Which one of the following is an 63x-z7j f yidgo3vf3nexample of a vector quantity?

  Which of the following operations w j q7(jab+t,wg)zfh8,zh v*yo ill not change a vector?

  Which of the following is /bj*cxb 1b(y f*xlc9ian accurate statement?

  The resultant of two vectors is the smallest when the angle between thegdtb4 cv8.i8-p ak3 wkm is

  Two displacement vectors have magnitudes of 5.0 bw9e.;1r el* rm4by (wobdmy9 m and 7.0 m, respectively. When these two vectors are added, the magb.yde;l e*bbo 1myw (wr9mr49 nitude of the sum

  Two vectors, of magnitudepbhrj +d*x(dr:-ng u7s 20 and 50, are added. Which one of the following is a possible answer f-u :g r p7*xjddbrn+h(or the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N,q -dvhpv /m8ra b7 2lcz//zf1q pull on an object in directions thbpzvc dz8/ar fh-lvq1/q/2m7 at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown qjpcgnd2l ;;dt; ,u4zu *kp5dvector is

  Ignoring air resistance, the horizontal component of a projectiledrs6s94yy ,/qvo* au z:ql c5j's velocity

  A ball is thrown with a velocity of 20 m/(xlpn*/hbt x*.hqk iz; ) w4bws 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 componmp3.hd+k tbg4ent of a projectile's accelerationbtdmh4+p .3g k

  A soccer ball is kicked with a velocity of 25 m/s at an anv0j4nsmuyq6o zl, ,w ,gle 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 objec nh joyeb pq9*la+,l *p.fgdw+ )an38xt is directed anti-parallel to the velocity npep da9 jha8 +,oy.nx+ flql )3*wg*bvector,

  If the acceleration of an object is always directed perperuh+evkr-, +i ow8i;fndicular to its velocitf ;krui,vhi 8 ++wroe-y,

  At what angle should a water-gun be aimedizz 0+xbn68a;es tj5f in order for the water to land with the greatex; b jzzf50 ne+i6t8asst horizontal range?

  An Olympic athlete throws -jbu bdovyspu5551x,xpm 2e59) rtjy a javelin at four different angles above the horizontal, each with the same ty,rdu b5o 555x2j ypjxmeupv)b9s- 1speed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 youctt zu)tl:jz( ax 4.jl8xk6* )aaigj-r hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first servel t8atlk:j*uic6jgxajazt )x (z .-)4) would be

  A ball is thrown at an original speedkkb3cbjqrxi : od 2,0, of 8.0 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 maxim1d1-uc+q h9lye+ gja1l*c 1 kkcdyhiq91p 2unum height, how does its speed compare to its initial skj-1candl+ci 2h*k 9g1uq9yq1c l1 d +eyphu1peed?

  A stone is thrown horizq11mkt zb7x t e77c yuz/ 1+hhqd.gql*ontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground belowe qzuzt1hb1 h77 yqlt*/g+ qm.71dx ck?

  A bullet is fired horizontally, and at the same instant a second bullet isnxh p4w5pc v.(f7)fq/ qi/njp dropped from the same height. Ignore air resistance. Co/ .nqfvi(/nh fj cp5p7)4wpqxmpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 78.5 m/s and at an ekqmat9np)f0ku5 m:y,+m :jow e2s4r elevation of 240 m drops a package. 2.2 seconds later it drops a second package. How far apart will the two packages su:0,)f9qmknm 4k m+j2 wrto5ae p:eyland on the ground?

  A package of supplies is dropped from a plane, and one second later an/0y7b5g0wo lh8x82ecipup8 g. jfih second package is dropped. N0nc57xhgp f l8ei0 8pi.guh2w/o 8bj yeglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speekvkqiavw.6y96+v y l1d. Neglecting air resistancyw6l9ka61 vv q+v.iyke, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on l c- vn/vhs)p 74vmy4qwz-qp;the Moon is only one-sixth of that on Earth. If you hit /ws-m l y-pvqhcqv;)474 znvp a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in t4y(sa8;blz- kirlj2a he +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relativa2b kz8j4;l y(sia-lre velocity of your car to the other car is

  You are trying to cross a river that flows due soppga 6s,b 8kop6c6lmwhnnco0rxc 18.,d *c)k uth with a strong current. You start out in your motorboat p) 6n.g8c0kmb1dp xc, s 8*opwn6kchlac6,ro on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Howh+kwros*q * r(yix6:e 7kb .ad much time will it take you to movikk.+b6raqws ory7 d*(* xeh:e 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle 68 nwe ubalj5v2*nl5b 4olkh,of 30 degrees below the +x axis. The y component of A ,eonul4 85vaklbnwj2 5l6*h bis

  If a ball is thrown with a velocity of 25 m/s at an *whz8m: zf:ucfw9imee aj1;5 angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight qow(p h5ra62 wmd )ovh t58o4iline in a direction north of east and you end up 2.0 km north and several kilometers east. How ma5hm5ptwv64(hod2a owq r8 i )ony degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity ic g 9 yf8x:nu8iw/m*aas 8.00 8 iafmw u:*gnycax8/ 9m/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 sha;1dbe z+pkc)ldow over a level ground. At what angle isk;b+e )dzplc1 the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What araeq;ite/ ( 4cpe t t;(e ec4i/qaphe components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) anrx2n l953(w9 lpwyw jed (-1, 3), respectively. What is mayj lwpr3( nwx52l9w e9gnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Wh -2p5x ,rggecohvvz);at is the magnitudep )v 2;v,ro gxhcze-g5 of C ?

  A car travels 20 km Wew 1)5f n4wsjg 7vgilc2s)4 8x4htjyx kst, then 20 km South. What is the magnitude of its displacement?jk14t f7sxy)wghj4gsv xw52 cn l)48 i

  Three vectors, expressed in C c4gw e7fvf5n+artesian 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 coordirih7*1d q +koinates, 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+a2x/4uze p-hb - qd7 +kj2odimaab+ g.0), what is the magnitude of vector C = 4a-b+do +m kixj72ge+hbp a/z2 qu -daA - B ?

  A runner runs halfway arou6 mm lx n4+c95spvjoh.nd a circular path of radius 10 m. What is the displal p4 xo+mn.c9mvs 65hjcement of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the ma)citj vy2n-x)gnitude of the resultant fx2ctj-i) )nvyorce?

  Two forces are acting on an object as shown in Fig. below. What is (ocm; c4ok/k96 3zu5 tdn t sjnq9b,bzthe direction onz obtknqtu5 ;boc9j64k 93 /(msd,czf the resultant force?

  Vector A is 3.7 cm lo gnfl3bz;6nh;dt3wq: e ,l r1hng and points along the positive x axis. Vector B is 7.8 cm long and p n;3 1 r: 6g3fqenlwh;bzdlht,oints at $+21^{\circ}$ 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 64 cm long and poi1-(q,cwv7rte fllt:x nts at $30^{\circ}$ above the positive x axis. Vector B is 23 cm long
and points along the negative x axis. Vector C is 29 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 with an initial speed of ml,kqtm 1:cl/22 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 2.3 s. What is the heighql 1lmtkc:,m/ t of the cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, from a bx, h3fas4 0p2he2ckb qw/y-ii ridge. It falls 15 m to the water below. How far does the rock travee3sp4/0i2hywia- f2 x h q,kbcl horizontally before striking the water?

  A ball thrown horizontally fx .zhz)dh xl;7 x/clr1rom a point 25 m above the ground, strikes the ground after traveling hohx;r.lxcd1 /h lx7z )zrizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 mrh zot*sb063 c/s at an angle of 0b s* z6c3hort$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump gos*)7,uq:mz iiqu8b wg es into the jump with a speed of 11 m/s at an angle o*7msi)wu: bz iu8q qg,f $25^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 25.5 m/s at an angle ok bpjo3inx8yw7;k23wf $15.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloc09jgirvlf762p:xx 5my e o)dn ity of 33.5 m/s at an angle of $32.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firef,ferd879ewuf m ss /5d at 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 horim 6vvanha53 3wzontally at 27.4 $m/s$ from the roof of a building 66.6 $m$ 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 ink;wfp)ht*d/)9m qi4(o gjgomitial speed of 65.7 m/s at an angle o mmk )(wpjo)/d4gg;t9qi *fo hf $41.7^{\circ}$ 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 a 1500-m race at a velocity of 4fkyke(.q:k 6r.0 m/s. If you ran the sameek6rf.k qk y(: race on a day 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,0 -wt4 .hr m;nsigh+)8cds zgc and is in a wind of 50.0 m/s to the West. The wti4 m ).;r8sdzcc0+shng-hg plane's speed relative to the ground is

  A plane is flying due Soutbi 9by*duox+0 yo/ )bxh ($270^{\circ}$) 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 spee(fb k544ycpbv/x jvo 4;uvu v*d of 120 km/h is headed $30.0^{\circ}$ 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 m/s horizt 2gmsdl t9h84ontally fires a projectile with speed 50.0 m/s in a 8t tg4m2dlsh9forward 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 in still water is 8.0 m/s, is directed across a rivop/cb2 7jk 4uqer with a current of /j oqup2kc47b 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that ca9 f*xvk qu9h u0e3fo;pn move at 12 m/s in still water wishes to travel directly across a river 1.5 km wide in which the current flows at 7.1 m/s. How long will it take to cross thkf3* ;vhf q0oxu99pu ee river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to travaeh 0 -c-o(tofel directly across a narrow strait in which the curhe-a- fooc(t0 rent flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a rukk/ apg e) 81tmk2vv1iver 200 m wide reaches the opposite bank in 6v)mk/ tku2egpav 11k8 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across z, d6,jnhth -pu9g 1;u gol2bla river 200 m wide reaches the opposite bank in g6lpo-g,hb unt2jdu9 1;,hzl6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in sto 7jb,fx xq.8ocg5w8 l(4s/dvnatp/m ill water is 1.71 m/s, must aim upstream at an angle of aj //7bw4d 5q ,(xcg8l.ovnxf op t8ms$31.9^{\circ}$ (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)  $m/s$