Which one of the following is an exampl v gub3,)wq1yy pec;j-e of a vector quantity?

  Which of the following operations will ne* vo*:0nskcq ; c6eoqot change a vector?

  Which of the following is an accuratevz;bd,l6k* ih statement?

  The resultant of two vecyja at9j1z2hvcy+p1+ llm2q3 yi8 vk3tors is the smallest when the angle between them is

  Two displacement vectors have magnitudanm6z )oav 3.n2gcg. des of 5.0 m and 7.0 m, respectively. When tdgvnz.6)a3ac n2m o.ghese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following) )0on owksk0g12cw va is a possible answer for the magnit20sa1gnv0oc wkw )o)kude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objecc5qbbr;6p:fm t in directions that are :pf5 q6bcbr;m $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tbxm90juyrvs5n))p j23 w:9bshgp 9 ethe unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velocit 3 r,ug+un(goi0pxhail+bn8 8 y

  A ball is thrown with a velocity of fn8cxw;isq .k02 4jth20 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 accelerat*h8muzb(co5 (p ynlm,ion,o (5*hm u( pcym8zlbn

  A soccer ball is kicked with a velocity of 25 m/s at aydkarq(ak h;d1omz*hjl .x w+91h-v+n 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 4pr9qu94uyrxs mmeec +m .m; 7jz5q/pof an object is directed anti-parallel to the velocity vector,urq u r5;e+e pjzmq97p4m scxm94ym/ .

  If the acceleration of an object is y6f mglvf d s2-jyzut02 er4(:always directed perpendicular to its velocity,- f0gf6t:2d 4yrl(e ujv yszm2

  At what angle should a water-gun be aimed in order f l y54j06yaj8ddoahu 7sx ,gp;or the water to land with the greatest,sdpyjyg d8x j5aha4 0o;76lu horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizo uii vf(+r-4p+7his8mgnc i4untal, each with the same speed:cg+uvsi 4uifm(rin -87+4p ih $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for cnypurql 43 i1yrs +.)ucp-wg i0:wo r (kxg(-the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizourgx1: i r.w cyu( y c)pi0l+(swr 34g-ponkq-ntal range R (compared to your first serve) would be

  A ball is thrown at an original speedm2p 7o abnu(zp7 m5q8q 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 maximum height, how does it43g w(gniti+jlj h7x2b e*,x hs speed compare to its i4l *3n7g (bxi e+2jhti,jxh gwnitial speed?

  A stone is thrown horizontally from th 98 t,ltvr2 xcnixv+6de top of a tower at the same instant a ball is drod r6tilx9xn 8, vv2+tcpped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontaloi4mnh4d u6 9gly, and at the same instant a second bullet is dropped from the same hh64u9n dm4og ieight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 57.9 m/s and at an elevatio+99gdx9 g pgtt5m drk1l5qt dob( ur/3n of 296 m drops a packag3x d1 gbqmgg9ko9ttp9rl( tur55/ d+de. 7.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped 7s:9sh35phl( rzakw k from a plane, and one second later a second package is dropped. Neglecting air k3:azhh sk (9ls7w rp5resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontc qy1gut8oe46 :kdde u-w+hd8aw/uls *ngv +,ally at a constant speed. Neglecting airg- sog+v6ca h1utd:q+ /,dnu4w8wuee*dykl 8 resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity ons awr1-k6(x;gsx:vq +x hki2v the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at x6vi(sq; k2xwg 1rs -ha+x:kvthe speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axsfu7k7 lhb,l+pc 97 ltis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative veb,7 s t7l9l pkhf7cul+locity of your car to the other car is

  You are trying to cross a river that flows due south with a strongg s42 z q7n,(zdldqw8tn.*xw): stthz current. You start out in your motorboat on the east bank desiring to reach the west bank directly west frxdw7t2n:s*4,8wgzt h qdz.sq () ntlz om your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time w zs 3p/,4pm2pbq/cwm: cmt6aa ill it take you to move 12 kq:w23 z tbcpmm, m/aapp6sc4/m downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrt8 j93uill,tua 3t i;bees below the +x axis. The y compoa3j;,tt 9u illt38ibu nent of A is

  If a ball is thrown with a velocity of 25 m/s qx1x4xt d 1zwa.ar,q9at 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 directionrm v3u-osize8jzg.9:imkvpo) .)b 6e north of east and you end up 2.0 km north and several kilometers eas) ikmgr .je9z. vm:68z os-eiuo3vb)p t. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. Tgch 5n*o*ojajf(8 7as,bw*w vhe x component of its velocity is 8.00 (oo8jcs va h57 *g*fbw,an*j wm/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 legv n5 t-it*:f 0ytp0ievel ground. At what angle is the Sun elev *ft:nt vii-0peyg0t 5ated above the horizon?

  Two vectors A and B have componentqm ,njunzp 9woe1)96ts (0, 1) and (-1, 3), respectively. What are the neqow pn zt9 ju),16m9components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. W;a e34syqae)pl+xj b(:xfmq, hat is magnitude of the sum of thes ;y:sq,+)bxxaj4 mq(lf3ea pe e two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vechy.v7pk +xh 5p:le 2qm 5f ovdzlj1v;6tor C = A + B . What is the magnitude of7;5f:h yexqo p+k5h2d1pljv6.vz mlv C ?

  A car travels 20 km West, then 20 km South. What is ths87t,qqq zl1gp 7q :h(w9 oe2wwozs9 ae magnitude of its displa9 z,swg wpah qq7t8s7:(2wo9lqqzo e1cement?

  Three vectors, expressed in Cartesia6d5 hyl8pg +han 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 Carj+cpz,v, f6w ktesian coordinates, 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), what is the magnitude emgrg)(fyl.3n vu+c( of vece uvr(c3mf( gny+ )lg.tor C = A - B ?

  A runner runs halfway around a circular pasguvx0mc +e,3km: l f,r ::umuo5sxc3 th of radius 10 m. What is the displacement of the jmcu: er:ux5usc: ,gkom0vfs l3xm 3+,ogger?

  Two forces are acting on an o;7 nf a)rd7cbvbject as shown in Fig. below. What is the magnitude of tf;77d cb)a vnrhe resultant force?

  Two forces are acting onq/92fbp(bv ;6u x sg r/p/lvevfl,q4f an object as shown in Fig. below. What is the direction of9v, sqx6vpbp/le u v/(2;fg 4/bfql rf the resultant force?

  Vector A is 4.5 cm lon.. am2 liaxeyq4;opd9g and points along the positive x axis. Vector B is 8.9 cm4; oe axda2pm. yq.l9i long and points at $+42^{\circ}$ 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 66 cm long and6 dzwkw.x:q 1d points at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 20 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 26 m/s from thl 75 uyid1kos i:p(o1e*ytda(e edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.1 s. What is the heio5sikaudp :t e1*7i(oyl( d1y ght of the cliff?

  A girl throws a rock horizontally, with a velocity o j8u i 6ayecllf*1.o(af 16 m/s, from a bridge. It falls 16 m to the water below. How far does the rock travel horizontally before striking the water?cy*o1l8f.eaul 6i(j a

  A ball thrown horizontally from a poi zme;5s6dc/o fcdqldy*t p2+ 6. 8by mur4tf:vnt 29 m above the ground, strikes the ground after traveling horizontd/y:t;dy2m fqr*4lb5pef 6dsu8 6z+c vm cto. ally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spee /0xnb) -3es,wsp riecd of 12 m/s at an angle of,3xi ) wrse -cnp0b/es $20^{\circ}$ 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 w -x z 5xu:jfxb*3dbsg47vgm+nith a speed of 13 m/s at an angle ofum53 4gjxzg-xbf b:d+7n*svx $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 36.7 m/.v; k4w zbt/ :ws0fnmzs at an angle of $25.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launchq 0ceo;z,:y m i,kzm().mnn pf0.k qdied with an initial velocity of 23.3 m/s at an angle of $32.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired abhd e2b.i* vcv:9 iyw6t 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 horizontallgcrqh))r m2(oy at 20.5 $m/s$ from the roof of a building 53.5 $m$ 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 fromq6jyrncg)yy 5cart )1k iu /2* ground level with an initial speed of 49.1 m/s at an angqiy)naygr6 / ctujr5k y)1c* 2le of $45.4^{\circ}$ 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 (d4vgln+5 c0ldecr/*p pw9f y1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had acw4np+eg (cd9vp 0/ rdyl*l5f 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 dlf y*y8mmur.pwzx,9w r d+-; of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's -m*.wdzxf+;u 8d rml ,r9pywyspeed relative to the ground is

  A plane is flying dunxj*6.sb o,gc(fic4 ae South ($270^{\circ}$) 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 speedo;oanx73 2wn); gdw9lxtb2 qh 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/x ;n-jncf: ono)f4 hp+s horizontally fires a projectile with speed 50.0 m/s in a forward djh :n-n o+f f)xnpc;o4irection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stilqrv +die0o o2ck3n84kl water is 8.0 m/s, is directed across a river with a currentke8q2 do4+30r ckon iv of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorw m ;ar7rki 1r(bwi7:oc7n7zn boat that can move at 18 m/s in still water wishes to travel directly across a river 1.4 km wide in which the current flows at 5.5 m/s. How long will it tak;ir rw77r 1 :k7 bwann(mci7oze to cross the river?

  The driver of a motorboat that can move at 10 m/s 4-t 4d lc;)k5jm7z7+zto dohcvpnc9xin still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver headt49x dz odtlockmvcp7)z4j n7+- c5;h the boat?

  A swimmer heading directly acr 8c3r 9+vr xb5r9stewa:*e xt z+(bslxoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still w+xxbc t :rlvt*3rs89xraz5es(+w e 9bater?

  A swimmer heading directly across a river 200 m wide 5kgszwd)/r . treaches the opposite bank in)zrw.td5g/s k 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in stilw/+b s;k +hlkil water is 1.01 m/s, must aim upstream at an angle of i+s; hbl+ k/wk$22.8^{\circ}$ (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)  $m/s$