themotionis given.Remember thatv:2nlT,wherc r is theradiusof thecircularorbit. You can usethis expressionto eliminatev in favor ofr or r in favor ofv in the expressionfor the centripetalaicceleration. All relativemotion problemsareessentiallyvectoradditionproblems.Identifi the two reference framesof interest.Identifr the velocitiesin the equationi pa= i ps+ i sn, write the equationin componentform and solvefor the unkno*rr quantities.Sometimesthe equationmustbe rewritten in tenns of mag,nitudes an6anglesratherthan in terrnsof comp-onents.
Questionsand ExampleProblemsfrom Chapter 4 QuestionI The figure below showsthreesituationsin which identicalprojectilesarelaunchedfrom the ground(at the samelevel) at identicalinitial speeds3a6 engles.The projectilesdo not land on the sarnetenain, however.Rankthe situationsaccordingto the final speedsof the projectilesjust beforethey land, greatestfirst.
(b)
(c)
q>t>c Question2 An airplaneflying horizontallyat a constantspeedof350 lcn,tr over level groundreleasesa bundleof food supplies.Ipore the effect of the ah on the bundle.What arethe bundle'sinitial (a) vertical and (b) horizontalcomponentsofvelocity? (c) Wlat is its horizontalcomponentof velocityjust beforehitting the ground?(d) Ifthe airplane'sspeedwere,instead,450 kmlh, would the time of fall be larger,smaller,or the same?
(q)
(b)
35o Ko/t,
I Cl
Z9o(nf'n
(,J)
tVv
aor,'-
Problemt Thevelocityi ofaparticlemovinginthexyplaneisgivenby n=6.0t-4.U\i+8.0j,with t in meten per secondandt Q 0) in seconds.(a) What is the accelerationwhent:3.0 s?(b) When (if ever) is the accelerationzero?(c) When(if ever)is the velocity zero?(d) When (if ever)doesthe speedequal 10m/s? '""""
-- | 1a"o,7r')t-( q"onfs') to ] t * (t.o,fs)! V-+
--t r-\ | /^\ Tt (o) = f'(t"-o^/s,)q- = dt a , (s"oef sr)t7 t /at
(- ta"/s) I (U) .^* u-",J[ ar = o ---) '" / t = (6"on/e)
( u-o,/t>)' 6t.o.lsz)t --o
/(r.o*ls')
-----)t= o"c75s
(c)
rd)
vx - r b.on/s
,l
((""Dnk)t - Lq.o^/s,)7\= -tn"or1r ---'a (-tt.o.fs)t\+ t "o,')/s^) tf 6"0n/5=o
f =g.r.
Problem 2
positionis givenby r = 1f.OO4i- 1+.OOl)j+ Z.OO;0, An elecfton"s wlTl
andr' in
meters.(a) In unit-vectornotatio& what is the elechon'svelocity t(t) ? At t : 2.00 s, what is i (b) in rmit-vectornotationandas(c) a magnitudeand (d) an anglerelativeto the +x-axis.
^g
J--
f'&) A^A
b l'l*Aon "u '.
+ (a.,".)p t - LU-oo,1t)t'J3 C(*) = l1z.oo,/s)t1
(o) i=J?/tt=
(:.oo"7,;i
')zl i -lG*"./'
(a.uos)i (b) 7(*=e.oor)= (a"oo'/s)i -Q"oo',,1') ( a . o o o / . ) ? - ( I t " . o , o / ii )
(c) lv'l /\\ \o/
-,(y;_\ n _ +__t /-tt .o-lr,\ - )F = d n v \ v,(/ )a!\ t;.r,r/
lIo.5 n/
o\ /. .Qylr "
* {: J" V"yt )Aa')t\ O: yqtVuyt t
o)
r/" = ?3or"'r \
I s'.o"\
V,
= or"' ! t= E,oo,
O
A,j='1'noqf sr
= JZo r, - \/oLz)53.o"(s.ao5) - 1-1:t-r,(s,a)\
vo--a,.li1=':",i'-'''::lil.;l 'o'qs,.o'(s'"ot)
V'=o."t
--J [U) X-X"=v,"t X=Vovt =(ral./')(s-oo';
x=7 = Vo" Llurq/r) ax"Eze = I b Irr1s (J )
(.)
V* = Vo*
Vy = Voy+ay f -= (-lozel)
-- t\tnlsl IV.7 a-.-.--t
I
(t'zo-/s') (rXj ooc53.oo1
r
Problem 9 In the figure below, a baseballis hit at a height h : 1.00m andthen caughtat the sameheight.It travelsalonlside a wall, moving up pastthe top of the wall 1.00s after it is hit andthen down pastthe top of the wall 4.00 s later, at distanceD : 50.0 m farfheralongthe wall. (a) Whal horizontaldistanceis traveledby the ball from hit to catch?What arethe (b) magnitudeand (c) angle(relativeto the horizontal)ofthe ball's velocityjust after beinghit? (d) How high is the walf? t=Z.oos it\\s
t=,1'b0t aaaat--
-
rT-'
AX= 5D.Orn Vtu9r, = AX =
At
d =Soos
At= q. oos
,',
5O.Orr
_
| ),.5efg
+ . o os
I
I
Nir/t
/y .^a e '1,,.^a'6'))
V1=V""= t=3.ooe f. Xfi fr,'-4j.*
&ffi'rq
Vu,x" -- I e"s '!/s
p.,J ua^" Vy =on1s
/,o
%r=?
Vy = %ytarf
'i::y:l1#
---
Vo, = -ayt
- - L-q.7oe/s')G"oos;
V"y'=X'ttrrt
O.y= -$,6o'e/9r
= lr"So,/s (") x"=:* V"" (o-Oo
x=(
f=
(u)q=
s
X-X"=Y"jt-
y =(re.Eol5)(ra""r)
\= f5.on
3r.1,ls
\--l (J /'r*1-,*}''r^4r*'t f=l.oo5 | ) ( l"os)r y - I'orr+(e i.q,)/ s)( t..os) * /t e9 ;o "ls) t/yaytr Y Yu":V"y*+ '
I'ofl
= )"5.5-
a
Problem 10 A sprinterrunning on a circulartrack hasa velocity of constantmagnifude9.2 m/s anda
:ftxi*3|"1".;}"**n
ofmagnitude 3.8nr./s2. wt'ut*" 1u;tn taci *ai* *J OirL"p"rr"a "r
V = l"Ark
. )/ A=V-,/r- a
(a) !
q: 3.znfst
:/
- Y>/ ,| - --'./^
/.
t- - (z"l n)s)^ __-_z"8nfs^
i- = ? l-= ?
T=
lr
( aa,-)
9.a '/s Problem11 (a) wbat is the magnitudeof the centripetaracceleration ofaa-objecton
Earth,sequatorovdngto tle rotationof Earrh? (b)whatwouldiheperiodof .otuti* orEurtn il, * ,n" h";;i; equatorto-bavea centripetalaccelerationwith a magnitude "1.i".* of 9,g nr,/s,?
= 6-3?x;66.
[-
T= bx (Ybr*)(W)
a ) V= '4I_r= -r \^
= r6,eoos
?,n (A"*
* l06n)
V - 463nf 5
86)qoos
r \
b)
t-
.7t u1r Q=
4.?r a
-)
v: \rr/r /'
),
q
T= s.l" lo3s x 6q ^wi\
q
/-\-., ' \ /tl \
-
?rlf -f1
4 r'(a.:?" ion) ?.so,r/s^
