Which one of the following is an example ofisyz ))-z3+chd v g*ui2jafv.o g8+no a vector quantity?

  Which of the following operations wil l:dajmuq5n;3 l not change a vector?

  Which of the following kd 8rij7x-d; pis an accurate statement?

  The resultant of two vectors is xx *vf zap9(sb,qr6a+ the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivelyg-3iq:ys0m ,atd 0 qor. When these two vectorysq00to,-dm :g arqi3 s are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Wi nronu/ gj4.g,ce;j5hich one of the following is a possible answer for r;ggoej /jc,nn.ui45 the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dir52fi2-fdjfw qbh vs 871xeo)f40djx uections that 8oeifxw q1s vd0fx47ufj-h2fjb )d 25are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the u*( kte,q w+k6r* q3*h zgk vo,j*szhqmnknown vector is

  Ignoring air resistance, the horizonta/,i+xda t);u /3 tm mou(b fa7wvfb1*1jzffxll component of a projectile's velocity

  A ball is thrown with a vewa5*srnd .0wolocity 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 horizontekk jdd;5b 8 6m4jew3ual component of a projectile's acceleratione83 6ew5 u4bkkjmjd d;

  A soccer ball is kicked with a velocity of 25 mrhp:;d) 4re,fzk gok 4/s at an 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 antzpz6m nu+80xi)pp yz- i-parallel to the velocity ve-m0)6 znipz8p+x pyuzctor,

  If the acceleration of an objck u4vs:mz5c+cxj *c8x)9o tject is always directed perpendicular to its velocity,umsj o+xcc jcx*vt8945 kz :c)

  At what angle should a water-gun be aimed in order for dxq.m.kc4vb8 the water to land with the greatest horkxmb8v.4 q.dcizontal range?

  An Olympic athlete throws a javelin at fw2ppoqps r)0t)/ f q,4eegfj:our different angles above the horizontal, each with the same speeqqjrtso gf,p)e4 02w :/pp)fed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 leaovj 18mdkd7vg d/.n :jves your hand with twice the velocity it had on your fivj/g md.n7: ojd1 kv8drst throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angtv j v/:9udpa):4( tktrott;k le 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 ijl)) :*h ahi5oyw .utdts maximum height, how does its speed compare to its initi wtd: hh5i)ya.jo u)l*al speed?

  A stone is thrown horizontally from the top of a tower oah ,)(p7xvxm at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the leve7xahm,op)(v xl ground below?

  A bullet is fired horizontab5 ekk 0ccsf1;l+v:fklly, and at the same instant a second bullet is dropped from the sefc1 f 50v l+;ks:kkcbame height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 119.1 m/s and at an elevation 8 ;2)iwn3qnaq7enap z of 252 m drops a 3)wi q7aqezan p2n ;n8package. 2.5 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one seconddvdon* o c(ao;ol5. dfj*n2(b later a second package is dropped. Neglecting air resistance, the dista*vdjo doc.na;fbd( onl o52(*nce between the falling packages will

  A pilot drops a bomb from a plane flying horizontallyc4n ,asnood6: at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of tono sa46,: ndche plane will

  The acceleration of gravity on the Meh *)dmmhknv9(j/tvb0k,-w zoon is only one-sixth of that on Earth. If m(-wm0z /) hj9vd*b,kk vhtenyou hit 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 the +x axis relative to aa*l b() zav/h-m 65hjktd9ef b straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car i j 5 69ad(/fz hvh)ea*-bktlmbs

  You are trying to cropm 39c6ifcj0gss a river that flows due south with a strong current. You start out in 96jg0cmc3if p your motorboat 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 stilxmxjmw 27w4.x)og:i)4cf bpgz-f m4al water. How much time will it take yo.-omw w4zxmfc: g74 paj)42gxifm)bxu to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axbvai sgj/ojnm:/-zei a an*+0q(sj 40 is. The y componenaj0iao/+aesi v*n bj - nsqzg(m:/04j t of A is

  If a ball is thrown with a velocity om+6l pd5w1jjva e2l7gf 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 line in a direction norg l5bw5ip6yn 3+auyz *th of east and you end up 2.0 km north and *l 5py5u ay63bgiwnz +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 itsworri lb27v. - velocity is 8.00 m/s. The angle between tblivrw7 -2 ro.he direction of its motion and the x axis must be

  A 400-m tall tower castsisa kpbt9po*2b(+q w2 a 600-m long shadow over a level ground. At what angle is the Sun elevated above thq(w+*2bi bokp 9 as2tpe horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), r t2ucko )hvi u,*os*k 92stm;w 0ogi)uespectively. What are the components of the sum of theoho sw,it;2uk9ukm ts)*20g c vo i)*use two vectors?

  Two vectors A and B have components vs/k.b xw(o zfzf 3a 4jg)wwkta0+ ,)n(0, 1) and (-1, 3), respectively. What is magnitude of the a+.(0jfg w4w wb) sx)z,kkav3nz t/ofsum of these two vectors?

  Vector A = (1, 3). w 0s xk,v;ajmc2gq(1z1u+mm0jgqqv 1Vector B = (3, 0). Vector C = A + B . What is the magnitude m1 kg+ ua0;(j ,vswqvzxqm1qc0g mj21of C ?

  A car travels 20 km West, then 20 km South. What is thek** +a)z.ziaxr*ov .aml (fhiy1uel4 magnitude of its displacementi)xl( hl*rum . .vz+io 1yaa*fe4*k az?

  Three vectors, expressed in Cartesian coo z3gp5:nr-fn/y (fnj2a uex4 rbv 0a:yrdinates, 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 coordinates, are poffa oi 2vfxlgw,fx8 5n+44;
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), what rqph 9km*yah(;/.w de is the magnitude of vector C ae9hm(w*/; .pqkd hr y= A - B ?

  A runner runs halfway around a circular - gvm ,tgl9+kzpath of radius 10 m. What is the displacement of the joggervg -l gk,t9zm+?

  Two forces are acting on an object as shown wal)jo py :q bwe00z*nn crj++g:e:)yin Fig. below. What is the magnitude of the re c:bqnee0* j+yzlwy j)w)r:gonp : +a0sultant force?

  Two forces are acting on an object as shown in Fig. below. What is thl,i:g)w 6j ueae direction l6,ig w)u:ejaof the resultant force?

  Vector A is 3.1 cm long and points along the positive x axis. Vector dth 6vi,8jl 5eB is 7.4 cm long and poie5,j vlih6 t8dnts at $+24^{\circ}$ 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 65 cm long an v cml1wfu qj,i*c,z)3d points at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 45 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 initi/ o * uq;(01btl5 3uxza:bqvwin6np hoal speed of 30 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 2.9 s. What is the height of the ; balt5ho6b nuwqn/ z*i vqu31(p:xo0cliff?

  A girl throws a rock horizontally, with a velocity o3:7ze ( iazsf(w 3bkh0xdy 8nmf 15 m/s, from a bridge. It falls 11 m to the water below. How far does the 0d3 zxfs a bny( kem3z:h8w(i7rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 25 m above the ground, strik:3.yb ophgr1uawho0 f*(vg7e es the ground after traveling horizontally a distance of 17 m. With what speeeah( gg*ur.h yo v:3pof107bw d was it thrown?

  A jumper in the long- g,/2yse 3tt nsvla4u7jump goes into the jump with a speed of 12 m/s at an angle of vl3u24seast ny/t, 7 g$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into the jutabb c)b8 y:c n4z9: f3ql.kudgh oo+:mp with a speed of 13 m/s at an angle of 8gzbb+f: acy )9 b 4 ulkhoc.t3n:qo:d$19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial vptw r28eqnmtbqk0qw4 hie + 5l( u7z(0elocity of 50.9 m/s at an angle of $37.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity w6-b x51;n1nagh2yydrh c g/vof 55.7 m/s at an angle of $48.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at 9 :fsi k.bqj/7v8d 6boaupln,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 horizontally at 24.jydn* uzvwi .u-j4 y aw521f7o(zbh :lo9s :vb7 $m/s$ from the roof of a building 68.9 $m$ 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 izwtb)vi0; b7 initial speed of 45.8 m/s at an angle o;b)w7t z0ii bvf $41.2^{\circ}$ 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 aiwinlwoa6ef; 6bh3*;lw95b;b p ;rkuf5)s zlt a velocity of 4.0 m/s. If you ran the same ;)iab 5 fohk6i*;b5lw p;l;efz9bwsuw6ln3rrace 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, and is in a wind of,+(a uegptm 1p 50.0 m/s to the West. The ampu+ge1t ,p( plane's speed relative to the ground is

  A plane is flying due Soxh:q 1de beb,n9(,m hxuth ($270^{\circ}$) 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 o2,yxxx*rv 9fof 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 h:gra3d/o v4 tvorizontally fires a projectile with speed 50.0 m/s in a forward direction o3d/rtv:a 4gv $30.0^{\circ}$ 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 direm,t20n* tb f/l jvfxm :ug:od4cted across a river with a current of 6.0 :m 4 mlx /t fjtfo*gdbnv0:u,2m/s. What is the speed of the boat as it crosses the river?

  The driver of a motornsz 96c kqv1yb025vuxboat that can move at 15 m/s in still water wishes to travel directly across a river 1.4 km wide in which the current flows at 5.2 m/s. How s0vxnvc 5ybz2q6uk 19 long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes t -y ytsrofdn) *kd174to travel directly across a narrow strait in which the7rt -sn *do1)dtk fyy4 current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposizd7k; flb4mi5*v 8ta1 01sooke :ra uwte bank in 6 min 40 s. Shft1:eo 81wa s;* rv d4mbk07alikz5 oue is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bankxcu atrk a5dz hjg;lbs 5d*f)v+.b(9* in 6 min 40 s. She is swept downstream 480 m. ;ktghdxb *l)559f z ac ra bdu.jv*+(s What is the speed of the current?

  A boat, whose speed in still water is 1.w 2 go9 8ql*mcb 7;lm82doiz ;blbhoe:61 m/s, must aim upstream at an angle of o7o2iz;* odhqmg8lm2ebb8l:cw ; 9 bl$30.8^{\circ}$ (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)  $m/s$