Which one of the following is an example of a vector quant xz6lo;ne e.7-v/b gbxhs0q-sity?

  Which of the following operations will not change a vector o-mcxrrqqg0(o/m fz, 9 (o*ci?

  Which of the following is an acw-*omk d/wgjhz9f7gj cq 6:3m pj 1k,bcurate statement?

  The resultant of two vectors is the smallest when the angle betwfts)2y,oxd6w:3hlw+ 8o d wxheen them is

  Two displacement vectors have magni gm*mndu7 f-tvu6l* ra(j -aim3r86x ftudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude*3u6 maglfnmtm* afr-rduv x86 j7- (i of the sum

  Two vectors, of magnitudes 20 a/6 2lrozjl 9ixs 5am8znd 50, are added. Which one of the following is a possible answer for t26ioszljz/a8 l mrx 95he magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull onncl.d 9a+cq4u an object in directions tha c.nu9q+la4 cdt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector9i fl+irubw( h)7+rk t is

  Ignoring air resistance, the hxkxnx;3 u7m8z orizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an fw56zi89xn /psj :)qn ,e npzet,(vzuangle 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 ofr)lb7+ lcccz)4 v3l zc a projectile's accelerationc bl+v)cr zc4l7c3 )lz

  A soccer ball is kicked with a velocity of 25 m/svlar db*d z kx a:79j/ky26x mcir1 ygyx1))u5 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 vectorif clger9hrdl5b6a4 8 7 o6f8i of an object is directed anti-parallel to the velocity fa8f 4l d6be96 rigc8o7i5rlh vector,

  If the acceleration of an or9 w.sz0*x so y;xyhtn g,3e.ybject is always directed perpendicular to its velocity zgysy*.09 wh o3 ,enyr.txxs;,

  At what angle should a water-gun be aimed in 8l*q em9ftop(v:8ec j order for the water to land with the greatest horizontal ( 88f*ojqtc m9ve:pl erange?

  An Olympic athlete throws a javelin at four different angles above the hori k:*e7zmg0 9mw:vrnwg/ s .nfjzontal, each with the same speed:.nf* 9gnwsr0w jkgez /vm7m:: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secdw)u1q lwa hzskqy/e/,5fec ,(p j:t4amuz8+ond time. If the ball leaves your hand with twice the velocity it had on your first throw, its hori4q/ ad me8, j+w ae)sz(wqupu hklzft,c y15:/zontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an anwck05xrz;w o ;gle 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 d+eptp ;kauu tqk) hsb kgl1*+z9)x*o- oes its speed comparubo)kzk9kaegut)++lt s1qp x;*h -p *e to its initial speed?

  A stone is thrown horizontally from the top of a tower at the,a;-h ):q qo*yqa wjgbef3hc1 same instant a ball is dropped vertically. Which object is traveling faster when it hi:j qhehc oq13*,qwa;ybg)-afts the level ground below?

  A bullet is fired horizontally, and at the same instant a6tt uw75gb;ff.fro4lcs0;uh second bullet is dropped from the same height. utfth6lo7gf 4u5r0fw b. ;s;c Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 83.9 m/s and at an elevation of 182 m wvplx +7- dmwl 34pgel5uyzk40 m3-qodrops a package. 3.3 seconds later it drops a second package. +-p705ull ompzexm4y3k vgqlww 34- dHow far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one secon) bc b5e(gif,,5 dvemhd later a second package is dropped. Neglecting air resistance, the distance between the fallee ,bi5v m5dcfh) (g,bing packages will

  A pilot drops a bomb from a plane flying horizon 7vjo/x5rh tgw4 +k5 j.nvzaf3tally at a constant speed. Neglecting air resistance, when the 5. + fo3a7 jjr5kgv/4 wzvtxnhbomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth owm-g:mykh8i: o (dqy d;rq5e. 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 Earteyrdd -8i5qm(g : ;qk .wymoh:h, the ball would land

  You are traveling at 55 mi/h inx mw)po07fi94kir 1xv the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity ofkfi4x17p)wi 0xo 9 rvm your car to the other car is

  You are trying to cross a river thatjq(;iwf+zutr /q (a( v flows due south with a strong current. You start out in your motorboat on the e( jf(qrqwt +(uzai/ ;vast bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at v zl3z.s c1yqd; -nwxxq2p( n430 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km wnxv23qp(zs-z nq;lx14cy. d/h?

  Vector A has magnitude 8.0 m at an .amxhw nx a/rb;nn:8v vod(9j 8)t2fg angle of 30 degrees below the +x axis. The y: h2 gr vxvfjxwd).9ta(88n/onbn m a; component of A is

  If a ball is thrown with a velocity s70qut9jy)l3 rx+aq 1vk v64fz8 jl pgi2w5 ntof 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 strainczph y:b im/qxal *up8di,k ui g5 9j77j:u,4ght line in a direction north of east and you end up 2.ji7d,/zi u x knghmu5y8:p 49: lcqpua,b7 ji*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 its vel +e)pshc1-a pgocity is 8.00 m/s. The angle between the direction -p) ah sp+c1geof its motion and the x axis must be

  A 400-m tall tower casts a 600-m long s2 tmmpa 1y; n2h/- wmkhosqs8vn6tyk0gp:j2 .hadow over a level ground. At what angle is the Sun elevated abs p6q.;hg0t2 k8sm 2/pwn2j o-nvhy1kat :mmyove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 39j.nov s5 x:(qqh hu x21dtje3), respectively. What are the components o.h1 xsd 5ue2vo9 t( j:njq3qxhf the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), g3m.l90p 1fn ore-dbw1 qymgv t6.5q rrespectively. What is magnitude of the sum of these.vyqf1gr -53w e01tmndb9grl 6mo pq. two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What9qs z2puem/ge 4 q 81cpg*6iya is the magnitude16up8 g 2zcqsme* gi4y 9qpa/e of C ?

  A car travels 20 km West, thenb1 t:e;1gw uwd 20 km South. What is the magnitude of its displacem:b11;tw u edgwent?

  Three vectors, expressed in Cartesian coording03* i- hrb7nqgl 6,lydflmq4ates, 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 Cazq j 4c.2a-gejrtesian 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)rbi;hj)sp5lm day . 5a /b2ox1 and vector B = (+3.0, -8.0), what is the magnitude of ve 2rhaajybo; x/bmpl5d)5s .1ictor C = A - B ?

  A runner runs halfway around a circular path of ra)64rhtgg0dmby a*+e upsc ,b1rb1ks+ dius 10 m. What is the displacement of the johs*16b rrtu)b, 0mps1+ag gcd4be k+ygger?

  Two forces are acting 2gi;n;z 2 uew6 kb6:oc*inh zkon an object as shown in Fig. below. What is the magnitude ofhzi;z6bw2 k*e6u:nic 2o ;nkg the resultant force?

  Two forces are acting on aax+wajxftmji99x 4h; 0(r +ven object as shown in Fig. below. What is the direction of w xit+vf9 +(mxx;ej 0arh4j9athe resultant force?

  Vector A is 3.7 cm long and p7sgtd3wnz9 ay+4v fw5q ;nc*joints along the positive x axis. Vector B is 6.8 cmjvnn9;qywac 4 +ts7*g3dz f5w long and points at $+56^{\circ}$ 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 73 cm long and points at fc j:*49xmq xe$30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 34 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 hori/og-o: k0mcie9 m2jj5vgxa8x zontally with an initial speed of 17 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 4.5 s. What is the height of the cliff?8 i/ojv m5a:gxe o-m02 jk9gxc

  A girl throws a rock horizontally, with a velocity of 15 m/s, from a +h6mf+k tunccum : 01zjuo8u-bridge. It falls 16 m to the w mcu+ h0muu61nc- ofz +k:t8ujater below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a (69w2 cz;i qlak(ie-wko6ujwpoint 25 m above the ground, strikes the ground after traveling horizontally a distance of6jwk eqliw26o cw- i;((azk9u 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s abhvqyh -m5 )y*.*zrag t an angle ofbv.5zymy* ah) *- gqhr $20^{\circ}$ 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 oyg0 nq9d22d.tk.agl a speed of 11 m/s at an angle ofy a2nd2l0.o kq9t.dg g $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 221og 4nbt ) up4d.cufq3.0 m/s at an angle of $44.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 24.4 m/s at 8 srrgyd0g(* dan angle of $14.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firj y2 cqn9 h-,dd3c4hbied 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 horizontally : jhg7yvvmpzd ;tcq )y/60zha)/rru7 at 22.7 $m/s$ from the roof of a building 68.7 $m$ 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 initx9 z qosm,p*bx62k0yqial speed of 41.5 m/s at an angl*,sqx96yp zxbqo mk 02e of $37.4^{\circ}$ 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 1500-m race at a velocity ou: hh0,5 -rt3yhbxphgpi p8b*f 4.0 m/s. If you ran the same race on a day when you had p:y0pt53*p-bh hu8rxig ,hhba 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 b* 05rolluhwpk: v 5.bto the West5wo hlubv.pb*:lr05 k . The plane's speed relative to the ground is

  A plane is flying dueu: tpr fk4n;gpx+7. bz 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 speed of ,ah*q q ez0t,q120 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 horizonbehxfi:(m:s:h)c :h u tally fires a projectile with speed 50.0 m/s in a f(::us hhh:m) b:cxfeiorward 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 acrf7l/a93 v-xy;h0sqr rqwwdo ;oss a river with a current of 6.0 m/s. What is the speed of the boat as it crosses th /wa9 d-qos;37 qlfh ;0rrvywxe river?

  The driver of a motorboat that can move at 12 m/s in still water7 z+ )t5u.q/x0 m7amqt if6ni(exase d wishes to travel directly across a river 1.1 km wide in which the current flows at 7.6 m/s. How long will it take u05 e+zqamme x q.6)f/t i7isdx 7ta(nto cross the river?

  The driver of a motorbox4:zl/ix us f,k13fqh at that can move at 10 m/s in 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 heax3sz4ffqi,:xuh1 lk /d the boat?

  A swimmer heading directly ac5vz t2jn hgu)p 40ocse*l e3s4ross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can sh3zlst s)h4vjneo0uc 4p*2e 5g e swim in still water?

  A swimmer heading directly across a river 200 m wide reac8d2a6 gnvynr57xdow1lx2 9d whes the opposite bank in 6 min 40 s. She is swea 2d 5y8w7d2xon6 gwv9ldnr1x pt downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.10 m/s, must aim upstream atudm28h ;q p -pcnfg,ocfnf; .* an angle of ;uc-pmd8 gf2 q on, hffp*n;.c$17.8^{\circ}$ (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)  $m/s$