.
Questionsand Example Problemsfrom Chapter I
QuestionI
For eachmotion diagram,write a short descriptionof the motion of an object that wili matchthe
diagram.Your descriptionsshouldname specific objects.
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1
2
3
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45
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Question2
Your roommate&ops a tennisball from a third-story balcony. It hits the sidewalk and bounces
ashigh as the secondstory. Draw a motion diagram,using the padicle model, showiag the ball's
velocity vectors from the time it is releaseduntii it reachesthe maximum height on its bounce.
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Problem 1 Interpret the following problem by drawing a motion diagram showingthe object's position
and its velocity vectors. Do not solve this problem or do any mathernaics.
A motorist is traveling at 20 m/s. He is 60 m {iom a stop light when he seesit hrrn yellow. His
reactiontime, before steppingon tho brake, is 0.50 s. what steadydecelerationwhile braking
will bring him to a stop right at the light?
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brql)
/If'-atc..J-aT
Problem 2
A car travels along a straighteast-westroad. A coordimte systemis established
on theroad,with
x increasingto the east.The car endsup 14 mi west ofthe intersection
with MulberryRoad.If its
displacementwas -23 mi, bow far fiom and on which side of MulberryRoaddid it start?
X5' -llni
AX = X g- X:
AX = -2.3vot
-AX
Xz' X.
'r
X,;=?
xi = - 14ni -
(:A-:"r) = '1*t
Problem 3
Keira startsat position r = 23 m along a coordinateaxis. she then undergoesa displacement
of
-45 m. What is her filal position?
X;
= )3ry1
-'+-X;
X
AX = -Ll5rn
Xs=?
'
=x
=
i + 0x
?.3* + (-ts .)
Xe = - ?-?.q
,'o
4q
Problem4 .
Alberta is going to have dinner at her grandmother'shouse,but sheis running a bit behind
schedule.As shegets onto the highway, sheknows t}at shemust exit the highway within 45 min
if sheis not going to arrive late. Her exit is 32 mi away. What is the slowestspeedat which she
could drive and still arrive in time? ExDressvour answerin miles oer hour.
+ AYr^h /"^Artfur',4 3 X.,, ,rz\45 ,.,,n
45.'q = o.?s hr
)+-)= @ble
e
3A tnt'
4z_t/n,
o . ? 5h e
)r^fi4r"l
Problem 5
It takesHarry 35 s to walk from x= - 12 mto x: - 47 m. What is his velocity?
At = 35s
-
X; - -llm
Xg' -et?rn
= X. -X;
n Y
At
y=
-41n
-
L- I4f.\ /i
=
-
J9
,l -- ?
f)
V=-l"ot,J- l >
Problem 6
In the United States,we often usemiles per how (mi,{h)when discussingspeed,while the SI unit
of speedis nr/s. What is the conversionfactor for changingm/s to mi/h? If you want to make a
quick approxirnationofthe speedin miAr given the speedin m/s, what might be the easiest
conversionfactor to use?
I*/n= t//t
*\
( Iri
\ I/= -36Do4\
1
lbDl(t' /
\
1-r'r'I
c,"ot"voa-alonW
Problem 7
Convertthe following to SI units: a)8.0in
b) 66 ff/s
c")
( b)
GL+tfs= r.u/t-/s(*rrf)
1 eua7" = J.o,.io' r/,
-l I
L__"__"____
- '
-l^/u x
-t--:
1n^z'/trn
,.a l'1
Problem E
List the following tlree speedsin order, from smallestto largest 1 mm per /pls, I km per ks,
1 cm perms.
a
,t,
Lry -- tk
A = ID-n
fi = ('
It K./"
tn>
L=lo-a ",
11=lo'
Probtemg
/,n_3-\
\;-;
l I l --.,
:\
n ^ ^/s
= ^1'ta3
(
)
)
tr" \ =
t ^^lt
- *"rt/S
9t*\/
fv^)\1e/
-- lK'1u"(
\/ait=\=
1L*/ns=Jc'/m5(!'" t/"*/(l":t/=
,4
-../
n
,-F
l,tW*l
l^^i!usl
l'
4"t^t"t
rxton'/s
tYslL'"/nst
Estirnatethe averagdspeedat which your fingernails grow, in both m/s and um/h. Briefly
describehow you arrived at this estimate.
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.'?a.-L cnrlc *[/t,t+
m,,&"{d a.l-ft
.{*qAf ,r}tp 4$ 'd-!vb'rI I nn $n+ul
a.t*n^2 tod,at*a,
-e'r>eryloaa,ra.
v=A). *h.(#;^)(ffi)(ffi)-
V = xj:l- f ro3.t^*
)/ t?
\ *
1oao4't \
J\ x^ /
lmn
"*^
,
'rn./.
-q
ltlo
'
lr
u/
I il.n 1n"t
/ \
Problem l0 -;
II
A city has streetslaid out in a squaregrid, with eachblock 135 m long. If you drive north for
tkee blocks, then west for two blocks, how far areyou from yom startingpoint?
7*n-*
^..6^it = 3(1a5.) = {o5""' ^r"aJt
X )rOxl+hr"At = &( t35-)
-
T"lo^
Aro lr
d,
4on n
I
al=
^rr"4*.
(lro")tt(qos^)1
-
F--r
,/ (r^'o*1a
n (4osn)' = 14rl"\ I
?= w (11?") -- ?3;1"
./ o b t',
-/
=_--
Problem 11A ball on a porch rolls 60 cm to the porch' s edge,drops40 cm, continuesroiling on the grass,
and eventually stops80 cm ftom the porch'sedge.What is the magnitudeof the ball 's net
displacement,in centimeters?
itloc."r
40 . 9
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gocn
,-
o ^n* = i(t'rot')&'*(rlb'',"'',it
A X t r u = 6 0 . . . - f 7 D " , ,=) 1 9 0 "*
a)u-a.4occ-r
=,iq?ft
li
,: /:5lo*..n|(a^a'-"Q a 8x+4r)
ld""l
probleml2
Wlat is the valueof eachof the anglesofa right trianglewhosesidesare 100, 150,and 180cm in
lensth?
7 loacm
\
)n9= t rrr-,/
d = ,a.^\ (t,r="^; =
lfDcq
??
,b
.-rt-
I O Oo t \
c-brg= lroo'^
1
'
/Eb.r
o=
\Yo'"' /
r o z - - t(' t p o - ' " I
lFoc''
)
=
5{o,3o
<:
Problem 13
An oceanliner leavesNew York City and travels 18.0"north ofeast for 155 km. How far eastand
how far north hasit gone.In other words, what are the magnitudesof the componentsof the ships
displacementvector in the directions (a) due eastand (b) due north?
T
rrq lt*
ay
AX
rC*) 19.o"
AV
l5.)Kr^
(b)
-
,\\t
^,^r 19.o" = _)9L/55Yr'>
- rt,--,.,
\
OY = ( tsrrr. ),lqrt,6"
A.
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.,
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i )
-
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