Which one of the following is an examplew-pi38ldu/bdhtuek-,8tu jh q-y/ 2o of a vector quantity?

  Which of the following operations will not cy ;pba t66olvvb6 4qm+hange a vector?

  Which of the following is an accurate state;p:-e6.p/xwzo ll gmua(5bki ment?

  The resultant of two vectors is the smallest when the angle between themc1bkudfdo co5lw//+9 w2ogh ( )s6tuc is

  Two displacement vectors havexyhto,m;-wc.d1c wz ( magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the sumw 1d ocxz.w;c,(mht-y

  Two vectors, of magnitudes 20 and 50, are added. Which one ofk fcukni :7fiq9*4v*/x)oc z5 r6vwqm the following is a possible answer for 5q:9*4k6ki w xn)oim7fccfz vuq*/ vrthe magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pfb 7cpt,sju :6ull on an object in directions tp7tsf bcu6j, :hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the undy9by mapow z2137 0fhdw 7c-tknown vector is

  Ignoring air resistance, the horizontal component of a projectk 3,rfr/jwv 3lile's velocity

  A ball is thrown with a dxn hmo,o9xf3 2fh;2 evelocity 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 component of a projectile's accelerati5r3al:,fmjr konmar3 fr 5jk,:l

  A soccer ball is kicked *j);6wfivhex with a velocity 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 i/*nml:bd2zjlzb(5ii* w +dxfnj i-6t s directed anti-parallel to the velocity vecti i l:b+*inzw/dn*2-tjm5x(z jl b 6dfor,

  If the acceleration of an object is always directed ie5; ti5p fbv(perpendicular to its velocity,;i(b5v te5p fi

  At what angle should a water-gun be aimed in order for the water to lan 16bx 17 2rwge . cqbk:vqs,//xezhkbxd with th2eb7 /:x,cz1 b6q. bs/g rwvqx1kkxh ee greatest horizontal range?

  An Olympic athlete throws a ja4fdqmqttxuv-m 0te 05zd9qj4,p y24gvelin at four different angles above the horizontal, eacmqzpe2t44q0d x,9dmjq y tg 4fu5v -0th 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 4 w jf8zhxs(hnfm..f9your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) xh jw.z.fh4s9f mfn(8would be

  A ball is thrown at an original speed of 8.0 my9 6,cy4r qpvq/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 reaches2( d(r+wu-z r3 e3u)q8c o o(qgyktdmf its maximum height, how does its speed compare to its initial speedow+ udfqr3d(t8eguc -o()23yk( qm rz?

  A stone is thrown horizontallyx) u -vps6e.aj from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level g6. -x uaejsvp)round below?

  A bullet is fired horizontally, ana3j:0l.6ksycb w 7fwi;t ,wmad at the same instant a second bullet is dropped0cy76a :3wjit.lf ,wkw;basm from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 8mm/g.oq1zk 3;gw0hls 0.2 m/s and at an elevation of 202 m drops a package. 4.0 seconds later it drops a second package. How far apart will the twms ;mk3g/w0 hqz.1lg oo packages land on the ground?

  A package of supplies is dropped from a plane,q;dj 1(tvecpvq; x -:e and one second later a second package is dropped. Neglecting air resistance, tht(dpq: ; e-cv1 ;vqexje distance between the falling packages will

  A pilot drops a bomb from a pgu3k.x k;t;ielane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hg. ;kuxeti k3;its the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. Iyrd+,ay 4- bnhf you hit a bas b-hd,ynyr4+ aeball 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 at 55 mi/hvgc+ eqab ab9 //-wje) in the +x axis relative to a straight, level road and pass a car tra) - wa9bgbcq/+eja ve/veling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to crossvc-)p n2:kzaywn m:r5 a river 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 stary w5n:pmvcazrk) n-2:ting point. You should head your motorboat

  Your motorboat can move at 30 kxlp6d(o h9 .rdd /(dclm/h in still water. How much time will it take you to move 12 km cpldxlrd9d .h/6 ((od downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m atxh78+ nju4ts- xkxe n xsl2.8k an angle of 30 degrees below the +x axis. The y component of A xsekh784 -8nlxu.+k xnt2 sxj is

  If a ball is thrown with a velocity of 25 m/s at an a v,i4kbtj :d+o/o3 ic wm6.jefngle 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 directioh4se1szg+ ( psn north of east and you end up 2.0 km north and sevsh(+z1 ge4ssperal kilometers east. How many degrees north of east have you walked?

  A butterfly moves with as z0sp k1 10fb8rnm v*i; v8mh2uiw*xy speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle 0rzvpwi ;10vkymb8f *nu12xissh*m8between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m mjbi 8 c,fm1mzp;qyb/a8m/jrx q 9c3n3n6 :qxlong shadow over a level ground. At what angle isnr pj 6y3ncqmf19q aq/8;8c :mxzx,3ijm m/bb the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) a8 5;r hwnssqf/nd (-1, 3), respectively. What are the comsn8 5rswq hf;/ponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiven -ttv:,v lwfcmb g:;4 .xlg,kly. What is magnitude of the s4;f. lw:vlkggctn,:vx t,b- m um of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is t l4x 0p.7kjbqf,3sik4 syepn;ic4 s8ihe magnitude ofks4 43 ;nxbli fs,pc7i 0y8es4q.jkip C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disr. 33scbivy wzh7 e2d-placement .hc-3zrb3vdy7i e2ws?

  Three vectors, expressed in Cartesian coordinajncdoqh1xuv 0yj 1. : b1d.6tbtes, 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 Cartescd9c) q1-*8kf ejhusc j2 rvc3ian 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 magnvq-q- n/xlzyluw 5p64e 7a7u gitude of vector C4y/76glnu7 xq av w-qeupzl-5 = A - B ?

  A runner runs halfway around a circular path of radius 10 m. Wha;tq,+zhm yx/ot is the displacement ox q; hmy/tz+,of the jogger?

  Two forces are acting on an object asj7 2 ;qzbbz nfnxx9hrt7 h dq4589+y9fs9berl shown in Fig. below. What is the magnitude of the rz brj +ny qn2ldhq7x;4 xztbeff 997s9h9r5b8esultant force?

  Two forces are acting on an object as shown in Fig. below. What i afa7sypiti400d8st* j 0 g26l4fa migs the direction of the resultant forceta*j i2dt7pia8f0i46g a 04lymg 0fss?

  Vector A is 3.5 cm long and pek7sl o+7f ub9oints along the positive x axis. Vector B is 7.8 cm long and points olkfbus977 +eat $+32^{\circ}$ 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 63 cm long and points at ,vgmitx9y/+ k $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 36 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 13c+3okc jn31ys+ mfdu* 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 bottom3ucf*co13ns+ km+ jyd to be 3.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, from,zlbq q1fsj. w3j2a ;kxo62 na a bridge. It falls 19 m to the water below. How far does the ro 1knafz6ljqx a jbo.;,w3s22 qck travel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes the 0n9zu1 h69w+r fcwbk vground after traveling horizontally a distance of 18 m. With what speed was+nk069hwv bz ucwr f91 it thrown?

  A jumper in the long-jump goes into the jump with a speed oe7,ke wfdpg5lu x;94z 8 huet+f 12 m/s at an angle , d5x8elkuf+e7; 4zhuegpt9wof $20^{\circ}$ 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 ofc.gi 4p5 50pf5 f;u*nievdgtw 11 m/s at an angle of gn4w pu0.id;f5c i5 tfe5vp*g$31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocit.y 3gk r(s7j-9)bk qn .tycckmz,pv l-y of 52.5 m/s at an angle of $47.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 39.3 m/s at an angle of oc2; nd) m44w(ka4tsieb ufz)$10.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle oko du3rx1,2nlxo4fc9 hv u 86on* je:vf $30^{\circ}$ 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 19f:w4 ty vod23fs--rg,i no1ni .3 $m/s$ from the roof of a building 60.3 $m$ 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 initial speejw4;amx90j2c( ,i1t kdilynycr-w t ;d of 52.3 m/s at an angle o-;jtwc(4l1i29cn0j xiryd aytw ;, kmf $37.4^{\circ}$ 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 17l q do7m0a:h- xwun7c500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the ti:n- 7cw uxm0ohal7 7dqme 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 of0fg6c gh(r yh02()nnhcu5(kx 9lc w tj 50.0 m/s to the West. The plane's cwc(02jng n gythulr((x6kf95ch)h 0speed relative to the ground is

  A plane is flying due So 9tu)q2vrebf .uth ($270^{\circ}$) 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 12eruune cw.z25l m vl:4+t g86i0 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 ht km*hxv,a ;.qfxwbr7ri 5/p 6orizontally fires a projectile with speed 50.0 m/ 7qphi6vk;5rbwr,ma*f x.tx/s 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 river with aqcmtm s,soo.b89gjv+ fu36 :a current ofov:,soag +9fj38qucs bm6t. m 6.0 m/s. 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 stiedwwic-j3 x+ )ll water wishes to travel directly across a river3e) +jxw-dwic 0.6 km wide in which the current flows at 4.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move atiqui9rzcghc 8u02xgx +37 5hn 10 m/s in still water wishes to travel directly across a narrow strait in which the current flo7rn89 ugx zci3hi2 0+chgqux5ws 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 t2 wyc.p0i *; xf9niy x2abyd1+p0xfluhe opposite bank in 6 min 40 s. Sh0y fn;a+ pc2wplxiybx0yf2i*91 xd.ue is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite**lk1 5bdhbbm sa*k v2 bank in 6 min 40 s. She is swept d**msav 2b1 l *kbkhb5downstream 480 m. What is the speed of the current?

  A boat, whose speed in still wategcl f,x -7wb,fdgd z/,r is 1.83 m/s, must aim upstream at an angle of /gzff7xcdl gd,b -, ,w$21.3^{\circ}$ (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)  $m/s$