Which one of the fol1/ knt+z qbcizl.0g6flowing is an example of a vector quantity?

  Which of the following opera1adfk)s0 jd3r tions will not change a vector?

  Which of the following is an accurate statemen79 rx2 e0f+a2pqvegh lt?

  The resultant of two vectors is the smallest when the(.ijkxzbu( *d angle between them is

  Two displacement vectors have magnitudes of 5.0 ml 5 +zmpdd*8as and 7.0 m, respectively. When these two vectors are addez ald5pms+*8 dd, the magnitude of the sum

  Two vectors, of magnitudes 20 w(joejucigw 77 8i9d5and 50, are added. Which one of the following is a possible answer for the magnitude of je( dic78 iojugww5 97the resultant?

  Three forces, each having a magnitu8z- o4qk q72lq 7afuqtde of 30 N, pull on an object in directions that q42t qzq8lk- qo7f7 uaare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown uxpu j1;( rnc,vector is

  Ignoring air resistance, ts 4ir) u;87 qdhg-y tywue3sb:he horizontal component of a projectile's velocity

  A ball is thrown with a velocitk1 w8 ;oi va-ltc,grzqj ,c;x7y 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 compone 7xm3z*eesx1+ g-lrox nt of a projectile's acceleration1el mz-xx* g+x esro37

  A soccer ball is kicked with a velocity of 25 m/s at an angle of+z3p5m +z:wa -e hckuc $45^{\circ}$ 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 anti-parallel to the velocmcd+ a63z 8a8bwjmmh.im6f +mity vectom ijfbhmwm368+.m+a amdz68 cr,

  If the acceleration of an object is always7 b2-a- j y5wlzgobb+v directed perpendicular to its velocitlbbg zbwy +7 5v2--aojy,

  At what angle should a water-gun be aimed in order foqdh (4vuq x;6izsu6p5 wb gc6)r the water to land with the greatest horizontal range(p6bs uuwigz;xv5dh 4) q c6q6?

  An Olympic athlete throwv o w961z bp5hlbu7gbbwj(67tw i,m (lqav7u) s a javelin at four different angles above the horizonta w bmz 175b6 ptu7q(ougwahwvbillj (6),9bv7l, 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;cpnc5 scsl2 tyr68 i; leaves your hand with twice the velocity it had on your first throw, its horizontal range R (cn;pcy56i 8c;2s clrstompared to your first serve) would be

  A ball is thrown at an original speed of 8.0 7n :a.n**-u jrxuuxkm mn d6u+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 ream,ngo3l*7) yxiz;o mjches its maximum height, how does its s;7m,3xojm y) gzlni*opeed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the dm f, 9o.:jfxmsame instant a ball is dropped vf dom9,mx:f. jertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and atdmfl+e) nznbdkc * )85eve/l0 the same instant a second bullet is dropped from the same heightl+n58vk )/c* 0bdmnz feedle). Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 81.3y,f3u7/d6jaj1ibug3y zk -j q m/s and at an elevation of 141 m drops a package. /a jd-u33u zyk17fbqi jg y6,j 4.9 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second laao6xj:n3j aa)m rg6 g,ter a second package is dropped. Neglecting air resistance, the distance between the falling p,:3 aoj6gnaa )xrmjg6ackages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neb1pj 3k6r+xe6+huhyw glecting air resistance, when the bomb hits the ground the ho pryeu6 h1 6+xkb+wjh3rizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixc)l3btwrpj 2+7 arhq .q z,6vjth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) aw)j ,q2+rjtv3cqh7p6lzr.b that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +wwj o7+0js7 mv, lbis-x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relati,0j+-b owisjms 77wvlve velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong curre03 zngq *t5cbwnt. You start out in your motorboat on the east bank desiring to reach the west bank dizg*tn w0bc35q rectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 hia60 iscoa9( km/h in still water. How much time will it take you to move 12 km da6 (ci9hia 0soownstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thhcy 95)to6ylsj2o ho9e +x axis. The y compo joyo96h)yols 9t5h 2cnent of A is

  If a ball is thrown with a velocity of 25 m/s at .y2 j*m0 16i,lgs k ia8lue,kxq7zdmyan angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight lo:qg0 8/z.gzm w nte5vine 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 you walked? t :zqz5.engmg0/ ow8v

  A butterfly moves with a spee9ayrl4ur endf3,3g q e -,vkx.d of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must3ey,xre4n v grd,3u .a9fql -k be

  A 400-m tall tower casts a 600-m long sh8f/ jocst: ,;elh+nyj adow over a level ground. At what angle e8nyjh tl+ojc , :;/sfis the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-gfjaf lza+(v1,8uns.vdo1 x + 1, 3), respectively. What are the components of the sums+1v(8 foaflgvja+ dnzxu,1. of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wha )cf,gi/3 jhzkrsn) /it is g hks,cjz)r/) /nifi3magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B .eyh2iaung n .f2.4 ;f:h /sebu What is the magnitude of C;u.2nbug snhfe/i.fe 2 :4yha ?

  A car travels 20 km Wes pd j hup)c:g/*wkjql.*rw;7 dt, then 20 km South. What is the magnitude of its displacemend7/gpqr jw*cdplku*; ).:hjw t?

  Three vectors, expressed in Cartesian coordinates, ay -9.aoi8; usvlxuum9 re
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 p08 5mjyg4dzly b4-dd u+1czfin 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), what is the magneg*lu0 *0k qq wmhi;4kitude of4w*;i keml*00 qqkug h vector C = A - B ?

  A runner runs halfway ar*ej 4skm :+qewound a circular path of radius 10 m. What is the displacement q+k4:eem *jswof the jogger?

  Two forces are actinclja-,l j)tnm( 0dx8lg on an object as shown in Fig. below. What is the magnitude of the resultant force? l 8,xtc n-d(all)jj0m

  Two forces are acting on an object as shown in Fig. below. vt1i tup vupo:/4s8+oWhat is the direction of the resultant force1i 4t+p8osp/ouuv :t v?

  Vector A is 5.8 cm long and points along the positi16c+ ekabt wzpp4aq98ve x axis. Vector B is 6.6 cm long and tpqe4wcaap68 +k9zb1 points at $+43^{\circ}$ 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 75 cm long m gzu(n,c a( hif6jow/:m1um;and 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 40 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 12 m/s from the edge ;*z l+yyyhz *.f cwqr/of a cliff. A hyl *c*; +fyy zw.qz/rstop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, f- z1pz7vio*lo/ s6ydv c+gn/m rom a bridge. It falls 26 m to the water below. How far does t7oc-o/v6im svylg*z p/z nd +1he rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, s+jt 4bccrf:6+ jgujb(trikes the ground after traveling horizontally a distance of 20 m. f+cj:b4ur6 j+ gj(ct b With what speed was it thrown?

  A jumper in the long-jump goes into3ks k w1(rjczfi80ko * the jump with a speed of 12 m/s at an angle ofk1 i83fc kkzj0r*sw (o $20^{\circ}$ 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 13 m/s atqo23ufgamwdhv3*y) 1d/: acv an angle dvcd3/:o aua)ygq3wm hv 2* 1fof $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 2kjs4 2w+:.q q0ffb iyn4.7 m/s at an angle of $27.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched wiao(6el9 -a; v n)0fac8xctyb fth an initial velocity of 38.2 m/s at an angle of $13.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an c uw(o/c( 7863onkv:nck nwnk 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 horizona8uf 7b-f;w hjtally at 25.6 $m/s$ from the roof of a building 68.3 $m$ 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 groun4 i1/ za8dhthrg rp5bo*5dzs4d level with an initial speed of 49.1 m/s at an angle of h4rdi4a1r5 s ph*tzg d85bzo/$42.7^{\circ}$ 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 4.0 m/s. Id1+x 0ccnr.q lbbahe17su m)- u0uzz1f you ran the same race on a day when you had a constant headwind which slows your spedehbuu-zz0nx cqu1ls1 cb.r1 7 m)0a+ed 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 vstg : bae,qpbv9itu a ;1656pin a wind of 50.0 m/s to the West. The plane's speed relativ v;s,uqpi: 9tt6v1pegab b 6a5e to the ground is

  A plane is flying due S6t4g ekvmqtb5, ez 2v :k-)f/hojb*tbouth ($270^{\circ}$) 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 heait7j q*nd+ra0 jw a:4pded $30.0^{\circ}$ 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 wfps+o;8tw+,k,rrhx) z ous h3jvz:3 qith speed 50.0 m/s in a , 3xjhhvrz),kf 38ous+ wz r+:;qtsop 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 ri( oksps9 -7pakver with a current of 6.0 m/s. What is the speed of the boat as o 9 (ap7-pksksit crosses the river?

  The driver of a motorboat that can move at 1 p2hv.nq1 v-4 2aj2kaexsgsv 99 m/s in still water wishes to travel directly across a river 1.7 km wide in whiceanh 9s2v-.g qjk1ps 2vx2a4vh the current flows at 6.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes dr mt5v4/ *ggmto travel directly across a narrow strait in which the current flows at 5.0 m/*grm d5mg /4tvs. At what angle upstream should the driver head the boat?

  A swimmer heading directly aclu;l . d b-ej 2r+wg4ccequb2(ross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swepb2ee (rl;gcju-qbl du+2 w. c4t downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide z o+/eu.hxw5ajy:u(e6h d8 znlt*8dtreaches the opposite bank in 6 min 4aho( .ztde*uhnl/5wd t+88y 6xe zju: 0 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in stillhddoxr2 gbp4i*r qob- p215t( water is 1.60 m/s, must aim upstream at an angle of qp h b1d gt*r(5or2id24 -boxp$17.0^{\circ}$ (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)  $m/s$