Which one of the followingeeibu6 7k,1d)u h(3mqege wvo/.ko7 a is an example of a vector quantity?

  Which of the following operations will not change a vecto6,p m-6fljd6ey ad0wgq+h9r a r?

  Which of the following is an accurate statex,5ili)4b a (m;x) x9q dribidment?

  The resultant of two vectors9 2s mifuc4y5s is the smallest when the angle between them is

  Two displacement vectors have magnituf;/, ht vipoz8des of 5.0 m and 7.0 m, respectively. When ttih,/ ;fpoz 8vhese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the foc0f ,myrs hj,8llowing is a possible answer for the magnitude of the resulf sj,8y0 ,rcmhtant?

  Three forces, each having a magnitude of 30 N, pull -ow/izg 7mau 2j;5pln on an object in directions that are -oj;zalnm/w7 u2i 5g p$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the tbdfzl m*8:c-n, vs it-op0(iunknown vector is

  Ignoring air resistance, the horizontal component of a projectile' vj;6nmjg8srjlj 4g ur7a-+u// 3nnfqs velocity

  A ball is thrown with a velocity of 20 m/s at an an:ftl) fb6 d5imkp 9-gfgle 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 tyur o (pr0hdkui c634y77;ye horizontal component of a projectile's accelerationu;yok4ti dh637 7ur(ye c0pyr

  A soccer ball is kicked with a velocity of 25 m/s at an angle o 7ej0tb, awt*;tczv (lf $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector oyo32yy1:ba1ggm wfhpad 2 ohv.58g6uf an object is directed anti-parallel to the velocith 2vyd2uf. mbp haggwo31yoagy58 :61y vector,

  If the acceleration of an object is alwaybk rj7ij+r irk/;at er wq, (6/oja))ys directed perpendicular to its velocity,ob r ki;6ie(r )/w )jjy+rjta 7aqr/k,

  At what angle should a water-gun be aimed in order for the water to .p.zzd)oy d w(hx-8wnland with the greatest horizontal.zw)n yhox-p. w dzd(8 range?

  An Olympic athlete thjd*m ;krh:kz 6rows a javelin at four different angles above the horizontal, eachmr; jkdzk:6h * with 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. I-n5w svb w; ebleo7h1*f the ball leaves your hand with twice the velocity it had on your first throw, its hewn lo 1;*bwhs-b ev57orizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s ai *e o 0wy9pc7gj:0wmzt 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 )q-ij i uu:e(d ji-w f0i2fa9jfield goal attempt reaches its maximum height, how does its speed compare to its initial s i :euii9)ufwd(afqij--j j20peed?

  A stone is thrown horizontally from the top of a tower at the s0 v .nvh5)jk a)k1dn ht,06nbak)rj ename instant a ball is dropped vertically. Which object ien5 n,j0a n)k)hhk6vd kbaj1 v0nr) t.s traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the samw j)yep*x4f +me instant a second bullet is dropped from the same height. Ignore air resistance. Compare tp w*xm)f4j+ey he times of fall of the two bullets.

  A plane flying horizontally at a speed of 102.0 m/s and at an elevation of 17k g+:tvu7:mtbu(ra8s p l8 (yp4 m drops a package. 4.1 seconds later it drops a second package. How far apart will the two packages land on the gryrv7k: t8u(m asgpt+p(bu8: l ound?

  A package of supplies is dropped from a qufs/k t )nx l *h 0)4wpck/dm3j tz6gkkb0h82plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packagktbk0fd)kx c p*ht8w k)4u/ 6nh0jl2szgq/m3es will

  A pilot drops a bomb a+jna ,y3hw5:gc3qo gfrom a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locatioa5ha 3w3+jy qg:ng ,ocn of the plane will

  The acceleration of gravity on the Moon is only one-six;o/4odw.0c dzw* qs ehth of 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 Earth, the ball would lw/4e 0 whqz;cs*d .oodand

  You are traveling at 55 mi/h-rw-j ixwgni (,t;yp+ in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity jr -ix, g-yt(;+ipnwwof your car to the other car is

  You are trying to cross a river that flows due south withmu d2g,: dp*qp5 e 9mlwen0h:q a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should dw,den *29 ge:pqqm0:5plumhhead your motorboat

  Your motorboat can move at 30 km/h in still wate2 eszx7 f l/vd,rjq,uy v:1u5pr. How much time will it take you to move 12se5y:,1j /dvu rfzuxv l qp,72 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 ax sy5-c1mgi. ;t3 c3tphog h,iqis. The y component of 5qo hi tg scmgcy-h3t1.i ;p,3 A is

  If a ball is thrown with a velocity of 25 nau i i4p1,vk4+*lcummq/vd*dex s()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 s0zmv c-tzo/;fz./ v jetraight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have y- vtjfe/z ./vm ;zz0ocou walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velo f-zfd;fk*ls- 592wemhy 5jkhcity is 8.00 m/s. The angle between the direction of its moti-km 5hk5 f9ldjhyf-wf*s2;ezon and the x axis must be

  A 400-m tall tower casts a 600-m long shasb,c:;m 9 jxhcrfpw: -dow over a level ground. At what angle is the Sun elevated ab:pc-;wh9rf:j cx msb,ove the horizon?

  Two vectors A and B have components (0, 1) ane i lna ;pxt/urh( *+f68fz)igd (-1, 3), respectively. What are the components of thearf (t6)n8*h l+xg fii;z/pue sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What i)ro 4etaq(ge3s magnitude of the sum of these tw)q4re 3(gtoea o vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vo)knwwe*j0 6f.kg5c i ector C = A + B . What is the magnitude of c .) j5fgkno6k0w*iewC ?

  A car travels 20 km West,nwo3 n0euki5 1mw n71e then 20 km South. What is the magnitude of its displac1on i0m13k5nwen7 wueement?

  Three vectors, expressed in Cartesian coordinates, aroqpuj- ( b3y5ce
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, expressev.af i*0a (k(*brnw rpd in Cartesian 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 fmhq,q- rhaqn;vw,8 : = (+3.0, -8.0), what is the magnitude of vector Cv:wma-n,r,fq q 8h;hq = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the displ(ycndpn62pwt*+d h ;qacement of the jny wdpdhq62*+( tnc; pogger?

  Two forces are acting on an object as shown in bg*:xyhk.ik-w/cgn :Fig. below. What is the magnitude of the resultant fob ykw: / n-xgk*c:.hgirce?

  Two forces are acting on an objecvdwyz zps:*h fjk;g(05 hg w77t as shown in Fig. below. What is the direction of the:z7y7dkgp 0z jh;s5hvfg(w *w resultant force?

  Vector A is 5.0 cm long and points along the positive x axis. Vector B is 7.7 9nh,6bm om 1.sut9c.tycsqq1 z6grk2 cm long and qztmk .gs uch6n191tb2s ,r6.9moc yqpoints at $+23^{\circ}$ 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 68 cm lon8rcza wgklry*f6 zy 1o v- e nuh0:(,ja:f:-kcg and points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 44 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 horizontaloy r4hh(mk8 n*h;6k6)f4opu ivrt 7blly with an initial speed of 15 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 3.9 s. What is the heighthbryrhotkiu47 )ko8vnfp6h (;*l 4 m 6 of the cliff?

  A girl throws a rock horizontally, with a velocity of 16 m/s, from a b 8f61u( uft5c/jn jbs*kzh sl;ridge. It falls 23 m to the water below. How far does the rock travel horizontally before striking the6u;*(hcz8tu fj51 nk/fbss lj water?

  A ball thrown horizontally from a point 24 m ab mtqxp*x))k :kove the ground, strikes the ground after traveling horizontally a distance ofpxkmt k*q)):x 15 m. With what speed was it thrown?

  A jumper in the long-jump goes into thed1f /0lwa stzn-c47 a8b0s qlu jump with a speed of 12 m/s at an angle of8 a-u7n4tlw 1b0a sz/ls0fq dc $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into t 2z kksoev 958;/mqroj-bojy 6he jump with a speed of 8 m/s at an angle of 9oj y25k ro v-/k6zqo jsb;8me$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloc5xcmwma 1g 8i-ity of 41.9 m/s at an angle of $34.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialy9 s9f tzydr.8nm2c q( velocity of 31.2 m/s at an angle of $19.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angloq :i p2.p3/qo yg.wfie 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 a9tzf9lk7 w frg:hk)rn*o7fgzmmy 2,. t 24.8 $m/s$ from the roof of a building 50.5 $m$ 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 from ground le7q6 rw k,neia:vel with an initial speed of 49.6 m/s at an ang k7:nqew6 rai,le of $38.5^{\circ}$ 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 4.0nh 0)lc37 q6p3*dcsj cwivyc, m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by c 33s6 nqi7wldv, h)*y0jccpc2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s 6m9dtu1 6f( nec5ktrbdue North, and is in a wind of 50.0 m/s to the We1ndc e6muftr(tk9 5 b6st. The plane's speed relative to the ground is

  A plane is flying due ih,i cz0wzxp6z9(;j5jru4 u5jd2wmg 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 ok hlu2*cgvr.(x fa8z*f 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 ;rjrk4wfs7 fi7dh d *0horizontally fires a projectile with speed 50.0 m/s if7w4fj dshr d;r0ik* 7n a 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 across a riveqk+ d41ykq8q kwlg )ntim 87u+r with a current of 6.0 m/s. mg41i8ydqqlk+)t87kqkuw+n What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 15 m/s in still watebtnmi-9:2f 7r r;ry)wb ) pbs:mo-ujhr wishes to travel directly across a river 1.0 km wide in which the current flows at 4.5 m/s. How long will it take to cm: -r; fpm7h ror-b)s)9 :yji 2twubnbross the river?

  The driver of a motorboat that can move at 10 m/s in still waj 7 qbup*dj*hdq6, dj)xr+b- xter wishes to travel directly across a narrow strait in which the current-)*+du jq7x ,xdjph dr6 jbb*q 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 +k3 dzrlyil+/ the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fa/zilry3l d k++st can she swim in still water?

  A swimmer heading directly across a river 2f q9 c(v v*7kmf d*xopi/czh+hwny3 ,500 m wide reaches the opposite bank in 6 min 40 s. She is9y*iv(pkv x+hnc57qzm*f c 3d f,wo/ h swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is v 03 ouq7ft2v jvmk:6j1.18 m/s, must aim upstream at an angle of3jjo: mv 2kv7qt0 uvf6 $18.7^{\circ}$ (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)  $m/s$