Chapter 2 continued
the
7. Position Two students compared
position vectors they each had drawn on
n of a
a motion diagram to show the positio
found
They
.
moving object at the same time
that their vectors did not point in the same
direction. Explain.
A position vector goes from the origin
to the object. When the origins are dif
t.
ferent, the position vectors are differen
t
vec
men
On the other hand, a displace
tor has nothing to do with the origin.
ght
8. Critical Thinking A car travels strai
to
store
along the Street from the grocery
you
the post office. Th represent its motion
at
n
origi
its
use a coordinate system with
is
the grocery store and the direction the car
r
moving in as the positive direction. You
ori
its
with
m
friend uses a coordinate syste
gin at the post office and the opposite
ld
direction as the positive direction. Wou
tion?
posi
the two of you agree on the car’s
val
Displacement? Distance? The time inter
the trip took? Explain.
The two students should agree on the
val
displacement, distance, and time inter
for the trip, because these three quanti
n
ties are independent of where the origi
The
of the coordinate system is placed.
two students would not agree on the
car’s position, because the position is
measured from the origin of the coordi
nate system to the location of the car.
Practice Problems
Position-Time Graphs
pages 38—42
2.3
page 39
For problems 9—11, refer to Figure 2-13.
150.0
-
S
100.0
50.0
N
0.0
,
,
1.0
3.0
5.0N7.0
\
Time(s)
—50.0
a Figure 2-13
9. Describe the motion of the car shown by
the graph.
The car begins at a position of 125.0 m
and moves toward the origin, arriving at
the origin 5.0 S after it begins moving.
The car continues beyond the origin.
to
10. Draw a motion diagram that corresponds
the graph.
5.Os
t
=
5
0.Os
t
=
0
S.....
0.0 m
125.0 m
I
d
11. Answer the following questions about
the car’s motion. Assume that the positive
ti-direction is east and the negative
d-direction is west.
a. When was the car 25.0 m east of the
origin?
at 4.0
S
b. Where was the car at 1.0 s?
100.0 m
12.
lb
‘t[
Atanzial
Describe, in words, the motion of the
two pedestrians shown by the lines in
Figure 2-14. Assume that the positive direc
tion is east on Broad Street and the origin is
the intersection of Broad and High Streets.
Physics: Principles and Problems
Chapter 2 continued
How
b. Will [leather catch up to Juanita?
can you tell?
No. The lines representing Juanita’s
and Heather’s motions get farther
apart as time increases. The lines
will not intersect.
Position-Time Graphs
pages 38—42
•
F
I
o
20
•
•
•
•
•
.
.
140m
Om
For problems 21 —23, refer to Figure 2-18.
Time Use the position-time graph of the
hockey puck to determine when it was
10.0 m beyond the origin.
0.5 s
//
page 42
particle
19. Position-Time Graph From the
ling
craw
baby
model in Figure 2-17 of a
across a kitchen floor, plot a position-time
graph to represent his motion. The time
interval between successive dots is 1 s.
•
•
()
Section Review
2.3
7.Os
t
=
7
0,Os
t
=
0
.
•
•
a
•
•
.
40
60
80
100
120
140
160
\
graph of
/ 22,) Distance Use the position-time
far it
how
mine
the hockey puck to deter
moved between 0.0 s and 5.0 s.
100 m
h
23J Time Interval Use the position-time grap
h
muc
how
for the hockey puck to determine
time it took for the puck to go from 40 m
beyond the origin to 80 m beyond the origin.
Position (cm)
2.0 s
a Figure 2-17
Critical Thinking Look at the particle
model md position time graph shown in
Figure 2-19. Do they describe the same
motion? How do you know? Do not
confuse the position coordinate system in
the particle model with the horizontal axis
in the position-time graph. The time inter
vals in the particle model are 2 s.
16or
g
z
4
140k120
looK
80H
60f- •
40[—•
20 [-•
0
12345678
Time (s)
•
.
model
20. 1 Motion Diagram Create a particle
from the position-time graph of a hockey
puck gliding across a frozen pond in
Figure 2-18.
•
.
•
•
•
.
10
0
-
Position (m)
12
E 8
C
0
0
a-
4
0
0.0
1.0
3.0
2.0
4.0
Time (s)
a
%
Selinions Alanual
5.0
6.0
7.0
1
2
3
4
5
Time (s)
a
Figure 2-19
Figure 2-18
Physics: Principles and Problems
Chapter 2 continued
The equation is Ad
Mixed Review
position-time graphs for
56. Figure 2-30 shows
ng canoes in a local
loszi and Heike paddli
river.
pages 53—54
Level 1
maintains a constant
54. Cycling A cyclist
time t = 0.0 s, the
velocity of +5.0 rn/s. At
nt A.
cyclist is +250 m from poi
graph of the
a. Plot a position-time
nt A at 10.0-s
cyclist’s location from poi
intervals for 60.0 s.
18
16
500
12
10
ZZZZ”2
400
C
0
350
‘I,
0
300
8
06
4
450
2
I
Z
14
0
550
2
EE
0
2.5
and Heike in
a. At what time(s) are Joszi
the same place?
1.0 h
zi spend on
b. How much time does Jos
Fleike?
the river before he passes
position from point
b. What is the cyclist’s
A at 60.0 s?
45
550 m
ent from the
c. What is the displacem
s?
starting position at 60.0
3.0X10 m
550 m 250 m = 2
C.
model for a chicken
Figure 2-29 is a particle
road. Time inter
casually walking across the
the corresponding
vals are every 0.1 s. Draw
ite the equation
position-time graph and wr
motion.
to describe the chicken’s
The other side
This side
.•••••..•
• •. •• •.• . .•
55.
mm
ear that
Where on the river does it app
t?
there might be a swift curren
the origin
from 6.0 to 9.0 km from
Jevel 2
car B leave school
/ 57. riving Both car A and
travels
stopwatch reads zero. Car A
when a
car B travels at a
at a constant 75 km/h, and
constant 85 km/h.
ph showing
a. Draw a position-time gra
w far are
the motion of both cars. Ho
en the stop
wh
the two cars from school
e the dis
watch reads 2.0 h? Calculat
your graph.
tances and show them on
I
I
5.
• Figure 2-29
dA
d
=
=
The other side
=
dB
This side
2.0
S Figure 2-30
200
50.0 60,0
0.0 10.0 20.0 30.0 40.0
Time (s)
Time intervals are 0.1
1.5
1.0
0.5
Time (h)
250
24
vAt.
=
VAt
(75 kmlh)(2.0 h)
150 km
=
VBt
=
(85 km/h)(2.0 h)
=
170 km
t
0
Solutions Manual
1,9s
s
Phvc ‘CS: Principles and Problem
_
____
____
Ghaçter 2 continued
60. figure 2-31 shows the position-time graph
depicting Jim’s movement up and down the
aisle at a store. The origin is at one end of
the aisle.
1TrET
14.0
12.0
—
Thinking Critically
page 54
61. Apply Calculators Members of a physics
class stood 25 m apart and used stopwatch
es to measure the time which a car traveling
on the highway passed each person. Their
data are shown in Table 2-3.
10.0
E
Table 2-3
Position v. Time
8.0
C
0
0
0.
Position (m)
Time Cs)
6.0
4.0
2.0
0.00
10.0
30.0
20.0
Time
40.0
50.0
60.0
(5)
Figure 2-31
a. Write a story describing Jim’s movements
at the store that would correspond to the
motion represented by the graph.
Answers will vary.
b. When does Jim have a position of 6.0 m?
from 8.0 to 24.0 s, 53.0 to 56.0 s, and
at 43.0 S
C. How much time passes between when
Jim enters the aisle and when he gets to
a position of 12.0 m? What is Jim’s aver
age velocity between 37.0 s and 46.0 s?
t = 33.0 5
—
24.0 s
=
tf
=
=
t1
3.00 m
46.0 s
—
1.3
25.0
2.7
50.0
3.6
75.0
5.1
100.0
5.9
125.0
7.0
150.0
8.6
175.0
10.3
200.0
the car?
200.0
9.0 S
—
0.0
Use a graphing calculator to fit a line to a
position-time graph of the data and to plot
this line. Be sure to set the display range of
the graph so that all the data fit on it. Find
the slope of the line. What was the speed of
o.o
Using the points (37.0 s, 12.0 m) and
(46.0 s, 3.00 m)
—d
1
d
0,0
C
0
100.0
0
50.0
0.
12.0 m
37.0s
0.0
2.0
4.0
6.0
8.0 10.0 12.0
Time (5)
—1.00 mIs
The slope of the line and the speed of
the car are 19.7 mIs.
62.
26
oluiions Manual
&ppiy Concepts You plan a car trip for
which you want to average 90 km/h. You
cover the first half of the distance at an
average speed of only 48 km/h. What must
your average speed be in the second half of
the trip to meet your goal? Is this reason
able? Note that the velocities are based on
half the distance, not half the time.
Physics: Principles and Problems
Chapter 2 continued
720 km/h; No
64. interpret Graphs Is it possible for an
Explanation:
Assume you want to travel 90 km in 1 h.
If you cover the first half of the distance
at 48 km/h, then you’ve gone 45 km in
object’s position-time graph to be a hori
zontal line? A vertical line? If you answer
yes to either situation, describe the associat
ed motion in words.
0.9375 h (because t =
It is possible to have a horizontal line
as a position-time graph; this would
indicate that the object’s position is not
changing, or in other words, that it is
not moving. It is not possible to have a
position-time graph that is a vertical
line, because this would mean the
object is moving at an infinite speed.
-).
This means
you have used 93.75% of your time for
the first half of the distance leaving
6.25% of the time to go the remaining
45 km.
—
=
63.
C
C
C-
45km
0.0625 h
720 km/h
Design an Experiment Every time a par
ticular red motorcycle is driven past your
friend’s home, his father becomes angry
because he thinks the motorcycle is going
too fast for the posted 25 mph (40 km/h)
speed limit. Describe a simple experiment
you could do to determine whether or not
the motorcycle is speeding the next time it
is driven past your friend’s house.
There are actually several good possibil
ities for answers on this one. Two that
should be among the most popular are
briefly described here. 1) Get several
people together and give everyone a
watch. Synchronize the watches and
stand along the street separated by a
consistent distance, maybe 10 m or so.
When the motorcycle passes, have each
person record the time (at least to an
accuracy of seconds) that the motorcy
cle crossed in front of them. Plot a posi
tion time graph, and compute the slope
of the best-fit line. If the slope is greater
than 25 mph, the motorcycle is speed
ing. 2) Get someone with a driver’s
license to drive a car along the street at
25 mph in the same direction as you
expect the motorcycle to go. If the
motorcycle gets closer to the car (if the
distance between them decreases), the
motorcycle is speeding. If the distance
between them stays the same, the
motorcycle is driving at the speed limit.
If the distance increases, the motorcycle
is driving less than the speed limit.
Physics: Principles and Problems
Writing in Physics
page 54
65. Physicists have determined that the speed of
light is 3.OOX 108 rn/s. How did they arrive
at this number? Read about some of the
series of experiments that were done to
determine light’s speed. Describe how the
experimental techniques improved to make
the results of the experiments more accurate.
Answers will vary. Galileo attempted to
determine the speed of light but was
unsuccessful. Danish astronomer Olaus
Roemer successfully measured the
speed of light in 1676 by observing the
eclipses of the moons of Jupiter. Hs
estimate was 140,000 miles/s (225,308
km/s). Many others since have tried to
measure it more accurately using rotat
ing toothed wheels, rotating mirrors
and the Kerr cell shutter.
66.
Some species of animals have good
endurance, while others have the ability to
move very quickly, but for only a short
amount of time. Use reference sources to
find two examples of each quality and
describe how it is helpful to that animal.
Answers will vary. Examples of animals
with high endurance to outlast preda
tors or prey include mules, bears, and
coyotes. Animals with the speed to
quickly escape predators or capture
prey include cheetahs, antelopes and
deer.
Solutions Manual
27
Multiple Choice
1 Which of the following statements would be
true about the particle model motion diagram
for an airplane taking off from an airport?
K The dots would form an evenh spaced
pattern.
The dots would be far apart at the
beginning, but get closer together as the
plane accelerated.
ct
The dots would be close together to start
with, and get farther apart as the plane
accelerated.
The dots would be close together to start,
get farther apart, and become close
together again as the airplane leveled off
at cruising speed.
2 Which of the following statements about
drawing vectors is false?
4.
when
is the person on the bicycle farthest away
from the starting poinU
point A
:
C
0 point B
point D
-
5, Over what inten’al does the person on the
biq’cle travel the greatest distance?
section 1
: section III
section Ii
point IV
6. A squirrel descends an 8m tree at a constant
speed in 1.5 mm, It remains still at the base of
the tree for 2 3 mm and then walks toatd tn
acorn 01: the ground for 0.7 ruin. loud nome
causes the squirrel to scamper hack up rue tree
in 0. 1 ruin tc the exact pus,tion on the branch
from JOicfl : sianed \\‘hiçh of ,he fod “:r
graphs n’orid aco!rareiv r!me:. tL
vertmc:jai
,
A vector diagram is needed to solve ad
physics problems properly.
The length of the vector should he
proportional to the data.
Vectors can be added by measu’ na 0
length of each vector and ther aJdin
them together.
Vectors can be added in stra$.
in triangle formations,
Use this
graph
c.
for problems a 4
1
7, Find a ms :1
,o
takes the t’Lm :riu mm.
north. C. I in sc 0 in s uth 0 4 in c 1st
Time
3. The graph shows the motion of a person on a
bicycle. When does the person have the greatest
ve!ocity?
<
section
1
cr)
point D
section
111
0
point B
nsh
/Test4aklng TIP
Stock up on Supplies
E3nnq al, ynar tesOtakag 1oo mOer Inn 4enc:s.
a
black and biue pens, erasers, correction
sharpener, a ru!er, a caiculator, ann a protractor
55
Chapter 2 Standardi2ecj Test Practice
Phy.Icflftne physicspp.com/standardized Jest
Multiple Choice
LC
4.C
2.A
5.A
3. 8
6.A
Chapter 3 continued
0.0 m/s 0.0 m/s
40.Os—0.Os
n of the
a. What is the average acceleratio
bus while braking?
—
—
—
a
—
=
s
2
0.0 mI
g the following
5. Plot a v-t graph representin
rest from the
at
motion. An elevator starts
shopping
ground floor of a three-story
2.0 s at a
mall. It accelerates upward for
a con
at
rn/s continues up
,
rate of 0.5 2
12.0 s, and
stant velocity of 1.0 rn/s for
nward
dow
t
stan
then experiences a con
rn/s for 4.0 s as it
acceleration of 0.25 2
reaches the third floor.
E
=
0.0 mIs 25 m/s
3.05
—
=
s
2
—8 3 mI
to stop,
b. If the bus took twice as long
pare
how would the acceleration com
a?
t
par
with what you found in
s
2
mI
half as great (—4.2 )
10.
stop for
Rohith has been jogging to the bus
at his
2.0 mm at 3.5 rn/s when he looks
time
of
ty
plen
has
watch and sees that he
10.0 s,
t
nex
before the bus arrives. Over the
in/s.
he slows his pace to a leisurely 0.75
during
What was his average acceleration
this 10.0 s?
>
U
0
ci)
a
-
>
0.0
15.0
10.0
5.0
Time
20.0
—
0.75 mIs 3.5 mIs
10.0 s
—
(5)
=
page 64
es from 4.0 rn/s
6. A race car’s velocity increas
interval. What is
to 36 rn/s over a 4.0-s time
its average acceleration?
s
2
—0.28 m/
t were to
ii. If the rate of continental drif
cm/yr
abruptly slow from 1.0 cm/yr to 0.5
t would
over the time interval of a year, wha
be the average acceleration?
0.5 cm/yr 1.0 cm/yr
a—
1.Oyr
—
36m1s—4.OmIs =80 mI
s
2
4.Os
problem slows
7. The race car in the previous
s. What is
from 36 m/s to 15 rn/s over 3.0
its average acceleration?
15 mls—36 rn/s
3.Os
=
s
2
—70 m/
downhill at a
8. A car is coasting backwards
er gets the
speed of 3.0 rn/s when the driv
car is moving
engine started. After 2.5 s, the
chosen as the
uphill at 4.5 rn/s. If uphill is
car’s average
positive direction, what is the
acceleration?
4.5mIs—(--3.OmIs) 2
=30m1s
—v
2.5s
when the driver
9. A bus is moving at 25 rn/s
the bus to a
steps on the brakes and brings
stop in 3.0 s.
()
c
Adanual
—
—
=
/yr
2
—0.5 cm
Section Review
3.1
Acceleration
pages 57—64
page 64
information
12. Velocity-Time Graph What
e graph?
can you obtain from a velocity-tim
e at
The velocity at any time, the tim
lar
ticu
par
a
which the object had
, and
velocity, the sign of the velocity
the displacement.
y-Time Graphs
1 3\, Position-Time and Velocit
city of
Two joggers run at a constant velo
= 0, one
7.5 rn/s toward the east. At time t
Physics: Principles and Problems
Chapter 3 continued
is 15 m east of the origin and the other is
15 m west.
a. What would be the difference(s) in the
position-time graphs of their motion?
16
Average Velocity and Average Acceleration
A canoeist paddles upstream at 2 rn/s and
then turns around and floats downstream at
4 rn/s. The turnaround time is B s.
a. What is the average velocity of the canoe?
Both lines would have the same
slope, but they would rise from the
d-axis at different points, +15 m,
and —15 m.
b. What would be the difference(s) in their
velocity-time graphs?
Their velocity-time graphs would be
identical.
Choose a coordinate system with
the positive direction upstream.
y+vf
2
——
=
2
=—lmIs
b. What is the average acceleration of the
canoe?
14. Velocity Explain how you would use a
velocity-time graph to find the time at
which an object had a specified velocity
Draw or imagine a horizontal line at the
specified velocity. Find the point where
the graph intersects this line. Drop a
line straight down to the t-axis. This
would be the required time.
a
-
—
15. Velocity-Time Graph Sketch a velocity-time
graph for a car that goes east at 25 rn/s for
100 s, then west at 25 rn/s for another 100 s.
25
E
>,
C
F
100
ci)
>
—25
C
>
I
I
200
)Time
(5)
—
1
V
Lit
(—4 m/s)
—
(2 mIs)
8s
=
0
2mIs+(—4mIs)
17.
2
0.8 mJs
Critical Thinking A police officer clocked
a driver going 32 km/h over the speed limit
just as the driver passed a slower car. Both
drivers were issued speeding tickets. The
judge agreed with the officer that both were
guilty. The judgement was issued based on
the assumption that the cars must have
been going the same speed because they
were observed next to each other. Are the
judge and the police officer correct? Explain
with a sketch, a motion diagram, and a
position-time graph.
No, they had the same position, not
velocity. To have the same velocity, they
would have had to have the same rela
tive position for a length of time.
C-
Physics: Principles and Problems
Solutions Manual
31
(lanpter 3 continued
Part 2: Constant velocity:
2
d
Vt = (18.0 mls)(60.0 s)
=
=
8X10 m
3
1.0
1 +
Thus d= d
=
8X10 m
3
81.0 m + 1.0
=
6X10 m
3
1.1
training
ing 5.0-km race. She starts out her
upcom
33. Sunee is training for an
n she accelerates
t pace of 4.3 m/s for 19 mm. The
stan
con
a
run by moving at
What is her
crosses the finish line, 19.4 s later.
at a constant rate until she
of the training run?
acceleration during the last portion
Part 1: Constant velocity:
d = Vt
=
(4.3 mls)(19 min)(60 s/mm)
4902 m
Part 2: Constant acceleration:
=
df=d+ vjt+Iat2
—
1
2(d
—
—
—
a—
=
5.0X10 m
3
(2)(
—
—
4902 m (4.3 mls)(19.4 a))
(19.4s)
2
—
s
2
0.077 mI
Section Review
ation
Motion with Constant Acceler
pages 65—71
3.2
page 71
deer on the road
driving at a speed of 23 rn/s sees a
34.’ Acceleration A woman
the deer. If the deer does
the brakes when she is 210 m from
ahead and applies
eleration
ore it hits the deer, what is the acc
not move and the car stops right bef
provided by the car’s brakes?
v2
2?(d—di)’
v
+
2
1
2
v
a= 2(df—d
—
—
=
mIs)
(23 2
(2)(210 m)
0.0 m/s
—
s
2
—1.3 mI
the constant
given initial and final velocities and
e
wer
you
If
nt
eme
plac
Dis
35.
the displacement, what
object, and you were asked to find
acceleration of an
equation would you use?
2 + 2adf
2 = v
V
6
Solutions Manual
Physics: Principles and Problems
Chapter 3 continued
36.
Distance An in-line skater first accelerates from 0.0 rn/s to 5.0 rn/s in 4.5 s, then
continues at this constant speed for another 4.5 s. What is the total distance trav
eled by the in-line skater?
Accelerating
—
f
1
L
—
1
i
f
1
V
+ V
2
(tf)
=
(0.0 mIs + 5.0 mIs
=
11.25 m
)(45 s)
Constant speed
d= vt
=
(5.0 mls)(4.5 s)
=22.5m
total distance
=
11.25 m + 22.5 m
=34m
37. Final Velocity A plane travels a distance of 50X 102 rn while being accelerated
. What final velocity does it attain?
2
uniformly from rest at the rate of 5.0 rn/s
=
2
Vf
0,so
+2a(d—dandd
2
1
v
=
2acI
v=v
+
2
=
)(5.0x10 m)
mls
2 + 2(5.0 2
\/(0.0 mis)
=
71
rn/s
38. Final Velocity An airplane accelerated uniformly from rest at the rate of 5.0
2 for 14 s. What final velocity did it attain?
rn/s
+at
1
v=v
=
39.
)(14 s)
2
0 + (5.0 m/s
=
7.OX 101 mIs
2 for
Distance An airplane starts from rest and accelerates at a constant 3.00 rn/s
ground.
the
30.0 s before leaving
a. Howfardiditmove?
2
d_Vt+
t
1
fit
3
=
2
(00 m/s)(30 0 s)2 +
2
)(30 0 s)
2
(43 00 rn/s
m
3
=1.35X10
b. How fast was the airplane going when it took off?
CC
v=v.+at
f
f
i
=
(300 s)
m/s
)
0.0 mIs + (3.00 2
=
90.0 mIs
Physics: Principles and Problems
Solutions Manwil
37
Chapter 3 continued
2 +
=
2ad
+ 2gd where a
1
and v
=
=
=
—g
s, so
0 at the height of the tos
25 m)
(0Is
m
)
rn/s) + (2)(9.80 2
2
V(0.0
2.2 mIs
ch time did it
as you released it, how mu
ght
hei
e
sam
the
at
it
b. if you catch
spend in the air?
+ atwhere a = —g
Vt =
=
=
=
2.2 mIs and
—2.2 rn/s
=
—g
—2.2 rn/s 2.2 rn/s
-9.80 rn/s
—
=
-
=
0.45
S
Section Review
Free Fall
pages 72—75
3.3
a
47
75
gravity on Mars is -thorn
Time Acceleration due to
ght
Fli
d
an
t
igh
He
um
same velocity
Maxim
throw a ball upward with the
you
se
ppo
Su
.
rth
Ea
on
t
one—third tha
on Mars as on Earth.
e to that on Earth?
maximum height compar
l’s
bai
the
uld
wo
w
Ho
a.
nce of the planet’s
t results frorn the influe
Acceleration of an objec
t on Earth, the
y on Mars is one-third tha
vit
gra
the
e
us
ca
Be
y.
gravit
be three times higher.
maximum height would
time compare?
b. How would its flight
ht time
ird that on Earth, the flig
-th
one
is
rs
Ma
on
y
vit
Because the gra
long.
would be three times as
o the air
throw a ball straight up int
you
se
ppo
Su
n
tio
era
cel
48 Velocity and Ac
scribe the changes in the
the velocity of the ball. De
in
s
nge
cha
the
ibe
scr
De
acceleration of the ball.
ms
Physics: Principles and Proble
40
olu lions Manual
Chapter 3 continued
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 until it reaches the height
from which it was initially released. At that point, the ball has the same
speed it had upon release. The acceleration is constant throughout the
ball’s flight.
49.
Final Velocity Your sister drops your house keys down to you from the second
floor window. If you catch them 4.3 m from where your sister dropped them,
what is the velocity of the keys when you catch them?
Upward is positive
2=
+2aidwherea= —g
2
1
v
vf=Vv2_2gAicI
=
2
\/(0.o rn/s)
=
9.2 m/s
—
(2)(9.80 m/s
)(—4.3 m)
2
50. Initial Velocity A student trying out for the football team kicks the football
straight up in the air. The ball hits him on the way back down. If it took 3.0 s
from the time when the student punted the ball until he gets hit by the ball,
what was the football’s initial velocity?
Choose a coordinate system with up as the positive direction and the
origin at the punter. Choose the initial time at the punt and the final time
at the top of the football’s flight.
+atfwherea— —g
Vf
=
0.0 rn/s + (9.80 mIs
)(1 .5 s)
2
=
15 m/s
51.s4aximum Height When the student in the previous problem kicked the foot
iball, approximately how high did the football travel?
2
+2a(d)where a= -g
2
id=
=
2
v
2
v.
—2g
—
(0.0 m/s)
2 (15 m/s)
2
(—2)(9.80 mis
)
2
—
=llm
52. Critical Thinking When a ball is thrown vertically upward, it continues upward
until it reaches a certain position, and then it falls downward, At that highest
point, its velocity is instantaneously zero. Is the ball accelerating at the highest
point? Devise an experiment to prove or disprove your answer.
The ball is accelerating; its velocity is changing. Take a strobe photo to
measure its position. From photos, calculate the ball’s velocity.
Physics: Principles and Problems
Solutions Manual
41
Multiple Choice
Use the following information to answe, the
first
wo questlon&
,\ ball rolls down a hill with a Constant
acceleration
. The ball starts at rest and
2
of 20 ms
travels for
3,0 s before it stops
150 m south
125 in north
J
1. How far did the ball travel before It stopped?
:
8. 1 he graph shows the motion of a
farmers truck
What is the truck’s total displacement? Assume
that north is the positive direction.
80 m
20rn
2. What was the bail’s ve1oci just before it
stopped?
2,0 rn/s
&OmIs
600 in south
15.0
—%
‘if:
4’
300 m north
0
25.0
l2na
.4.
0
2
S 5.30
0 0.30
t_—._.
5.00
..__—_,
150
2 0
350
45.0
Time is)
12 rn/s
3. A driver of a car enters a new ilOthm’h speec
zone on the highway The dnver begins
to
accelerate immediately and reaches
113 kin, h
after drrvtng 500 in. lf the original
speed was
so n’h, what ssus the drivers ra’e of chaerauon?
044mw
0.60 m,s
9. Hots can the instantaneous acceleration of an
object with eaRing aert’leration be calculated
1
5 the slope 01 the tangent
aLu1atn
Oil
a dislatt’tint’ gtapn
b” ca.ct/anng tne
under the urar’h
on dntan’e:jm,. g:apn
bs cal ul ring tie arca undc i the gt it
on s clot Its t me gr cc
di ea4uotiug ths si ‘r’e ce ‘ff,
aea
4, A flowerpot fail off the b ilcons
suite 55 in abose the street 11
take to htt the grruna?
f s pertno ise
oflg
Ocs
I
4.2s
835
m e:I,
5,
or r
rock climber shoP’ no
s’hnthing budd’. a’ 6
‘hat the rock toes 3 2
low hrgh ti. c
‘\
a
ISbn’.
C
.s ar trasec t,
turnoff fe a
driver slants
41’
s”
‘.‘,“it’
14 0 in
23Cm
I, Isnat is ‘he cotror’:
a ‘elerauon when is zt
I
Physloflhjfle
in
phyw it’”
‘S
Oac.s
85
A
Multiple
Choice
1. c
2, B
3. A
4. A
5. C
6. C
7.0
B. B
9. D
Extended Answer
10. ope
369 mis
‘
St ‘n’s
‘
‘IC
2
4.80 mt
area under graph
area under graph = area ot rectangle
+ area of triangle
= (8,10 mis/i? SOS)
1
acceleration
displacement
=
-i
r
57
.
2
-‘{l
.G
OO/ mis)
443
m
65.7
E 51.3
>‘
36.9
0
0.00
6.00
9.00
Time (s)
1.