Which one of the following is an eq.8lbsx+;d9y i 96apj dal6d example of a vector quantity?

  Which of the following operatiosk o:pqvrqarfs -y)e: d;g+i( d;e;6qns will not change a vector?

  Which of the following i; jv)rq)b7rs7yg qda+s an accurate statement?

  The resultant of two vectors is the sq gh7)/4ov4ub*zgee 5mn oif9mallest when the angle between them is

  Two displacement vectors have mau.p hbcss* 8 qlu x3t;88mhha6gnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the m.laq;hc t 38u*s pxh88ubh ms6agnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of thb* sgbe7s u*r *hoas26p+s6m ke following is a possible answer fs+ hmspar*eub6g* ko *s2b7s6or the magnitude of the resultant?

  Three forces, each having a magnitude z 4m fn(912astrmi6fnof 30 N, pull on an object in directions thn(4z9 at 6m2s1rffin mat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tc(t b f*7b bk()f2kabyhe unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's veloci ygot14*e,nvt qy )0ifty

  A ball is thrown with a velocity of 20 m/tj-h)+rq ug- ks 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 prw-w)tbru/ z)n-k ey6xojectile's accelerationnzwky 6ru/w ))eb xt--

  A soccer ball is kicked with a velocihuczq 7t:8dalqd c03 lctr x++8 fv3:uty 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 u qibewd7mkd ;6ku019w/1ag k0b 1wfq is directed anti-parallel to the velocity vector,kfa1b uw 0ud1m91eqgbq 6d0wwk7i/k;

  If the acceleration of an object is always directed perpendicular to its velocczudbprq78 m)dny.* d:jb9r8itr8cd bpym 79j zbun8)* d:.drqy,

  At what angle should a water-gun be aimed in order for the water to landy4oer49 s6dfp with the greatest horizonrf ep4 os469dytal range?

  An Olympic athlete throws a j8,xh) j3eamzzvi.wm4 avelin at four different angles above the horizontal, each with the ,.4 3j8maiwhz vz)xem 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 s3o*gw*f p 5nkfecond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would b3kpf*f5ow n* ge

  A ball is thrown at an original speed of 8h9(s l9d0z bk;)q p l6(pbwx2 stnp3dl.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 maxi.tikh)e9c 8b3931q kcosd)p i sm+srimum height, how does its speed compare to its i9s)tdmik 13c khi 8rc os9seb+ 3.q)ipnitial speed?

  A stone is thrown horizontally from the top of a tower at the same instant xydhh(j-owb: 6a et5 gm1b;1 sa ball is dropped verti yh16dag5w-1shjt e; x(b: mobcally. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the s0 veo5dgu8 zwbn h-xz -j7dd4f(/ajg+ame instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of tgngbd/fv -w+ 8 d7 jxdu4z(o5ez-aj0 hhe two bullets.

  A plane flying horizontally at a speed of 63.5 m/s and at an f dj,o)lq,z3vk iq v3jm i9,fm90wgb8elevation of 169 m drops a package. 4.0 seconds later it drops a secodoqj v,j ,93 l)38,fkiw9mv0qzigbf mnd package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later )x j* (poxuc6f(mod p)a second package is dropped. Neglecting air resistance, the distance between the faj(d )u*c(opx6of) mxplling packages will

  A pilot drops a bomb from a plane flying horizontally at a constanw eie9*0v)xv2jaro4 mt speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the 2w ev jrxio)90ae4 *mvplane will

  The acceleration of gravity on the Moon is only one-,fsxrz t.tvmd (k 6(mktkf/w j2 70e0ysixth of that on Earth. If you h.xtm (06 tr0/y zvj7, fkew2sfmdk( tkit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling athzromf0 /93o;4q ajhmxf j *;c 55 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. T*x3 f9 fj /;j;hrzohaomc4m q0he relative velocity of your car to the other car is

  You are trying to cross a riv)9 5 1)/aawvjk htquqkowed66er that flows due south with 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.k1k)tv 6 9)qajd65wh/oq wae u You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take 56mhk9tos- nioh k07jhvg*2n.l d d1yyou to move 12 km downstream, in a river flowing a9so*mkt-1 d ohkjv.0n7h2y6i 5nhgd lt 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below tav55ks e+oe 430txrk hhe +x axis. The y componen oe 5r+4ev50sha3xkktt of A is

  If a ball is thrown with a aql:i85p5hic)v egr )velocity of 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 straight line in a direction north of eat(csemoz+ ,2b+zw*yj st and you end up 2.0 km north and sever2z*ws +c(bzeo j tm,+yal 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 v s1.cx 34zvir3-r3h(uq0git r2pdn6u dn dnv+ elocity is 8.00 m/s. The angle between the direction of its motion an +nix.t zp- dvv 4u3r30qn3rghcd6di1(nu2 srd the x axis must be

  A 400-m tall tower casts a 600-m long shadow*i08lxcbubds3.zlj c 7 p 1oy1 over a level ground. At what angle is the Sun elevated above the horizobjc lbzc3 .l8ys710 *pix1d uon?

  Two vectors A and B have components (0, 1) and (-1, 3), res7m -jzc9wv :hl j; -v/sq,ejggpectively. What arqw9 mv;j-z egg7jshc-/ jlv:,e the components of the sum of these two vectors?

  Two vectors A and B have componentf +2vmj kyxa-xa-3q3l s (0, 1) and (-1, 3), respectively. What is magnitu3+jk-fx a mqv ay32l-xde of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3amn-yv b b*87v, 0). Vector C = A + B . What is the magnitude of b-a v*nb7yv8 mC ?

  A car travels 20 km West, then 20 km South. What is the magnitude ofle;v8q7kc sc rz.i06h its displacemeehs08ccvl 7zq ;kr.6int?

  Three vectors, expressed in Cartekvz;zb)+g3 w wsian 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 Cartesian coordinu kkpuxg *a)o*,9fb* zates, 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 *2mbrw9sir3ja r374rm :k dpph;7mrdthe magnitude of vectorrrpi9 a:dkd;bj7* srw47m pm3r2mh3r C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the disjd0.- ;sdnmzj -v qt 9yto.74mjeqg lhr)*ej 4placement of t hy 7lmg9s.*- d;j0-.t4jmnze 4djqje rovt)qhe jogger?

  Two forces are acting on an object as shown in Fig. b+k vglu c ap(+d8*pi:kelow. What is the magnitude of the ri(l+ua :cd8 + v*pgkpkesultant force?

  Two forces are acting on an object as shown in Fig. below0npv ip -n;g5 (zfnec/ ndt.-u1)pd uw. What is the direction of the resultant force?e/t-wp) 1piv n dgnpnfu(;ndc.5u z-0

  Vector A is 4.1 cm long and points along the positive x axist,gt ue* mw4x+l.h9 hh. Vector B is 5.8 cwl,mht+ge .*txh4uh9 m long and points at $+60^{\circ}$ 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 64 cm long andur 3v7,5v4zw* rgleoh points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 28 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 14 m/s from the edg4t /xwj :rxicdym*- b3e of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.6 s. What is the ty/mw-4icxj:r d *bx3height of the cliff?

  A girl throws a rock ho ug52k-8d(xzy:iev v 8+fpgqlrizontally, with a velocity of 8 m/s, from a bridge. It falls 15 m to the water below. How far doeszgydlq:f ek-ig5 vu x28v(+p8 the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 25 m aboveicuv, a /u0.abq4chx2 the ground, strikes the ground after traveling horizontally a distance of 23 m. With what speed0h iu4ac .x2v,a/bquc was it thrown?

  A jumper in the long-jump goes into the jump wc6t6 1m ld8tdpith a speed of 12 m/s at an angle ofcpd81t6t d 6ml $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goum; 8ud(bpxl 7es into the jump with a speed of 10 m/s at an angle u7up;bl md(8xof $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial y6n v;i)9b7v,,xwg os xrct-bvelocity of 54.5 m/s at an angle of $30.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of p(r 0ukq s43nnp)t 1i *4v9b whijvd3u36.4 m/s at an angle of $33.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofw; fm40ay7guw $30^{\circ}$ 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 at 2k/lb3q8uyvisj gsd.; r wt/913.2 $m/s$ from the roof of a building 54.3 $m$ 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 ground level with an iniaft fx;f gwvg5s/.3x9 tial speed of 56.4 m/s at an angle of / t9ggxav5.sfw f;xf3$46.9^{\circ}$ 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 ;(uz v(lgddwjo 3l l9-a velocity of 4.0 m/s. If you ran g(l3uz9l dov-w; djl( the same race on a day when 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, and is in a wind of -eka ymp;8)io50.0 m/s to the West. The plan8;ykm )iop-a ee's speed relative to the ground is

  A plane is flying due z*pwroy ( x qq0zm+l44South ($270^{\circ}$) 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 iskyzy-f7gmf 45 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 horp*c*f57 vr;zje9gf k9k u/gc bizontally fires a projectile with speed 50.0 m/s*uc7rk e;/zp*g9gc bvk5jff9 in 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 rifdmp:d0ou ,d s1lo/04 zi0ritver with a current of 6.0 m/s. What is the speed of the boat as it crosses t0t:uz/ofrd idmp,d soi0 04l1he river?

  The driver of a motorboat that can move at 17 m/s in still water wishes to tra c29ocejk;1ri.6kl n nh25o oivel directly across a river 1.9 kkr i5cln1eijo6;no .2o2ch 9km wide in which the current flows at 6.9 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 to trasc*r+1ny) cwxy)rh ve8b tz xhtn q9641o 2c6qvel directly across a6bvh1r4h o r19c)cns8cqn xx)qz ywyt 2et6 +* narrow strait in which the current 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 the o7;6vl:qz9axw g skv(v mkw3e5pposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still waterxv eal7wkw: g(q;s v5k9mz6v 3?

  A swimmer heading directly ac 2kz0. +lpiiwag6b1 odross a river 200 m wide reaches the opposite bank in 6 minwz. ail2b 0o1+6dki gp 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in sl(6safbwr- (p till water is 0.90 m/s, must aim upstream at an angle of arb6-fs (wl(p$26.9^{\circ}$ (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)  $m/s$