Which one of the followx9 .siu1 e:10noa4ksga og,euing is an example of a vector quantity?

  Which of the followingvo g+t 4-1o(bm2s 7anrccrt. r operations will not change a vector?

  Which of the following is an accuzw tc o bz0lp5ea6x3(.rate statement?

  The resultant of two vectors is the rm;i1yb/go.)c+v/ynhjv v;p smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m -cx+ l lkb /d*66kn;q0zudkomand 7.0 m, respectively. When these two vectors are added, ulc 6b0qkm/z +kx;k6dlo*-nd the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of t: /+hdg.ews8wtj mu e(tthf(c*d*u,* guiv b4he following is a possible answer. duj 8htw t ,bw4*ug i+tm(* egvs*fcd/heu(: for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in 3 ltc+wbd( ltip*+7:9k uywo2ekrohn +gk .b) directions that areb .:e7 bwuk 3o l cg+ltprw+kd+yn(9h2*tio) k $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoe; ef2 o:mj i nqw5o.xjyp;8y7wn vector is

  Ignoring air resistancm) 0*7 qwqvucgf )f7fke, the horizontal component of a projectile's velocity

  A ball is thrown with a velocw-y d1v la-b*iity of 20 m/s at an angle of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's accelerationt vt ffzt5+* dnu;zy+ 9(5acwpw5 v +ua+9fyzpd;t(c5tfz n*t

  A soccer ball is kicked with a velocity of 25 m/s at ,lf1pfzl* 4igan angle of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of an object is directed ant go41.q sbitb+i-parallel to the velocity vects +. 41qoibgbtor,

  If the acceleration of an object is always directed perpeds e.oud ioaof03t- :+ndicular to its velocittuoe.ds 3 -i:0aodo+ fy,

  At what angle should a water-gun be aimed in order f /tp8-k2on2 tcsjnbw8 or the water to land with theb2 8n/oknt8 wpj 2sct- greatest horizontal range?

  An Olympic athlete throws a javelin at fou6+m 9;wkpck l)+gidrp r different angles above the horizontal, each wi kcm+r9p wi p+k)gdl;6th the same speed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. If the ball leaves yoa *bo mhq)xbm25 4.i9 qdjk6ygur hand with twice the velocity it had on your first throw, its 4*oxqbq6bh)2ga d. m5y9kjim horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 n/lx4dexoza2/ b2uj7 m/s at an angle of $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a field goal attempt reaches its maxisfgjm9 ;w/pdm,f ek+ne2 1;ip mum height, how does its speed compare to its /nwjp,g1f;mi e+d9e kfp2;sminitial speed?

  A stone is thrown horizontally from the top of a tower at the same instant sehix)kw 578ra ball is dropped vertically. Which ohx7srek8w) 5i bject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at t1 h( 6(43uxv n eic4nhwsuafm6he same instant a second bullet is dropped from the same height. Ignore air resistance. Compare tu4u 6h6nf43scv1 (ih e(waxnmhe times of fall of the two bullets.

  A plane flying horizontally at a speed of 68.6 m/s and at an elevation oi k pvay(wpj8f*lo ,k (v-)i6of 170 m drops a package. 3.0 seconds later it drops a secondpijv,k6 v k*)a-( ofw(op8iyl package. How far apart will the two packages land on the ground?

  A package of supplies is dropped fr w w9/2+nd(er,c s7bl sck0szwom a plane, and one second later a second package is dropped. Necwsz nr,e(+s/ 9d0c7lwbwk 2sglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane qqidstwy6 42bd40jflg.9jj9 flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane w ddqq 4 6lsi4y0jbjjg2fw9 9t.ill

  The acceleration of gravity on the Moon is only one-sixth oa*p. mpyn ,0f(h0-j epgc91ka2caiwpv u q-x /f that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Eartn(.pa,a- i /h0-ayppkqfu1x9*2 wmcp eg vj0ch, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road )q+h( hih0ccey-i re 3and pass a car travelingyheiei3h0)-cqh( r c+ at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strat hb))+,uxp ndbitjx ;k8s+4 ong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shoubt) s+xx;tj,+a dibhup 8)4nk ld head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it t333afyb +eg tdake you to move 12 km downstream, in a river flowing at 6.ag 3 eydfb3+3t0 km/h?

  Vector A has magnitudesd sf2;+uy2odfq*khlcda o / 46i:o3k 8.0 m at an angle of 30 degrees below the +x axis. The y componen6* io32dd dl s+o:fuy4osak; kc 2hf/qt of A is

  If a ball is thrown with a veqfjtmfz mqz t5 -*5:h+locity of 25 m/s at an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight lw 2nz -y8x 7zsfsch 3e9j*enp-ine in a direction north of east and you end usnh j9ecszx p ny-zewf-*7238p 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of it ,qa9y)r-i) fhpi03gzmw)9 h ykudep0s velocity is 8.000)k9eazqpm r)ypgiw , 3 h-9hudi0 y)f m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what an p .q,mfzoq3x5/ cod8ty-gx8ygle is the Sun elevated-.5ofq /xoc8y t83 qpgxd,yzm above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respecti3f efhlj v5, tcs:;jtas3lidg ot(.4 3vely. What are the comp:sl tet,lhjjdao5(c v3s34igft;.3 fonents of the sum of these two vectors?

  Two vectors A and e3*uci x ruz-+B have components (0, 1) and (-1, 3), respectively. What is magnitude o*- +zxri3 cuuef the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnik5nqst+z bg :hpb)p 4)tude of C pb)tkq5 n4+p)szb gh: ?

  A car travels 20 km West, then 20 km South. What is the magnitude 2cwj2xdwnx u)b/qr/7-(qr qhof its displaceq /u/()djr wr2x n-xbqh2 qc7wment?

  Three vectors, expressed in Carte tam-98* sgrwz tze+*mxk 2l6bsian coordinates, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the magnitude of the resultant vector S + T + U ?

  Three vectors, expressed in Cartesian coordinatss0fm z,,nq+oes, are
S = (-3.5,+4.5)
T = (0,-6.5)
U = (+5.5,-2.5)
What is the angle of the resultant vector S + T + U measured from the positive x axis?

  If vector A = (-3.0, -4.0) and vector B = (+3.0, -8.0), wz -n/. e,mjua)smq 2pzhat is the magnitude of vector2p zq- ,/juae)mzm.ns C = A - B ?

  A runner runs halfway around a circular path of voo( -rbn* zb kj 9y0yrq*)z+wradius 10 m. What is the displa9o(n b zvo0ky)qwyrrz-*jb*+ cement of the jogger?

  Two forces are acting on an object as shown in Fig. below. x e /og58gorx r9a)v6lWhat is the magnitude of the resultant foox5 gl8x)e9gr6 a/vo rrce?

  Two forces are acting on an object as shown i- wl85si(-od v jzdj9nn Fig. below. What is the direction of th 8djov 5ld(- szij-w9ne resultant force?

  Vector A is 4.7 cm long and points along the p 2,a8q,:rj7hzm ovala ositive x axis. Vector B is 7.0 cm long2jlv:mq 7,razo,aa 8h and points at $+50^{\circ}$ to the negative x axis.
(a) Determine the x component of Vector A $A_x =$ (数值)  $cm$ and y component of Vector A $A_y =$ (数值)  $cm$
(b) Determine the x component of Vector B $B_x =$ (数值)  $cm$ and y component of Vector B $B_y =$ (数值)  $cm$
(c) Determine the sum of these two vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(d) Determine the sum of these two vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the posive x axis rotated in the counterclock wise direction) $\tan \theta = $  (数值) 
Please only fill in numerical values in the above blanks!

  Vector A is 60 cm long and p1*csl+a)c ag4 ig 0rl-nw0yaioints at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 37 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A: $A_x=$  (数值)  $cm$ and $A_y=$  (数值)  $cm$
(b) Determine the x and y components of Vector B: $B_x=$  (数值)  $cm$ and $B_y=$  (数值)  $cm$
(c) Determine the x and y components of Vector C: $C_x=$  (数值)  $cm$ and $C_y=$  (数值)  $cm$
(d) Determine the sum of these three vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(e) Determine the sum of these three vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the positive x-axis rotated in the counterclock wise direction) $\tan \theta=$  (数值) 
(Please only fill in numerical value in the above blanks!)

  A stone is thrown horizontally withx1igdb 6 qmj4) an initial speed of 23 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.8 s. What xj16gq dm)b4iis the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 1x;grix1s v v+9 m/s, from a bridge. It falls 13 m to the water belowi v rxg;v1x+1s. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the gl/e1/ -hgklqe u a7c+tround, strikes the ground after traveling horizontally a di/ lt u lae1kc+q-egh/7stance of 17 m. With what speed was it thrown?

  A jumper in the long-jump goes into thkgtf- (:p-hmde jump with a speed of 12 m/s at an angle of gth(fdk-mp:- $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goegvge4j0d n1h*s into the jump with a speed of 9 m/s at an angle on ed*41jg0gvhf $15^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 28.1 m/s at an angle ofbto+ i.1t+k .v0 g:qe ci*poso $22.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vf 1yhq6vuq3 r9elocity of 35.2 m/s at an angle of $46.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired k i*8dt(-nw bfat an angle of $30^{\circ}$ below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below?

  A projectile is shot horizontaby sj92t rf3 zuq7m7e:kvfq59/p4ntk lly at 20.1 $m/s$ from the roof of a building 65.7 $m$ tall.
(a) Determine the time necessary for the projectile to reach the ground below.  (数值)  $s$
(b) Determine the distance from the base of the building that the projectile lands.  (数值)  $m$
(c) Determine the horizontal component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$
(d) Determine the vertical component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$

  A projectile is fired from ground level with an 3ew3/s5govt tmcawf,zo 7 +m :initial speed of 56.8 m/s at an e3 sfm 3:+ ,5mz o7ag/woctwtvangle of $38.7^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.  (数值)  $s$
(b) Determine the maximum height reached by the projectile.  (数值)  $m$
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height. horizontal:  (数值)  $m/s$ vertical:  (数值)  $m/s$
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height. horizontal:  (数值)  $m/s^2$ vertical:  (数值)  $m/s^2$

  On a calm day (no wind), you can run qf8b ms80 fx:la 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a mlbf sq x:8f08day when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s t5kj ;1l8ynera1 nlas(7 ocr+go the West. To(5k g n;+sn ecjayl817lrr1ahe plane's speed relative to the ground is

  A plane is flying due Southq1atzl;h 1nr 2 ($270^{\circ}$) at 500 km/h. A wind blows from East to West ($180^{\circ}$) at 45.0 km/h. Find the plane's velocity with respect to the ground.

  An airplane with a speed of 120 km/h is hkf5 /emlc4 0n.;w3agedgnd t6eaded $30.0^{\circ}$ east of north in a wind blowing due west at 30.0 km/h. What is the speed of the plane relative to the ground?

  A fighter plane moving 200 mzjny f azl-.st)1hs:5 /s horizontally fires a projectile with speed 50.0 m/s in a hjyzs:z-) .tslaf n15forward direction $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed i/4a0vkrz l7s an still water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the s0rvs la/4za7kpeed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/sa1p.v cxrc,/ , e3mzqi in still water wishes to travel directly across a river 1.4 km wide in w .izc/ev r3ax p1,q,cmhich the current flows at 3.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes m89 y k*gdp)f 5xmf8ppto travel directly across a narrow strait in which the current flows at 5.0 m/s. mg)x*p9d8 pkfpmy5f8At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide/zl swg5g n3n5 9v;qca reaches the opposite bank in 6 mingcl5 nz9s qa;w3n/vg 5 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a riy4),*1h5zhv vo e 8hagjf h(stver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is t)h4ts1h ah8vf vh ,5eyoj*g( zhe speed of the current?

  A boat, whose speed in still w 6q:,z6;ui xsmv)m tsgater is 2.01 m/s, must aim upstream at an angle of 6v:su )mq;,tmxsg6 zi$24.9^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.  (数值)  $m/s$
(b) Determine the resultant speed of the boat with respect to the shore  (数值)  $m/s$