Which one of the following is an example of a vector quang9l;wb )3r 2co8re6z4w abjlktity?

  Which of the following operations will not q i30e nlwlj93change a vector?

  Which of the following is an *cm.a; w qhxk)accurate statement?

  The resultant of two vectors is the s)2p.l x7lj5iv dp;z 2,j d5;es sxncfwmallest when the angle between them is

  Two displacement vectors ha9 atph4wf 8c+vve magnitudes of 5.0 m and 7.0 m, respectively. When thesepc h av9ftw+48 two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the fa6(+izzeanoz +d9vo- ollowing is a a+ze9+ voi zd-(n oz6apossible answer for the magnitude of the resultant?

  Three forces, each having a magnhu c)juz((t65a d*jw9ghdt e1 itude of 30 N, pull on an object in directions t(e tj5u)6wd 9ch 1(ztgh*ud jahat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tn f2+5 x*a qqw8zi+exthe unknown vector is

  Ignoring air resistance, the horizontal component of a projectil o)d 3 jwy7wap 0ze0tyg7u6m44pqnw0pe's velocity

  A ball is thrown with a velocity of o3rz.tgm): xa 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 of a projectile's accehb*7q gic+,fgs t td8.leration *+g8.,t hgbfst7diq c

  A soccer ball is kicked with a velocivzv)e *q2uu0k y;(keg+snz ; lty 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 directed yqj.0n z:)/h go 5rdkganti-parallel to the velocity vzd :oj g /5.nhqkyg)r0ector,

  If the acceleration ofer7sz03 )rxog an object is always directed perpendicular to its velocit)7rszgro03e x y,

  At what angle should a water-)o ab7jih6z,igun be aimed in order for the water to land with the greatao,z 6i jh7)ibest horizontal range?

  An Olympic athlete throoqgr w5-yq1)yws a javelin at four different angles above the horizontal,y- qy 5go1wr)q each 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. If the ball leaves yourr 2y9/6 cxkar,2gfw pu hand with twice the velocity it had on your first throw, its horizontal ran wr k/ay2 gpfuc,rx629ge R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angy e(xxf) 085 rrm:mvqvle 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 ma*sm dn+sec);jx b)b6 fximum height, how does its spe xb*esmc fjb ;)n6+ds)ed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at th16i7mi ys6 fz 8tl7pfge same instant a ball is dropped vertically. Which object is traveling faster when it7 s6 zi1lpf786mgyfi t hits the level ground below?

  A bullet is fired horizontally, and at the same instant a sec2alk/ p.ug;* 08gu, oc:feu vekzx za:ond bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of te0a 8f*uvup/lkag: g ko. zcex:,;u2zhe two bullets.

  A plane flying horizontally at a speedjjb6 cx5a c,m) ozs*6x of 93.6 m/s and at an elevation of 161 m drops a package. 2.9 seconds later it 5mcsj j 6c*b)zx,oa6 xdrops a second package. How far apart will the two packages land on the ground?

  A package of supplies is b1gh32lnzb 0d9 34we iwel0bedropped from a plane, and one second later a second package is dropped. Neglecting airb4 30w309zbelhb l en i2edw1g resistance, the distance between the falling packages will

  A pilot drops a bomb wetmu9 ro:bht4y:pxl e/0 54pfrom a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground thwt/thmup59b 4 :4ep0y:oxlere horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of t *bk-rphu 7ln8iv*2:bhd -mughat 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 u7*2ghu* :lpbb nvkm- d-rih8land

  You are traveling at 55 mi/h in the +x axis relative to a straight, levjgkm-+ctz( in7f; ruz m6(pu,el road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other carz(ui7jcmmk, g( 6;t+pun f-zr is

  You are trying to cross a .7 sqaeqp-n6wc,k;ja ng4b ,uriver that flows due south with a strong current. You staru ,a7kn4n-ga qc6;ejpbw ,.qst out in 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 still water. How much time will,tfxzpc)a6kyh;- .yh it take you to move 12 km downstream, in a river flowing at 6.0 km/ht c)hhxy;y pz.k-6,af?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below)- hry5uvntllr9v2z; c 6wk+w the +x axis. The yy u9l ntvrl 2-z+)5;w6 cwkhrv component of A is

  If a ball is thrown with a velocity ob b7 bnvi1fk:k+6 hpyy u9a.+bf 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 straijk ya+2umtpy7m, x .(gght 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 have7+axj,g mt.ym (k2uyp you walked?

  A butterfly moves with a speed of 12.0 m/s. The n 0mtm8 ahcrepz95m-0x component of its velocity is 8.00 m/s. The angle betz0c etm80m a-n9r hp5mween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m+daf,,7yhbcji7 hfwq ;nn:e3 long shadow over a level ground. At what angle is the Sunj7faidc7f3b:h wen,yq +,n;h elevated above the horizon?

  Two vectors A and B have components (0, 1) an9rwo7 z 4fiuxg ()yox.d (-1, 3), respectively. What are the components of the sum of these two vectoro x()i. gf y4z79woxurs?

  Two vectors A and B have components (0, 1) and (-1, 3), respe w2evo+: r-2.oase c; 8ytxklkg rxy(*ctively. What is magnitu l-+wykx2:*so;e.e(ycg artx2v8 okrde of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C x*) fb,g jsfjdx1u5r. = A + B . What is the magnitude ofxg., 1)dub jf*jrfs5 x C ?

  A car travels 20 km West, then 20 km South. What is the 1z*idzoe :*blmagnitude of its displacement?*ze:l1bz od i*

  Three vectors, express6j*wc b6s2n kq; qmi)+7xlttzed in Cartesian 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 ib+9w gc5p buio5 ru1f:n 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 = (+3.0, -8.0, azyj+gpvzd72x- z n5), what is the magnitude of vector C = A -7- zyapdgj,nz5 xz 2v+ B ?

  A runner runs halfway around a circular path of radius 10 m. What isat0s7 wueo09 aa/ r5bgda 96is the displacement of tid70b0 ss6oaa9/wu9gr e5a a the jogger?

  Two forces are acting on an object as shown oao95 llcx/o e91 0jsain Fig. below. What is the magnitude of thxca9lo/a9j el1 5o0so e resultant force?

  Two forces are acting on an object as shown in Fig. below. ku m/ezqeaf9n/1e.+f What is the direction of the resultan.+qake /z9mfe/fn ue 1t force?

  Vector A is 4.4 cm long and points along the positive xqja p8uak7 8ue/v.g 7w axis. Vector B is 7.5 cm long and points at aup/vu ej87g 7.8qkw a$+45^{\circ}$ 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 62 cm long and points at 8;vki3mkq4rl $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 21 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 27htz, kv6/ wk:eb aj)dnq-kn7bw i+ a76 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time fro-nv7j6wk7kb da/zn) e,ai :q6hw+b ktm the top of the cliff to the bottom to be 2.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velociwhyq b art40ug *74 -k/ xq.rp lny7ckr;fe11pty of 16 m/s, from a bridge. It falls 25 m to the water1ler ; q*cp4k0hp7- xbqgyt ar 4r17/ukw.fny below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, strikl43if7hmnl(-p p g)eaes the ground after traveling horizole3)-4nf 7l gpaip h(mntally a distance of 20 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spebzp:-wa 5ii 7ued of 12 m/s at an angle -5iwpb7: iuaz 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 8 m/s at an angleph+j7m87 iez x5 ygg .,bg7nnw of nyb7578.g7 ne ,j gpimh+zg wx$18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched4u28- vir.oxfjeks 9y with an initial velocity of 34.9 m/s at an angle of $47.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 32.0 m/s at an angle of g9u2tjha 2,g+fpkt d :$46.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of,4c-vst uh6.apacq hxwi b:n) t7 +6ww $30^{\circ}$ 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 horizontallflaoyi7m emnhj3vc)tn h4nc :k)kk829k47 d 6y at 23.9 $m/s$ from the roof of a building 40.1 $m$ 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 47.0 m/s 4;r.8oyq1zsst/jap wf3 ce2y at an rsye wa4.81;ot q2/c3zpjyf sangle of $43.8^{\circ}$ 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 o+ecfg- 2pp)j9zycm 4zf 4.0 m/s. If you ran the same race on a day mc-f2j )+ z9cype zg4pwhen 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, and2zt.,)66 dzp jsb(-xvngdz zq is in a wind of 50.0 m/s to the West. The pnxzz,bpvd j-z.s)(6 ztg26 qdlane's speed relative to the ground is

  A plane is flying dueu2qd4vxnei 9c,f up0 6 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 120 km/h r*3g/ s83 akwrq 7en, aedrko0is 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 horizontally fires a projectile with speed 50.09/x(fs zph usl-uoe: * m/s in a forward direction:xzpsh( *euol fs/u-9 $30.0^{\circ}$ 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 directe*uj w9s ewd:nbi4,e0md across a river with a current of 6.0 m/s. What is the speed o0j w4:9w b, n*eieudsmf the boat as it crosses the river?

  The driver of a motorboat that can move at 19 m/stgw+5-1o-upzbovnxi:fy*f kfbg : q/mf45, k in still water wishes to travel directly across a river 1.2 km wide in which the current flows at 5.4 m/s. How long will iogbpob:m wi 4nqv,* t-k:zf/5xuf f1 g5+-ykft take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wisio6/5.kb (/ gpmahfzq,n* y-m(mtdwrhes to travel directly across a narrow strait in which the current flows at 5.0 m/gtmi mha/5./- nfwyp( 6o*rqk(bd ,mzs. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a r7(k gdo1scw8kq zf5ay f /5xp)iver 200 m wide reaches the opposite bank in 6 min 40 s. She i75 /opdqkyf1 ) 5fsxca(kg w8zs swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly a2ominhn2x7os 7 w085s*pzgl x(f w;h7lgd dw.cross a river 200 m wide reaches the opposite bank in 6 min 40 s.o( d;g5iox.0l7shf zp wg*7nnd 2wh m7sw 2xl8 She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.81 m/4 *jwwoj-ji:kdk6 /* pm(.6: da6 syscdvqjp es, must aim upstream at an angle ofq 6p -a miy d6jk6cje:dwp dk*j(w.v4o:ssj*/ $30.3^{\circ}$ (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)  $m/s$