A mountain climber jumps a 2.8-m-wide crevasse by leaping horizontally with a speed of 7.8 $\mathrm{m} / \mathrm{s} .$ I(a) If the climber's direction
of motion on landing is $-45^{\circ},$ what is the height difference between
the two sides of the crevasse? (b) Where does the climber land?

Vipender Yadav

Numerade Educator

Problem 20

Predict/Calculate A white-crowned sparrow flying horizontally
with a speed of 1.80 $\mathrm{m} / \mathrm{s}$ folds its wings and begins to drop in free
fall. (a) How far does the sparrow fall after traveling a horizontal distance of 0.500 $\mathrm{m} ?$ (b) If the sparrow's initial speed is increased,
does the distance of fall increase, decrease, or stay the same?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 21

Pumpkin Toss In Denver, children bring their old jack-o-lanterns
to the top of a tower and compete for accuracy in hitting a target on the ground (FIGURE 4-21). Suppose that the tower is 9.0 m high and that the bull's-eye is a horizontal distance of 3.5 $\mathrm{m}$ from the
launch point. If the pumpkin is thrown horizontally, what is the
launch speed needed to hit the bull's-eye?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 22

Fairgoers ride a Ferris wheel with a radius of 5.00 m (FIGURE 4-22). The wheel completes one revolution every 32.0 s. (a) What is the
average speed of a rider on this Ferris wheel? (b) If a rider accidentally drops a stuffed animal at the top of the wheel, where does
it land relative to the base of the ride? (Note: The bottom of the
wheel is 1.75 m above the ground.)

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 23

Predict/Calculate A swimmer runs horizontally off a diving board
with a speed of 3.32 $\mathrm{m} / \mathrm{s}$ and hits the water a horizontal distance of
1.78 $\mathrm{m}$ from the end of the board. (a) How high above the water was the diving board? (b) If theswimmerruns off the board with a reduced
speed, doesit take more, less, or the same time to reach the water?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 24

Baseball and the Washington Monument On August $25,1894,$ Chicago catcher William Schriver caught a baseball thrown from the top of the Washington Monument $(555 \mathrm{ft}, 898$ steps). (a) If the ball was
thrown horizontally with a speed of 5.00 $\mathrm{m} / \mathrm{s}$ , where did it land? (b)
What were the ball's speed and direction of motion when caught?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 25

A basketball is thrown horizontally with an initial speed of 4.20 $\mathrm{m} / \mathrm{s}$ (FIGURE 4-23). A straight line drawn from the release point to the landing point makes an angle of $30.0^{\circ}$ with the horizontal. What was the release height?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 26

Predict/Calculate A ball rolls off a table and falls 0.75 $\mathrm{m}$ to the floor, landing with a speed of 4.0 $\mathrm{m} / \mathrm{s}$ . (a) What is the acceleration
of the ball just before it strikes the ground? (b) What was the initial speed of the ball? (c) What initial speed must the ball have if it is to
land with a speed of 5.0 $\mathrm{m} / \mathrm{s} ?$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 27

CE A certain projectile is launched with an initial speed $v_{0} .$ At its
highest point its speed is $\frac{1}{2} v_{0}$ . What was the launch angle of the
projectile?
$$
\begin{array}{lllllll}{\text { A. } 30^{\circ}} & {\text { B. } 45^{\circ}} & {\text { C. } 60^{\circ}} & {\text { D. } 75^{\circ}}\end{array}
$$

Sheh Lit Chang

University of Washington

Problem 28

CE Three projectiles $(\mathrm{A}, \mathrm{B},$ and $\mathrm{C})$ are launched with the same initial speed but with different launch angles, as shown in FIGURE 4-24. Rank the projectiles in order of increasing (a) horizontal com ponent of initial velocity and (b) time of flight. Indicate ties where
appropriate.

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 29

CE Three projectiles $(\mathrm{A}, \mathrm{B},$ and C) are launched with different initial
speeds so that they reach the same maximum height, as shown in FIGURE 4-25. Rank the projectiles in order of increasing (a) initial speed
and (b) time of flight. Indicate ties where appropriate.

William Dunkerton

William Dunkerton

Numerade Educator

Problem 30

A cannonball is launched at an angle above level ground, giving
it an initial vertical and horizontal velocity that are each positive.
The cannonball lands at a time $T$ after it is launched. (a) Which plot $(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},$ or $\mathrm{E})$ in FIGURE 4-26 best represents the horizontal component of the cannonball's velocity? (b) Which plot best represents the vertical component of the cannonball's velocity?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 31

A second baseman tosses the ball to the first baseman, who catches
it at the same level from which it was thrown. The throw is made with
an initial speed of 18.0 $\mathrm{m} / \mathrm{s}$ at an angle of $37.5^{\circ}$ above the horizontal. (a) What is the horizontal component of the ball's velocity just
before it is caught? (b) For what amount of time is the ball in the air?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 32

A soccer ball is kicked with a speed of 15.6 $\mathrm{m} / \mathrm{s}$ at an angle of
$32.5^{\circ}$ above the horizontal. If the ball lands at the same level from
which it was kicked, for what amount of time was it in the air?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 33

In a game of basketball, a forward makes a bounce pass to the center. The ball is thrown with an initial speed of 4.3 $\mathrm{m} / \mathrm{s}$ at an angle of $15^{\circ}$ below the horizontal. It is released 0.80 $\mathrm{m}$ above the floor. What
horizontal distance does the ball cover before bouncing?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 34

Predict/Calculate Snowballs are thrown with a speed of 13 $\mathrm{m} / \mathrm{s}$
from a roof 7.0 $\mathrm{m}$ above the ground. Snowball $\mathrm{A}$ is thrown straight
downward; snowball $\mathrm{B}$ is thrown in a direction $25^{\circ}$ above the horizontal. (a) Is the landing speed of snowball A greater than, less
than, or the same as the landing speed of snowball B? Explain.
(b) Verify your answer to part (a) by calculating the landing speed
of both snowballs.

Ankur S

Numerade Educator

Problem 35

In Problem $34,$ find the direction of motion of the two snowballs just before they land.

William Dunkerton

William Dunkerton

Numerade Educator

Problem 36

A golfer gives a ball a maximum initial speed of 51.4 $\mathrm{m} / \mathrm{s}$ .
(a) What is the longest possible hole-in-one for this golfer? Neglect
any distance the ball might roll on the green and assume that the tee and the green are at the same level. (b) What is the minimum
speed of the ball during this hole-in-one shot?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 37

What is the highest tree the ball in the previous problem could
clear on its way to the longest possible hole-in-one?

William Dunkerton

William Dunkerton

Numerade Educator

Problem 38

The "hang time" of a punt is measured to be 4.50 s. If the ball was
kicked at an angle of $63.0^{\circ}$ above the horizontal and was caught at
the same level from which it was kicked, what was its initial speed?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 39

In a friendly game of handball, you hit the ball essentially at
ground level and send it toward the wall with a speed of 16 $\mathrm{m} / \mathrm{s}$ at
an angle of $37^{\circ}$ above the horizontal. (a) What amount of time is
required for the ball to reach the wall if it is 3.3 $\mathrm{m}$ away? (b) How
high is the ball when it hits the wall?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 40

On a hot summer day, a young girl swings on a rope above the
local swimming hole (FIGURE 4-27). When she lets go of the rope

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 41

A certain projectile is launched with an initial speed $v_{0}$ . At its
highest point its speed is $v_{0} / 4 .$ What was the launch angle?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 42

Punkin Chunkin In Dover, Delaware, a post-Halloween tradition
is "Punkin Chunkin," in which contestants build cannons, catapults, trebuchets, and other devices to launch pumpkins and compete for the greatest distance. Though hard to believe, pumpkins
have been projected a distance of 4694 feet in this contest. What is
the minimum initial speed needed for such a shot?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 43

A dolphin jumps with an initial velocity of 12.0 $\mathrm{m} / \mathrm{s}$ at an angle
of $40.0^{\circ}$ above the horizontal. The dolphin passes through the
center of a hoop before returning to the water. If the dolphin is moving horizontally when it goes through the hoop, how high
above the water is the center of the hoop?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 44

A player passes a basketball to another player who catches it at
the same level from which it was thrown. The initial speed of the
ball is 7.1 $\mathrm{m} / \mathrm{s}$ , and it travels a distance of 4.6 $\mathrm{m} .$ What were (a) the
initial direction of the ball and (b) its time of flight?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 45

A golf ball is struck with a five iron on level ground. It lands 92.2 $\mathrm{m}$
away 4.30 s later. What were (a) the direction and (b) the magnitude of the inittial velocity?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 46

CE Predict/Explain You throw a ball into the air with an initial speed of 10 $\mathrm{m} / \mathrm{s}$ at an angle of $60^{\circ}$ above the horizontal. The ball returns to the level from which it was thrown in the time T. (a) Referring to FIGURE 4-28 which of the plots $(\mathrm{A}, \mathrm{B},$ or $\mathrm{C})$ best represents the speed of the ball as a function of time? (b) Choose the
best explanation from among the following:
$$
\begin{array}{l}{\text { I. Gravity causes the ball's speed to increase during its flight. }} \\ {\text { II. The ball has zero speed at its highest point. }} \\ {\text { III. The ball's speed decreases during its flight, but it doesn't go }} \\ {\text { to zero. }}\end{array}
$$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 47

A football quarterback shows off his skill by throwing a pass
45.70 m downfield and into a bucket. The quarterback consistently launches the ball at $38.00^{\circ}$ above horizontal, and the bucket is placed at the same level from which the ball is thrown. (a) What
initial speed is needed so that the ball lands in the bucket? (b) By
how much would the launch speed have to be increased if the
bucket is moved to 46.50 m downfield?

Nishant Kumar

Numerade Educator

Problem 48

A clever inventor has created a device that can launch water balloons with an initial speed of 85.0 $\mathrm{m} / \mathrm{s} .$ Her goal is to pass a balloon through a small hoop mounted on the observation platform at the top of the Eiffel Tower, 276 $\mathrm{m}$ above the ground. If the balloon is to pass through the hoop at the peak of its flight, at what
angle above horizontal should she launch the balloon?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 49

Predict/Calculate Volcanoes on lo Astronomers have discovered
several volcanoes on Io, a moon of Jupiter. One of them, named
Loki, ejects lava to a maximum height of $2.00 \times 10^{5} \mathrm{m}$ . (a) What is the initial speed of the lava? (The acceleration of gravity on lo is
1.80 $\mathrm{m} / \mathrm{s}^{2} . )$ (b) If this volcano were on Earth, would the maximum height of the ejected lava be greater than, less than, or the same as
on lo? Explain.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 50

Predict/Calculate A soccer ball is kicked with an initial speed
of 10.2 $\mathrm{m} / \mathrm{s}$ in a direction $25.0^{\circ}$ above the horizontal. Find the magnitude and direction of its velocity (a) 0.250 s and (b) 0.500 s
after being kicked. (c) Is the ball at its greatest height before or
after 0.500 s? Explain.

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 51

A soccer ball is kicked with an initial speed of 8.25 $\mathrm{m} / \mathrm{s}$ . After
0.750 $\mathrm{s}$ it is at its highest point. What was its initial direction of
motion?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 52

An archer shoots an arrow over a castle wall by launching it
with an initial speed of 28 $\mathrm{m} / \mathrm{s}$ at $65^{\circ}$ above horizontal. Assume
the arrow lands on the other side of the castle wall at the same elevation as the launch point. (a) What maximum height does the
arrow attain? (b) What is the range of the arrow's flight? (c) What is
the vertical component of the arrow's velocity just before it lands
on the other side of the castle wall?

Supratim Pal

Numerade Educator

Problem 53

CE Child 1 throws a snowball horizontally from the top of a roof;
child 2 throws a snowball straight down. Once in flight, is the
acceleration of snowball 2 greater than, less than, or equal to the
acceleration of snowball 1$?$

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 54

ce The penguin to the left in the accompanying photo is about to land on an ice floe. Just before it lands, is its speed greater than, less than, or equal to its speed when it left the water?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 55

CE Dolphins may leap from the water just for the fun of it. At the
instant a leaping dolphin lands, is its speed greater than, less than,
or equal to its speed when it left the water?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 56

CE Predict/Explain A person flips a coin into the air and it lands
on the ground a few feet away. (a) If the person were to perform
an identical coin flip on an elevator rising with constant speed, would the coin's time of flight be greater than, less than, or equal
to its time of flight when the person was at rest? (b) Choose the
best time of flight when the person was at rest? (b) Choose the
best explanation from among the following:
$$
\begin{array}{l}{\text { I. The floor of the elevator is moving upward, and hence it }} \\ {\text { catches up with the coin in mid flight. }} \\ {\text { II. The coin has the same upward speed as the elevator when it }}\end{array}
$$ $$
\begin{array}{l}{\text { is tossed, and the elevator's speed doesn't change during the }} \\ {\text { coin's flight. }} \\ {\text { III. The coin starts off with a greater upward speed because of the }} \\ {\text { elevator, and hence it reaches a greater height. }}\end{array}
$$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 57

CE Predict/Explain Suppose the elevator in the previous problem
is rising with a constant upward acceleration, rather than constant
velocity. (a) In this case, would the coin's time of flight be greater
than, less than, or equal to its time of flight when the person was
at rest? (b) Choose the best explanation from among the following:
$$
\begin{array}{l}{\text { 1. The coin has the same acceleration once it is tossed, whether }} \\ {\text { the elevator accelerates or not. }} \\ {\text { II. The elevator's upward speed increases during the coin's flight, }} \\ {\text { and hence it catches up with the coin at a greater height than }} \\ {\text { before. }}\end{array}
$$
$$
\begin{array}{l}{\text { III. The coin's downward acceleration is less than before because }} \\ {\text { the elevator's upward acceleration partially cancels it. }}\end{array}
$$

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 58

A train moving with constant velocity travels 170 $\mathrm{m}$ north in 12 $\mathrm{s}$
and an undetermined distance to the west. The speed of the train
is 32 $\mathrm{m} / \mathrm{s} .$ (a) Find the direction of the train's motion relative to
north. (b) How far west has the train traveled in this time?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 59

A tennis ball is struck in such a way that it leaves the racket with
a speed of 4.87 $\mathrm{m} / \mathrm{s}$ in the horizontal direction. When the ball hits
the court, it is a horizontal distance of 1.95 $\mathrm{m}$ from the racket. Find
the height of the tennis ball when it left the racket.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 60

A person tosses a ball for her puppy to retrieve. The ball leaves her
hand horizontally with a speed of 4.6 $\mathrm{m} / \mathrm{s} .$ If the initial height of
the ball is 0.95 $\mathrm{m}$ above the ground, how far does it travel in the
horizontal direction before landing?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 61

An osprey flies horizontally with a constant speed of 6.8 $\mathrm{m} / \mathrm{s}$
when it drops the fish it was carrying. How much time elapses
after the fish is dropped before the speed of the fish doubles?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 62

Predict/Calculate A hot-air balloon rises from the ground with
a velocity of $(2.00 \mathrm{m} / \mathrm{s}) \hat{\mathbf{y}}$ . A champagne bottle is opened to cel-
ebrate takeoff, expelling the cork horizontally with a velocity of
$(5.00 \mathrm{m} / \mathrm{s}) \hat{\mathbf{x}}$ relative to the balloon. When opened, the bottle is
6.00 $\mathrm{m}$ above the ground. (a) What is the initial velocity of the cork, as seen by an observer on the ground? Give your answer in terms of
the $x$ and $y$ unit vectors. (b) What are the speed of the cork and its
initial direction of motion as seen by the same observer? (c) Determine the maximum height above the ground attained by the cork.
(d) For what amount of time does the cork remain in the air?

Supratim Pal

Numerade Educator

Problem 63

In a friendly neighborhood squirt gun contest a participant
runs at 7.8 $\mathrm{m} / \mathrm{s}$ horizontally off the back deck and fires her squirt
gun in the plane of her motion but $45^{\circ}$ above horizontal. The gun
can shoot water at 11 $\mathrm{m} / \mathrm{s}$ relative to the barrel, and she fires the
gun 0.42 s after leaving the deck. (a) What is the initial velocity of the water particles as seen by an observer on the ground? Give
your answer in terms of the horizontal and vertical components.
(b) At the instant she fires, the gun is 1.9 m above the level ground.
How far will the water travel horizontally before landing?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 64

Spitting Llamas An agitated llama may spit to assert dominance, or to ward off threats. Llamas can spit a considerable distance, and people handling them need to keep this in mind.
If the spittle from a llama is launched from an initial height of 1.8 $\mathrm{m}$
with a speed of 6.1 $\mathrm{m} / \mathrm{s},$ and at an angle of $12^{\circ}$ above horizontal,
how far will it travel horizontally?

Nishant Kumar

Numerade Educator

Problem 65

A particle leaves the origin with an initial velocity
$\overrightarrow{\mathbf{v}}=(2.40 \mathrm{m} / \mathrm{s}) \hat{\mathbf{x}},$ and moves with constant acceleration
$\overrightarrow{\mathbf{a}}=\left(-1.90 \mathrm{m} / \mathrm{s}^{2}\right) \hat{\mathbf{x}}+\left(3.20 \mathrm{m} / \mathrm{s}^{2}\right) \hat{\mathbf{y}}$ . (a) How far does the particle move in the $x$ direction before turning around? (b) What is the
particle's velocity at this time? (c) Plot the particle's position at
$t=0.500 \mathrm{s}, 1.00 \mathrm{s}, 1.50 \mathrm{s},$ and 2.00 $\mathrm{s} .$ Use these results to sketch
position versus time for the particle.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 66

Bio When the dried-up seed pod of a scotch broom plant
bursts open, it shoots out a seed with an initial velocity of 2.62
$\mathrm{m} / \mathrm{s}$ at an angle of $60.5^{\circ}$ above the horizontal. If the seed pod is 0.455 $\mathrm{m}$ above the ground, (a) what amount of time does it take
for the seed to land? (b) What horizontal distance does it cover
during its flight?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 67

Trick Shot In an Internet video an athlete launches a basketball
from a stadium platform that is 16.2 $\mathrm{m}$ higher than the hoop. He
makes the basket by launching the ball at an angle of $14.5^{\circ}$ above horizontal with a speed of 11.6 $\mathrm{m} / \mathrm{s} .$ What horizontal distance
does the ball travel before passing through the hoop?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 68

A shot-putter throws the shot with an initial speed of 12.2 $\mathrm{m} / \mathrm{s}$
from a height of 5.15 $\mathrm{ft}$ above the ground. What is the range of the shot if the launch angle is (a) $20.0^{\circ},$ (b) $30.0^{\circ},$ or $(\mathrm{c}) 40.0^{\circ} ?$

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 69

Two marbles are launched at $t=0$ in the experiment illustrated in FIGURE 4-29. Marble 1 is launched horizontally with a speed of $4.20 \mathrm{~m} / \mathrm{s}$ from a height $h=0.950 \mathrm{~m} .$ Marble 2 is launched from ground level with a speed of $5.94 \mathrm{~m} / \mathrm{s}$ at an angle $\theta=45.0^{\circ}$ above the horizontal. (a) Where would the marbles collide in the absence of gravity? Give the $x$ and $y$ coordinates of the collision point. (b) Where do the marbles collide given that gravity produces a downward acceleration of $g=9.81 \mathrm{~m} / \mathrm{s}^{2} ?$ Give the $x$ and $y$ coordinates.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 70

Rescue Swimmers Coast Guard rescue swimmers are trained to
leap from helicopters into the sea to save boaters in distress. The
rescuers like to step off their helicopter when it is "ten and ten," which means that it is ten feet above the water and moving forward horizontally at ten knots. What are (a) the speed and (b) the
direction of motion as a rescue swimmer enters the water follow-
ing a ten and ten jump?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 71

A football player kicks a field goal, launching the ball at an angle of
$48^{\circ}$ above the horizontal. During the kick, the ball is in contact with the player's foot for 0.045 s, and the ball's acceleration is 290 $\mathrm{m} / \mathrm{s}^{2}$ .
What is the range of the football?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 72

A ball thrown straight upward returns to its original level
in 2.75 s. A second ball is thrown at an angle of $40.0^{\circ}$ above the horizontal. What is the initial speed of the second ball if it also
returns to its original level in 2.75 s?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 73

Predict/Calculate To decide who pays for lunch, a passenger
on a moving train tosses a coin straight upward with an initial
speed of 5.25 $\mathrm{m} / \mathrm{s}$ and catches it again when it returns to its initial level. From the point of view of the passenger, then, the coin's
initial velocity is $(5.25 \mathrm{m} / \mathrm{s}) \hat{\mathbf{y}}$ . The train's velocity relative to the ground is $(12.1 \mathrm{m} / \mathrm{s}) \hat{\mathbf{x}} .$ (a) What is the minimum speed of the coin
relative to the ground during its flight? At what point in the coin's
flight does this minimum speed occur? Explain. (b) Find the initial speed and direction of the coin as seen by an observer on the
ground. (c) Use the expression for $y_{\text { max }}$ derived in Example $4-14$ to
calculate the maximum height of the coin, as seen by an observer on the ground. (d) What is the maximum height of the coin from
the point of view of the passenger, who sees only one-dimensional
motion?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 74

Predict/Calculate A cannon is placed at the bottom of a cliff
61.5 $\mathrm{m}$ high. If the cannon is fired straight upward, the cannonball
just reaches the top of the cliff. (a) What is the initial speed of the cannonball? (b) Suppose a second cannon is placed at the top of
the cliff. This cannon is fired horizontally, giving its cannonballs
the same initial speed found in part (a). Show that the range of this cannon is the same as the maximum range of the cannon at the
base of the cliff. (Assume the ground at the base of the cliff is level,
though the result is valid even if the ground is not level.)

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 75

A golfer hits a shot to an elevated green. The ball leaves the club
with an initial speed of 16 $\mathrm{m} / \mathrm{s}$ at an angle of $58^{\circ}$ above the hori-
zontal. If the speed of the ball just before it lands is $12 \mathrm{m} / \mathrm{s},$ what is
the elevation of the green above the point where the ball is struck?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 76

Shot Put Record A men's world record for the shot put, 23.12 $\mathrm{m}$ ,
was set by Randy Barnes of the United States on May $20,1990 .$ If
the shot was launched from 6.00 $\mathrm{ft}$ above the ground at an initial
angle of $42.0^{\circ},$ what was its initial speed?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 77

Referring to Conceptual Example $4-13,$ suppose the two cats
jump from an elevation of 2.5 $\mathrm{m}$ with an initial speed of 3.0 $\mathrm{m} / \mathrm{s}$ .
What is the speed of each cat when it is 1.0 $\mathrm{m}$ above the ground?

William Dunkerton

William Dunkerton

Numerade Educator

Problem 78

$\mathbf{A}^{\prime \prime} \mathrm{Lob}^{\prime \prime}$ Pass Versus a "Bullet" A quarterback can throw a receiver a high, lazy "lob" pass or a low, quick "bass. These passes are indicated by curves 1 and 2, respectively, in FIGURE 4-30. (a) The lob pass is thrown with an initial speed of 21.5 $\mathrm{m} / \mathrm{s}$ and its time
of flight is 3.97 $\mathrm{s}$ . What is its launch angle? (b) The bullet pass is
thrown with a launch angle of $25.0^{\circ} .$ What is the initial speed of
this pass? (c) What is the time of flight of the bullet pass?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 79

For summertime fun, you decide to combine diving from a
board with shooting a basketball through a hoop. (a) During
several practice runs you stand at the end of a diving board and
launch the basketball horizontally from a position 4.50 $\mathrm{m}$ above the water. If the average landing spot is 6.25 morizontally from
your initial position, what is the average launch speed? (b) Now
you step off the diving board and launch the ball in order to make
a basket in a hoop that is 3.75 m horizontally from the ball and 1.00 m above the water as shown in FIGURE 4-31. At what time after stepping off the board should you launch the ball? Hint: Consider
the time required for the ball to travel the required horizontal dis-
tance. (c) What are the horizontal and vertical components of the
ball's velocity at the instant of launch?

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 80

Landing on Mars when the twin exploration rovers, Spirit and
Opportunity, landed on Mars, their method of landing was unique
and elaborate. After initial braking with rockets and parachutes to a
virtual standstill several meters above the ground, the rovers inflated
four air bags with six lobes each. The rovers were then detached
from the parachutes and allowed to drop in free fall $\left(3.72 \mathrm{m} / \mathrm{s}^{2}\right)$
to the surface, where they bounced about 12 times before coming
to rest. They then deflated their air bags, righted themselves, and
began to explore the surface. FIGURE 4-32 shows a rover with its surrounding cushion of air bags making its first contact with the Martian surface. Assume that the first bounce of the rover is with an initial speed of 9.92 $\mathrm{m} / \mathrm{s}$ at an angle of $75.0^{\circ}$ above the horizontal. (a)
What is the maximum height of a rover between its first and second
bounces? (b) How much time elapses between the first and second
bounces? (c) How much time elapser travel in the horizontal direction
between its first and second bounces?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 81

Collision Course A useful rule of thumb in piloting is that if the
heading from your airplane to a second airplane remains constant, the two airplanes are on a collision course. Consider the two
airplanes shown in FIGURE $4-33 .$ At time $t=0,$ airplane 1 is at the
location $(X, 0)$ and moving in the positive $y$ direction; airplane 2
is at $(0, Y)$ and moving in the positive $x$ direction. The speed of airplane 1 is $v_{1}$ . (a) What speed must airplane 2 have if the airplanes
are to collide at the point $(X, Y) ?$ (b) Assuming airplane 2 has the
speed found in part (a), calculate the displacement from airplane
1 to airplane $2, \Delta \overrightarrow{\mathbf{r}}=\overrightarrow{\mathbf{r}}_{2}-\overrightarrow{\mathbf{r}}_{1} .$ (c) Use your results from part (b) to
show that $(\Delta r)_{y} /(\Delta r)_{x}=-Y / X,$ independent of time. This shows
that $\Delta \overrightarrow{\mathbf{r}}=\overrightarrow{\mathbf{r}}_{2}-\overrightarrow{\mathbf{r}}_{1}$ maintains a constant direction until the collision, as specified in the rule of thumb.

Surendra Kumar

Numerade Educator

Problem 82

As discussed in Example $4-14,$ the archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream
of water expelled from the fish's mouth. Suppose the archerfish
squirts water with a speed of 2.15 $\mathrm{m} / \mathrm{s}$ at an angle of $52.0^{\circ}$ above
the horizontal, and aims for a beetle on a leaf 3.00 $\mathrm{cm}$ above the
water's surface. (a) At what horizontal distance from the beetle
should the archerfish fire if it is to hit its target in the least time?
(b) How much time will the beetle have to react?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 83

Find the launch angle for which the range and maximum
height of a projectile are the same.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 84

A mountain climber jumps a crevasse of width $W$ by leaping
horizontally with speed $v_{0}$ . (a) If the height difference between
the two sides of the crevasse is $h,$ what is the minimum value of
$v_{0}$ for the climber to land safely on the other side? (b) In this case,
what is the climber's direction of motion on landing?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 85

Landing on a Different Level $A$ projectile fired from $y=0$ with
initial speed $v_{0}$ and initial angle $\theta$ lands on a different level, $y=h .$
Show that the time of flight of the projectile is
$$T=\frac{1}{2} T_{0}\left(1+\sqrt{1-\frac{h}{H}}\right)$$
In this expression, $T_{0}$ is the time of flight for $h=0,$ and $H$ is the
maximum height of the projectile.

Sheh Lit Chang

University of Washington

Problem 86

A mountain climber jumps a crevasse by leaping horizontally
with speed $v_{0} .$ If the climber's direction of motion on landing is $\theta$
below the horizontal, what is the height difference $h$ between the
two sides of the crevasse?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 87

Projectiles: Coming or Going? Most projectiles continually move
farther from the origin during their flight, but this is not the case
if the launch angle is greater than $\cos ^{-1}\left(\frac{1}{3}\right)=70.5^{\circ}$ . For example,
the projectile shown in FIGURE $4-34$ has a launch angle of $75.0^{\circ}$
and an initial speed of 10.1 $\mathrm{m} / \mathrm{s} .$ During the portion of its motion
shown in red, it is moving closer to the origin -it is moving away
on the blue portions. Calculate the distance from the origin to the
projectile (a) at the start of the red portion, (b) at the end of the
red portion, and (c) just before the projectile lands. Notice that the
distance for part (b) is the smallest of the three.

William Dunkerton

William Dunkerton

Numerade Educator

Problem 88

If pellets shot at the same angle are compared, which of the
following is true?
\begin{equation}\begin{array}{l}{\text { A. Alighter pellet travels farther because of its higher ejection speed. }} \\ {\text { B. A heavier pellet travels farther because it is launched more }} \\ {\text { horizontally. }} \\ {\text { C. Pellets of all masses travel equally far because the launch angle }} \\ {\text { is the same. }}\end{array}\end{equation}

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 89

What is the maximum height above its launch site of a $20-\mathrm{mg}$
pellet that's launched at an angle of $20^{\circ}$ above the horizontal?
\begin{equation}\text { A. }5.5 \mathrm{cm} \quad \text { B. } 4.5 \mathrm{cm} \quad \text { C. } 1.2 \mathrm{cm} \quad \text { D. } 6.0 \mathrm{mm}\end{equation}

William Dunkerton

William Dunkerton

Numerade Educator

Problem 90

A pellet launched at $30^{\circ}$ above the horizontal that spends 0.15 $\mathrm{s}$
in the air before returning to its original level has approximately
what mass?
\begin{equation}\begin{array}{lllll}{\text { A. } 2 \mathrm{mg}} & {\text { B. } 9 \mathrm{mg}} & {\text { C. } 14 \mathrm{mg}} & {\text { D. } 20 \mathrm{mg}}\end{array}\end{equation}

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 91

What is the maximum range of a 5 -mg pellet that lands at the
same height from which it is ejected?
\begin{equation}\begin{array}{lllll}{\text { A. } 14 \mathrm{cm}} & {\text { B. } 20 \mathrm{cm}} & {\text { C. } 40 \mathrm{cm}} & {\text { D. } 78 \mathrm{cm}}\end{array}\end{equation}

William Dunkerton

William Dunkerton

Numerade Educator

Problem 92

REFERING TO EXAMPLE 4-9 (a) At what launch angle greater than
$54.0^{\circ}$ does the golf ball just barely miss the top of the tree in front
of the green? Assume that the ball has an initial speed of $13.5 \mathrm{m} / \mathrm{s},$
and that the tree is 3.00 $\mathrm{m}$ high and is a horizontal distance of
14.0 $\mathrm{m}$ from the launch point. (b) Where does the ball land in the
case described in part (a)? (c) At what launch angle less than $54.0^{\circ}$
does the golf ball just barely miss the top of the tree in front of the
green? (d) Where does the ball land in the case described in part (c)?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 93

REFERING TO EXAMPLE 4-9 (a) Suppose that the golf ball is launched
with a speed of 15.0 $\mathrm{m} / \mathrm{s}$ at an angle of $57.5^{\circ}$ above the horizontal, and that it lands on a green 3.50 $\mathrm{m}$ above the level where it
was struck. (a) What horizontal distance does the ball cover during its flight? (b) What increase in initial speed would be needed
to increase the horizontal distance in part (a) by 7.50 $\mathrm{m} ?$ Assume
everything else remains the same.

Margaret Shawver

Margaret Shawver

Numerade Educator

Problem 94

REFERRING TO EXAMPLE 4-11 Suppose the ball is dropped at the horizontal distance of $5.50 \mathrm{m},$ but from a new height of 5.00 $\mathrm{m}$ . The
dolphin jumps with the same speed of 12.0 $\mathrm{m} / \mathrm{s}$ . (a) What launch
angle must the dolphin have if it is to catch the ball? (b) At what
height does the dolphin catch the ball in this case? (c) What is the
minimum initial speed the dolphin must have to catch the ball
before it hits the water?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 95

Predict/Calculate REFERRING TO EXAMPLE $4-11$ Suppose we change
the dolphin's launch angle to $45.0^{\circ},$ but everything else remains
the same. Thus, the horizontal distance to the ball is $5.50 \mathrm{m},$ the
drop height is $4.10 \mathrm{m},$ and the dolphin's launch speed is 12.0 $\mathrm{m} / \mathrm{s}$ .
(a) What is the vertical distance between the dolphin and the ball
when the dolphin reaches the horizontal position of the ball? We
refer to this as the "miss distance." (b) If the dolphin's launch speed
is reduced, will the miss distance increase, decrease, or stay the
same? (c) Find the miss distance for a launch speed of 10.0 $\mathrm{m} / \mathrm{s}$ .

William Dunkerton

William Dunkerton

Numerade Educator