Which one of the following is an examp1o mbcezsoh1e- 1c o+)le of a vector quantity?

  Which of the following operations wil 7x5-ns*5 3cqc yz burzvt+ac1l not change a vector?

  Which of the following is an accurate statm730cnijmi o5ement?

  The resultant of two vectors is the smallest whel;o hy,ht;*zg n the angle between them is

  Two displacement vectors haven/qq.0 3rdleu v u,g.wt3v65dkdu4an magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitu.a v5u 6qgtu3d/ dru04.,ql n3 vdnwkede of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which oneu.m qg0 (6t(rk)dje2wkms vi, of the following is a possible answer for the magnitude of the res6q uw s( 0g.ir)dmktmvke 2(,jultant?

  Three forces, each having a magnitude of 30 N, pull on tr tu,j ,74eihan object in directions that are 4 ,ruetihj t,7$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkn9 3hcbv ym7 i61x jws,j(ouqn*own vector is

  Ignoring air resistance, the horizontik9ug:k+w2 l eal component of a projectile's velocity

  A ball is thrown with a cd*sn5+emz 9evelocity 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 k+z / n2p6i0jr *i t2gjr.sp*kg+c hsfof a projectile's accelerationf 6js jt2. p2p+gs *rgickz*i hkn/0r+

  A soccer ball is kicked with a vegfjat :jue) hb3g7sh 4gzs3:2locity of 25 m/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 directedr)hn1lyxaa(g k, l 1clyvw:l1 t *0py2 anti-parallel to the velocity vec2y*)g, n1k a (x:vp1chwlryl0la1ytltor,

  If the acceleration of an object is always directe 10jijg br62,bjkt wt:d perpendicular to its velocity,6 rtj t2j,0w:gk1jbbi

  At what angle should a water-gun be aimed in order for the water to gsg 1lq1ibq/ .land with the greatest horizontal ra1bqs/qli1gg . nge?

  An Olympic athlete throws a javelin at four different 7l 8z(t9pf tbkangles above the horizontal, each witl( ktz b7fpt98h 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. x 1lmcks2,o78 kq(xrs If the ball leaves your hand with twicoqsrms 2(k k 8l1c7x,xe the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0v-cxs8puon a6.1/uc f 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 maximum6l11az(p o7 p ofoe(jm height, how does its speedefl (j op1pz67(ooa 1m compare to its initial speed?

  A stone is thrown ho6r92 po1ipm mpf2 mmc0lexl88rizontally from the top of a tower at the same instant a ball is dropped ver0 mcm 92iol pp1 86e82rfmmlxptically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and mp 2*r tgqjhj1fegk653 h;yt:v)+qv s at the same instant a second bullet is dropped from the sa;+hg12g*q5rh)vm 63:pe yktqstjjv fme height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 79.3 m/+ bse n4ah0u++yit8g9 hwzk2a s and at an elevation of 251 m drops a package. 5.7 seconds later it drops a second package. How far apart will the two packages land on the g++ik ehn284+buzwhtaa9gy s0 round?

  A package of supplies is dropped from a plane, and one second later 2x *z :wwzcbm3frv 8z;-l9 oboa second package is dropped. Neglecting air resistance, t o8oz9l :rb* zf2bmw;v-wc3 zxhe distance between the falling packages will

  A pilot drops a bomb from a p4bhoi w bf 1:xaw;5rm9lane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the 49baw fimoh1bx5w :; rground the horizontal location of the plane will

  The acceleration of gravity on the Moonq xaxt1vr)j6* is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angv)ja1*x 6qx rtle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a 5qe2aihb+/tg straight, level road and pass a car traveling at 45 mi/h. The relatiti52eh+ bag/q ve velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong currekcoc *v76my r1nt. You start out in your motorboat on the east bank desiring to r yk1m vr*c6c7oeach 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. How much time will8zge(y/ q4bx ih4g,eg it take you to movgg(be4qiz4 gx8 /h ,eye 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 axis.ftifepbw7jo3 ,y;i7he 0 /9qs The y component 03bjohf/i p7is e,wt9e7; yqf of A is

  If a ball is thrown with a velocity of 25 m/s at an .()* xglp40 qir30i fekpsx abhi)w4g 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 dk 1 i8fd8ynvf3v,vy6girection north of east and you end up 2.0 km north and several kilometers east. How6v,1iv kd3 vf8yfy8 ng many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is uccai 6ia886v 8.00 m/s. The angle between the direction of its motiu i866ca 8acvion and the x axis must be

  A 400-m tall tower castqg 7 eaxv.e8eehhj 4..s a 600-m long shadow over a level ground. At what angle is the Sun elevated above.xh4hqag . ve8e7ee.j the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wc w*dk.48i 6 :e2qvaqgoiso q7 3mzs2yhat are the components of the sum of i6v:s 3k d7oe.*82mg4is aqqc zq yo2wthese two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What is0 qo( 82kmcq1j mp2wzs magnitude of the sum of 8qk2 qmjwp2zs m1(0octhese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector s,(:6 qop x1fc4r memlC = A + B . What is the magnitudexp:m46 m1q,fr(s oc le of C ?

  A car travels 20 km West, then 20 km South. What is the ma2lz8efun) )fkqkp/ x.gnitude of its displac zxf)p8f.kqu elk/ n2)ement?

  Three vectors, expressed in C.;rbbr 1dxm 65zg7np dartesian 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 coorv(, fhn ,oq8xxw)lot*c i /ig- ep5y3zdinates, 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), whavj;s cj) e -)nq.mj/kn wst h+4.oqrj9t is the magnitude of vecto q)+h)wjsn..kr cj/;e9n4 j- svmjt qor C = A - B ?

  A runner runs halfway around a circular pathivrj 9b,c)wp5*uf9 gj of radius 10 m. What is the displaceme rp*9fgu)5jv9w,cj ibnt of the jogger?

  Two forces are acting on an object acvpk6*i i 3y1lt) sn-as shown in Fig. below. What is the magnitude of the resultant ny c6-1 vpa* )ik3slitforce?

  Two forces are acting on an objjox*s1r** hu)5 3ju vrcp9pllect as shown in Fig. below. What is the direction *jusj *) roc9hru1xp*ll pv35 of the resultant force?

  Vector A is 5.5 cm long and points along the positx j; vld4f4ib18(a gtgive x axis. Vector B is 7.0 cm lon ;v(1fl4bj dgtax84 gig and points at $+41^{\circ}$ 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 76 cm lo:4 .jx /doclysng and points at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 22 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 spee72c;stvsvt sq4 or 4c0d of 26 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 ts4q 0r t7s4vc2tsco;v o be 3.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velm*92qguit/ei3od. o fl snn2-ocity of 13 m/s, from a bridge. It falls 30 m to the water em2isg-u. if qt92nn*o/l 3dobelow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 25 m above the grx1cr+aus(cpn( 0*jbi ound, strikes the ground after traveling horizontally a distance of 21 m. Wi0sxa1+bcp i( (j*urncth what speed was it thrown?

  A jumper in the long-jump goes into the jjfl4e;h m0cv9r+jh9 y*y2u npump with a speed of 12 m/s at an angle 9 40my*ru +plenhh fj92 vjcy;of $20^{\circ}$ 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 jump with a speed of 14 metb 3-a al:e i4lq4boh( ur98kw-.douyc./jv /s at an angle of v-hwe 3:d 4o.uu.9a ek-(4t8oblr cjabilqy/$23^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial vets4: b 5iaix,b(d;hljlocity of 39.6 m/s at an angle of $21.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an nsw r42 ,dkge+initial velocity of 23.1 m/s at an angle of $10.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang 4gykpqu4(5v sle 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 odz dc 3e1-pl425.1 $m/s$ 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 initial speed of 67.3 m/s re3fe; nj+0vo ey9+)s1 tolji at an angle of fye03) n++ osejjl9etiv;r1 o$38.9^{\circ}$ 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), youx6hn0pg91kq b can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same 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 top6h gxn91b qk0 finish would be

  A plane has an air speed of 200 m/s due Nojqn4n lm6: q e2j )fmg (a0o).uh/pqntrth, and is in a wind of 50.0 m/s to the West. The plane's speed relative.2nq t a(fjmul 6n4p)oh g)mnjeqq/0 : to the ground is

  A plane is flying due jj/ .k;*1ivqzvt i b,bSouth ($270^{\circ}$) 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 heade:hhj */swey imke7z77 d $30.0^{\circ}$ 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 horizontally fires a projectile with spefpp6wy v*8np;(v *z mred 50.0 m/s in *z*(yv 8pv nmwp6r;p fa forward 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 gj.+ din 6ycs2across a river with a current of 6.0 m/s. What is the speed of the boa 2i+nsy6.cdj gt as it crosses the river?

  The driver of a motorboat that can move at 16 m/s in still water wishes to travepn2y /nvt++g- f(deufgo9v 0l l directly across a river 1.5 km wide in which the current flows at 6.9 m/s. v+ yg+ft v0-l2ep 9du/nof (ng How long will it take to cross the river?

  The driver of a motorboat that kf;6mva .us-r0 kg/agcan move at 10 m/s in still water wishes to travel directly across a narrom-;6rkvuag.fa gs/ k0w strait in which the 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 t82 f)wbd wur8bhe opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swi2dr8u f b8ww)bm in still water?

  A swimmer heading directly across a river 200 m wff+ /y 1dvllta0 7jhsud:8*voide reaches the opposite bank in 6 min 40 s. She it offv1vl:djdyl/s *8 +0uha 7s swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.57 m/s,up8 o(xa m-b)c must aim upstream at an angle ofa(ob-8cx u)pm $12.6^{\circ}$ (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)  $m/s$