Which one of the following is an -6oq:9hcf b :u l79hpbazu:9. fgozhwu93 cswexample of a vector quantity?

  Which of the following operations will not change a bm,)z8jf2ys h 3/hib6z +sixhvector?

  Which of the following is amtikbl; .v:/hjq)un3 w9x-uen accurate statement?

  The resultant of two vectors ic(la3e*;cro ys the smallest when the angle between them is

  Two displacement vectors have(g svveb 3ntmz9)yrtqv;( ,4 c magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the mag r9 gt4(q nsv; zeyc)3vtbvm,(nitude of the sum

  Two vectors, of magnitudes 20 and 50, are 7* ;uf;nt9/xydgcx zk added. Which one of the following is a possible answer for the magnitude of the resul ;f9y*kgxxnzcdu ;/t7tant?

  Three forces, each having a.3b4o5mu / 5ai4y fhwulsj ;vq magnitude of 30 N, pull on an object in directions that4/.a vfj3u5 5oyl m 4wh;usibq are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoi5d tx)d;w hi.wn vector is

  Ignoring air resistance, the horizontal component of a projectile's veeeq953 fjyo;x locity

  A ball is thrown with a velocity7 eujo:q )kv1m 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 compo5 rda3 l+6japr6n(nvz nent of a projectile's accelerationar5ln arzndv6+ 63(pj

  A soccer ball is kicked with a velocity of 25 m/s at an913ppxmngv r5s j *am, 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 o ++kew +,gbdvbbject is directed anti-parallel to the velocitbd+ k g+vebw,+y vector,

  If the acceleration of an object is always directed perp-f/bwko4 fl/yb (j 8quendicular to its velocityyuwfj4 8fkbb-o/ql (/,

  At what angle should a water-gun be aimed in order for the water to land with th3dw rmw aa25mii9tct. .0qi6we great3m5rq2t t.6 maiwi dw.0iaw9 cest horizontal range?

  An Olympic athlete throws a javelin at four different anrj4d0pll0 b 5sgles above the horizontal, each w jrdb54 lls0p0ith 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 6is84y cy5qbfa umgeg* j2+w: second time. If the ball leaves your hand with twice the velocity it had on your firs a5* :iyyj4 f2cwg mbe6us+8gqt throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an ori2e lwzcox*5( ppq* ;wfw;ytd t:e+q5n ginal speed 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 maximum hecr8e -qbpq:) zight, how does its) ezqrc-b:8pq speed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower ajcpj445 uszg7t the same instant a ball is dropped vertically. Which object is traveling faster when it hits t j74sz4c5j pguhe level ground below?

  A bullet is fired horizontally, and at the same instant a secw.(vf;/qbqr ;az *yprond bullet is dropped from the same height. Ignore air resistance. Compare the times oq wzq/.rr p*( b;;yavff fall of the two bullets.

  A plane flying horizontally at a speed of 54.3 m/ ui .lidmpe2qg/h4):ns and at an elevation of 203 m drops a package. 7.8 seconds latelqi2 ep) h4mid: g.u/nr it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped frotv xr 959-wf 3r, ced4;b4 utsjgy8oeqm a plane, and one second later a second package is dropped. exj5w4bd r4c;tgtu3 vfo8yq-,ser 9 9Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizont3ooza1 lqfv*6ally at a constant speed. Neglecting air resistance, when the bomb q v3la6*1ozf ohits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of thawhhxm(4g+5c3so7 jzi kh2e3c t on Earth. If you hit a baseball on the Moon with the same effort (and at 3+hmc( e5 ocz 4hsj7g2wh3ix kthe speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level 7)hn-ebtecx.cd(9t.oav -j* c;x b a uiei )y/road and pass a car traveling at 45 mi/h. ee tucc7xce. vt;bi.a *9/hd--i)y)nxjab(oThe relative velocity of your car to the other car is

  You are trying to cross a river that flop 5+thadrn pr,//er *kws due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly weska/edh /* 5 nrrpr,+tpt from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stifrg rdptv7s2,v a1s:8 ll water. How much time will it take yo2s7t,1s8fdvgp r r:vau to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 4lsu-0,l:psc2zki .b )l3re rb 1bvxo m at an angle of 30 degrees below the +x axis. The y component of A iso)r13 lxs b,u: -4lkzis.e2 vrp 0cblb

  If a ball is thrown withg7:r2 ipmb2emp* e0+6g whfik a 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 east anis2 k q:x:69x7aq crdfd you end up 2.0 km north and several kilometers east. How:xq2asi: 9c6 fkdx7rq many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x l6br2dw50+mdf7fwil component of its velocity is 8.00 m/s. The angle between the direction of its motion and the xfr7b dwml+65l0 iw2f d axis must be

  A 400-m tall tower casts a 600-m long shadow over a level gc)d zx6vkt n(jcu43n8round. At what angle is th34cu6 n8czxdvtj (n)k e Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3on7ds vw.bb hx*eji 4n4ys *q:js7a4/), respectively. What are the components of the sum of these tsb n js:*/.dbhaj*swiyevo x4q 7n744 wo vectors?

  Two vectors A and Bpopl)2 y -m1ip 8qwls9gn6 .hy have components (0, 1) and (-1, 3), respectively. What is magnitude of the sumqhsl2-g6wm9)p81ny ypil o.p of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mag9v5e exgnn 5h76f iu6gnitude of C ? x5n 6gue6f 7gi9hevn5

  A car travels 20 km West, then 20 km South. +u*0trt:p6u-aakyj8m/ i0as f1b i cgWhat is the magnitude of its displacementy-1rp uitafut im ac0/j8*kba: +s60 g?

  Three vectors, expres( iwr1t8i9nhyue5c9fsed 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 in Cartesian coordipwz95 ;6qsavh*h) pd jnates, 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),f h01bp dxe11qokh8sie)x+ y . what is the magnitude of vector C 1xpiby)dx1.ehf8s+h keo1 0q = A - B ?

  A runner runs halfway around a circular patneepkn :1.to.h of radius 10 m. What is the displacement oeoe1p:nk.. t nf the jogger?

  Two forces are acting on an object as shown in Fig. below. What wmcg ha3uc7;pnmm.1 -d1ujt :is the magnitude of the resul7nm1gj;1ht cup wducm: a3 -.mtant force?

  Two forces are acting on an o(rl,7k iiraf kthfl,k t5,g -e ac8jr5)2 yxy4bject as shown in Fig. below. What is the directio ( fliic2,t,xrt8 kl7 gr)5ay4yja e5fhk,k r-n of the resultant force?

  Vector A is 4.0 cm long and points*k e::x x*vd.eieflp: along the positive x axis. Vector B is 5.8 cm long and pointspx*i edk:vxle: .:fe* at $+46^{\circ}$ 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 60 cm long ajf40) huz7ifsnd points at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 32 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 horizontall*vm70psb, at b:dm m/iy with an initial speed of 21 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff t,mab0/mmi:*dp v ts b7o the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizojsrkdn76c6 *3 +en6 1bwrei vv86okswntally, with a velocity of 17 m/s, from a bridge. It falls 30 m to the water below. Hk8d ke nw*nb7vj +rv6 isw666sc1o3reow far does the rock travel horizontally before striking the water?

  A ball thrown horizo0r/2+exyy2i xtnf) i6kd g-dontally from a point 29 m above the ground, strikes the ground after traveling horizontally a distance of 21 m. With wha )d0k2d-r gientf2o/x yy6+xi t speed was it thrown?

  A jumper in the long-jump goes inttwv)f*+1 3bgr c;k0 fpw;lj ngo the jump with a speed of 12 m/s at an angle of ft ;wlbg)vj3pf1;r* cgwk n+0 $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes i/nt4 2aquf g;tnto the jump with a speed of 12 m/s at an angle of q;t2gta/nuf4 $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 30.0 m/s atxh3197h3i juv)yn zgbsvz/*g an angle of $14.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initiale jrq0tvka;jj+c*88m( 8ircd velocity of 42.8 m/s at an angle of $23.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of/ac8v ;t2*l ivmu hf8p $30^{\circ}$ 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 horizontallyk)o8*z2m *xzhg3do nl wakl)*0 zll+f at 26.0 $m/s$ from the roof of a building 59.4 $m$ 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 an3k( ;q 8mbavlp initial speed of 57.9 m/s at an a;bqvpl8km3 (angle of $40.7^{\circ}$ 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 ofgq*.;w g2 0llzcw g*rl.vxq9co4w0mp 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed bpm2; wrll.. ql c qgxw40 0o9gwg*zv*cy 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 wze 3dnlq -:b .2by+qvm/s due North, and is in a wind of 50.0 m/s to the Web2n qdq: bl.y-e +vzw3st. The plane's speed relative to the ground is

  A plane is flying duefbk k:0pw)+r q 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 120kf b m*yig78r- 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 horizontally fires aro1r5gf* +yfp projectile with speed 50.0 m/s in a fg o+pfy rf1r5*orward 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 st:n uryisd30m26ga 19i om7k4p8rkivuill water is 8.0 m/s, is directed across a river with a current ospi7uromak kv1m9u gidr2 603 :y8 i4nf 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 19 m/s in still water wiyn6axv bqa1a /dg9 uts;m6w+6 fc+3 krshes to travel diar/bn6+a+yu 6dm91sk 36;v w fctqgaxrectly across a river 1.1 km 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 2+ 2tjmw.vcsowater wishes to travel directly across a narrow strait in which th.+omct2v 2j wse 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 bank )s eq styt b,ku(::kt*txg4)fin 6 min 40 s. She is swept downstream 480 m. How fb u: : eytkt x)ttsf,g)*(kqs4ast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reachessqnbi-y-b7gn4* 6lso the opposite bank in 6 min 40 s. She is swept downstream 480 m.nyln - -s64*sq7gbiob What is the speed of the current?

  A boat, whose speed in still water is 2.01 m/s, must aim upstream at an angle7w,xt m8cjbir4(qxmz d)g+ y+ of xczgjtiw4r+x,q7m(yd )b +8m $29.6^{\circ}$ (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)  $m/s$