Which one of the followwzr/d. -ij5 bi+/km vhing is an example of a vector quantity?

  Which of the following operations will not change a skt5+tvg*w0 )mfh/hyvector?

  Which of the following is anf u-j hxj;m(,khz8o71 8 fgwkj accurate statement?

  The resultant of two vectors is the smallest xt y1a k;*gwmqi9eri42 9b-bpwhen the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, 41e qr8q*09tfz 6ypiid+xn fr respectively. When these two vectors are added f qrp4e+diqzt0x18f*6ynri9 , the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are add-4+. taa1 nmppivjizg 1dt+lth6h8 n- i-lh+ded. Which one of the following is a possible answer forzn dtn-a-mh+v.l4h d ilpah6-i t++ 1ijg18pt the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in 7ehh+j:du e w7q59vctdirections that jq7e5c:v eh7u9d t+whare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, ti *ag m1;os6g89/ir :c tsrfllhe unknown vector is

  Ignoring air resistawqf54c n7h zy0e4 0adlj( u;xynce, the horizontal component of a projectile's velocity

  A ball is thrown with agf+ nq 66iu wiqy/r ef8uwe2czi47*o ( velocity 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 horizouua 8 db1owr(7fpj(4g 0hm*nyntal component of a projectile's acceleration4(r8g*oju hwm fb7u y1 pa0(dn

  A soccer ball is kicked with a velocity of 25 m/s at an arwb*1i;a0spx ngle of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vectorpf+*rytk0y im-:w0me;ppgc 8s,nnz0 of an object is directed anti-parallel to the velocity vector *eywgs00tnz,f-ck 0p ;yp mr+inm: 8p,

  If the acceleration of an object is always directed perpendicular to 3s(b3k:wqv fw k1n2-+z bfapaits velocity3sp(2b kkq a wb+3zf1n:fwa- v,

  At what angle should a water-gun be ailx) *)6pahvxl h**zo bmed in order for the water to land with the greatest horizontal *lxp v*l)a*b6h )zh oxrange?

  An Olympic athlete throws a javelin at four different angles above oy: id2mm 3wvv 8ihw8r 3sc.5mo(;udu tzz;9othe horizontal, each wd5uv(h z3 ;o8.;m8m 2 o9ics tiyo:w3rwmdvu zith 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 foryt49hwwzhj(/l4hgb*2p05cjo sg 4u8:s xvrs the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizojc8rw : opjlbx4s ( 42 05usv t/hsggzhh*4wy9ntal range R (compared to your first serve) would be

  A ball is thrown at an original speep 7b0j(u9uhns3,kjga/ jb 2v9c 7;twf ege2 qud of 8.0 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 maximumbu:jjqhdar z/ c ,y, k7+8,nbp height, how does its speed compare to its initial spqnhu:+/bjja,crb 7, k z8,dpyeed?

  A stone is thrown horizontally from vkh8l8j5 6h8 inacx e)the top of a tower at the same instant a ball is58enl k i6hc 8jhv8x)a dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second.pfzqu +fyup 0 80ap h1kcs2e0 bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the tac f.hu0pzs0p1yk+8 f p02uqewo bullets.

  A plane flying horizontally at a speed of .vhh cqfv+q7-)(od 2wg.-6bd2hhzokjnl) m z113.0 m/s and at an elevation of 229 m drops a package. 3.h2l czqofqbz)-djv.2n7ok-)dh w h . 6g(+vhm3 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 onmjri+.ko *npzfy0dm ysr9+*4e second later a second package is dropped. Neglecting air resistance, the distance br+9rm0n4yp+f. z imk*oj y*sdetween the falling packages will

  A pilot drops a bomb from a plane flying horizontalul8ld4(wiv :gly at a constant speed. Neglecting air resistance, when the bomb hits the ground the hou84vld ilg(w:rizontal location of the plane will

  The acceleration of grfz f:6sbm,p fjwh:ro/+8 6gctavity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moofjmc6 rs :z+:gffo,t 6wp/8bhn with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis re62ycoz jxs-l8 lative to a straight, level road and pass a car traveling at 45 mi/h. l8cxzy j-26os The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strof w1 .;;lfwy3hw:i*idzfbfu+ (yiex 2ng current. You start out in your motorboat on the east bank desiring to reach the wes uwi1l 2fwy fw;ffi*z.+diy:;xbh3( et 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 wg 5+td9suz , vr:s-fhbill it take you to -9tu+d5 grsb ,z:hvfs move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitu--la3/ces hectea5*ovf l,/ dde 8.0 m at an angle of 30 degrees below the +x axis. The y component of v lec// fla,tdeo -ec3 h-*5asA is

  If a ball is thrown with awc)mlh1l04 nl 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 straig40 r.dc gko+ax,a ,nuaht line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north o0,. aagd au,r+4kncxof east have you walked?

  A butterfly moves with a u wl9 2+pg/jjqspeed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direcjl9u+ pqgw2/j tion of its motion and the x axis must be

  A 400-m tall tower casts a 600-m longpp xi +l7/y96bqg/5a if*jyuu*ct a+z shadow over a level ground. At what angle is q96lyppi u+uf5x*ca*aiztg y7+j //b the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. 0(c re59q yhn(k c8b- wmbrn*pWhat are the components of th(ccb- k 5b0wer np*(rm 8yhq9ne sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What ispf /b)cbp4n/67jofuirj6 v( q magnicj4o 6 )ubpij b6fp/nvrf/q (7tude of the sum of these two vectors?

  Vector A = (1, 3). Vector B =) j3 eo1eglcy( (3, 0). Vector C = A + B . What is the magnitudee 31loecy)g( j of C ?

  A car travels 20 km West, then 20 km South. What is teg. wvx deq 9+fpvq4m ,21lbt(he magnitude of its displacement?. pqbv+ 4 vl9xgeme(f,2dt1wq

  Three vectors, expressed in Cartesian c, .e2*og1tdc .hfuer3ggx ,rw0unma8 oordinates, 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, expre oh)jtansky)qv 7r/ f7(mi6, kssed 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) ap6 :k7lo4z ayu(dovf9 nd vector B = (+3.0, -8.0), what is the magnitude of vector C = A - Bauldo9 :7kop6 vfy (z4 ?

  A runner runs halfway around a circular path of radius-rakw5*xe c :r 10 m. What is the displacement of the jogger?*r-wrack 5x: e

  Two forces are acting on an object as shown in Fig. below. Whatwd p-n7m7jrf*k)ohu ( af .i:s5ct;fy is the magnitude of the resultan5o7ci- fjrh*k ypt mf)f.d7su(: a;wnt force?

  Two forces are actinql5o nu64w)ry(,c1vha(( o v6qybto wg on an object as shown in Fig. below. What is the direction of the resu(6wabv) ,yl4 rn6t(o1vuw oc yq5ho(qltant force?

  Vector A is 5.9 cm long and points along the positive x axis. Vector B is3;i.crsim,w1 w) w aat 9.8 cm long and points w3 w,t1;rm) awica. isat $+24^{\circ}$ 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 72 cm long and points at, zr pw5 wuiy4.den./a $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 41 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 21 me,z1vvrg*ppa1(8 vk u/s from the edge of a cliff. A stop watch measures the stone's tra1* (gevr u1zv pvp,a8kjectory time from the top of the cliff to the bottom to be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity xtz3u6 1- qe3irteg9hf 77zhaof 9 m/s, from a bridge. It falls 18 m to the water belhua3 -i rx6htq91f7e t37zg ezow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a poiiz8 04qh jfanmq 56f;uwd/ -kynt 18 m above the ground, strikes the ground after traveling horizontally a distance of 14 m. Wi5m6 0nf8uqw4;fqzajy k -ihd/th what speed was it thrown?

  A jumper in the longo:vdhy c, ,ite+rff9f*udz52c ,/xxz -jump goes into the jump with a speed of 12 m/s at an angle xc9+r5 zfofx 2uf /,yv,di*,htd :cz eof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes vhoz;(5z c -x fbc01:bin-nsr5c4hghinto the jump with a speed of 11 m/s at an angle of b0x4n 1r vnc-bhz5(if zo-cgc;5hhs:$33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocit6c+etkp p-u8)e9bz319dtx ak zssed - y of 24.4 m/s at an angle of $32.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 38.2 a7(-brnkis;n m/s at an angle of $49.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an a3p3 lk nieq; xuzio;:( 3utz0cngle 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)4bcdxp 6 .arr r4n9l /x.r;fw*ymrq w at 27.6 $m/s$ from the roof of a building 65.2 $m$ 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 fired5,rq cyqi+* cp2b qdbm+ng20h from ground level with an initial speed of 53.9 m/s at an anq i2pqmh5+ ybn0cgcrd,+ q*2 bgle of $45.2^{\circ}$ 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 ;r+szhqx0i di3q6)tjw gdp3, run a 1500-m race at a velocity of 4.0 m/s. If you ran the same racw3st +idxj;qq6i ,30 zrgd)hpe 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 ww+6cmt-kgk 8jind of 50.0 m/s to the West. The plane's speed relative to the grouncg j+-kktm6w8d is

  A plane is flying duepe-tjme dw;wg-3, ,fu 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 is p, t iyk9m -(nrm+,kdmp2b.isheaded $30.0^{\circ}$ 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 project,5j.yg9rx hk;0)lvl ky t 3pdvile with speed 50.0 m/s in a forwar0vr.xl5 t)9gk 3,jvdpkl yyh; d 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 sti( u64z1zqjal vll water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. Wzu lj14vz6 aq(hat is the speed of the boat as it crosses the river?

  The driver of a motorbou(+larh0m s +uat that can move at 12 m/s in still water wishes to travel directly across a river 1.6 km wide in which the currentms+ l+0huau (r flows at 6.9 m/s. How long will it take to cross the river?

  The driver of a motorboatp m sz9b1me9:zeh4e h/ that can move at 10 m/s in still water wishes to travel direct41 emsmpz/hb e99:hzely across a 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 opposite bana1stb6ja bfl 1h1;h05o p-hc z /-abwnk in 6 min 40 s. She is shh 5lh-abp sc01w;6zjot nb aa bf-/11wept downstream 480 m. How fast can she swim in still water?

  A swimmer heading dir( usbz61cme3 sectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is th16su bs3(mzece speed of the current?

  A boat, whose speed in still water is 1.26 m/s, must aim upst;+vqrpvhg xz-521p liream at an angle of 2vpx 5-pqr vh1giz+l; $29.7^{\circ}$ (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)  $m/s$