Which one of the following is an example of a vector quanti.h u7l+vvs.3xd6ztb9bsy 0v t ty?

  Which of the following operations will not change a veii3x9 t bhp9n(ctor?

  Which of the following is an djcdy yaf.sfx,p2 /81accurate statement?

  The resultant of two vectors is the smallest when the 9htc :mqei,*hangle between them is

  Two displacement vectors have magnitudes of 5p4tdne copm8sr3xfg : 02 7y4f2 1ipho.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude opfo4 0r7yxg2ppohm1 i384dfenc st: 2 f the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following /+2*xllg)xjg xxfsd d1yc9/, jn4xi iis a possible answerxc9xj)j*14dsxi+ldg2 xf /in,x/gyl for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N,jlbe(o.0q6 c88tgzc w pull on an object in directions that aqzb l0j cgw8 eoct68(.re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknow nq: fg2(fes8tn vector is

  Ignoring air resistance, the horizon, bn:zp) s;ae 1soy ia*j+fi(btal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angl *wc*9*zqwvite 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, 5),jyl1 r9adwib1pxmagvbu22pv7 2 othe horizontal component of a projectile's accelerationvmpw52 1b7bi)2alguvjy 2dp9ox a ,r1

  A soccer ball is kicked with a velocity of 25 m/s at an g +kziog./lh- 8z9udsangle 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 is directed anti-n pfjnm/5 qzpx n; zha45g5m9-parallel to the velocity vectojxaphgznnqp4 ;z59-5/5 mmnf r,

  If the acceleration of an object is always di 86vv x7(cc xfou*2azfrected perpendicular to its velocit( x6f7o vz8*2xfaccv uy,

  At what angle should a water-gun be aimed in order for the waterindbg g0+h324r j4c qt to land with the greategbdg3 thq0r + nj42i4cst horizontal range?

  An Olympic athlete throws a javelin *i2d4iie, s nrat four different angles above the horizontal, each witsn ii24ird *e,h 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 bal rhpd.+2vhp f(l for the second time. If the ball leaves your hand with twice the velocity it had on your fir2hfh( vrp.pd +st throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an orii2h:tg4ae-t 9cc jzkr3 20dfyginal 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 at6ishy26q ce;p 1./ xdbf- auqgtempt reaches its maximum height, how does its spy6 bqd .qpc1 hse;agif 26u/x-eed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instau kk y nr:umylp k),;ao.8ux;3nt a ball is dropped vertically. Which object 83 y ya:u;u nmrulkkk,o.p;x)is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same kt64t 0 n0ayx0b ap;gdinstant a second bullet is dropped from the same height. Ignore air resistpa kdtg6b0 4nta; y00xance. Compare the times of fall of the two bullets.

  A plane flying horizoca p)m;cv,g+zrh* 8rtwggs4( ntally at a speed of 96.6 m/s and at an elevation of 166 m drops a package. 4.2 seconds later it drops a second package. How far apart8gsm p, av4t+z*wrchgr)cg; ( will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one secoc tpjj5u/(9ueyo obwt 992eg*nd later a second package is dropped. Neglecting air resistance, the distance between the falling packageswpj9/*gtu(t95jo b oye92uec will

  A pilot drops a bomb from a plane flying horizontally at a constant se;8a3;rp2 lvesrm gefzwv53o s; /o :hpeed. Neglecting air resistance, when the bomb hits the ground the horizontal locatizmo8ha2se ;veg3e :3vo sp r/r5;lw;f on of the plane will

  The acceleration of gravity on the Moon is onlyecp4kcpno xf( nus1ag*/:(42l ea o0z one-sixth of that on Earth. If you hit a baseball on the Moon with the same ef4csauxa2/ zo4f l n ngp1oeepk((*:0cfort (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 relative tbp)qvu;;k*hv-(dp x7q gk j;mo a straight, level road and pass a car traveling at 45 mi/h. The relatik; pxb( m kqjpuvqd ;7-*hg)v;ve velocity of your car to the other car is

  You are trying to cross.; jqg gsegb 2s0t3def430hgk a river that flows due south with a strong current. You start out in yourgkbdj g eg.40 e qt23;sgf0s3h motorboat on the east bank desiring to reach the west 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 will it a8allgl6*nb17* np*jsamd a9take you to move 12 km downstream, in a river flo d**jnngpsa79l6*laa 1 al8mb wing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. The yu :npnyh g 8qbl.7zu96);ip jk component of j) h7 qbpkgzyn8; up:.n9i6lu A is

  If a ball is thrown with a velocity of 25 m/s al ,;0 ulz3i:6 sfhpzeyt 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;ps dubu r-n2qev0q4( in a direction north of east and you end up 2.0 km north ndq0e2rvu-p4sbu( q ;and several 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 t/ aw2*p w im .)daz5cq,padz9velocity is 8.00 m/s. t.95/zp aaw2mw*cdd)a ziq p, The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m lkxpuvq*rms:8 yu-q65/ hhj2song shadow over a level ground. At what angle is the Sun elevated above/h k p*2:hu8uqmsrjvq5y x-s6 the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), regr8,t3 l qr0se +h 5-+hatqbjvspectively. What are the components of the sum of theqbq+tal8, +tev3 rjrs-h0h5gse two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What is,ftoit8;8 o zl5er2bo2 ,eu 5ywhqd 2p magnitude of the sum of these two vectors hfty52u; deoo2t,o 2e5 w8pq r8il,zb?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = y,jd4wqg9tp 1n/:n (x:yp4 epnsfrpp h,u/1bA + B . What is the magnitude of 4g yr/,:p wnbns(pjpfhypd 1et9 ,1xp4nqu/: C ?

  A car travels 20 km West, then 20 km South. What is the magnituu1/ jq*c3qcvb xb nl rte-7a))de of its displaceme))n xqbq lav-cj*3u 1/t crb7ent?

  Three vectors, expressed pav(+jk ) mbtrl:.gh3in 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, expressedyu1 t62cu 1avx3shc7tp+sc2e 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) and vector B = (+3.0, -8.0),tx6v( wa1hj1p what is the magnitude of vector C = A pj 61a1wv(txh - B ?

  A runner runs halfway arounuf,i(7a4t g cdd a circular path of radius 10 m. What is the displacement of the jogged,f g7cau4i(t r?

  Two forces are acting on an object as7e9ji:jbr9g q ea0*t p shown in Fig. below. What is the magnitude of the aiet0*9:gr 7 qpebjj9resultant force?

  Two forces are acting on an object as shxlr7s 3d/byx1c*1a kx own in Fig. below. What is the direction of th/l3 *k a7 r1xxsxyc1dbe resultant force?

  Vector A is 6.0 cm longamupjd;) o4mo3ya5q(;zw i*a and points along the positive x axis. Vector B is 5.8 cm lon; ad4; 3zoa jm(pu)oiwq*y5m ag and points at $+53^{\circ}$ 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 80 cm long and po2 .0j5rww:a)aaruqk h ints at $30^{\circ}$ above the positive x axis. Vector B is 19 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 o)e:j id7*vi3lh4jm)t fs2i5oby 2 i8ne3 qngxf 29 m/s from the edge of a cl2 5d4ix onf*yi7m)i: hvne qjg8 3bst2)ij3eliff. A stop watch measures the stone's trajectory 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 horizhw t245aguhw:e6o fxc3q z:q5ontally, with a velocity of 13 m/s, from a bridge. It falls 14 m to cqxhf w g3 oqa64:w2:z e5uht5the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from asv9oa-k,7fa:mbw * mw point 30 m above the ground, strikes the ground after traveling horizontally a*s9bwwk7maf v,-a: o m distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angftpey f-l79y*4m9b j ale ol y f9b-aptj94fym 7*ef $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-+t;px gesis.. jump goes into the jump with a speed of 15 m/s at an angle o ep+.tsig. sx;f $18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initi1ap6e/h 9-bjp x5dqu,x:w a,(twbs xo)a 1n snal velocity of 35.3 m/s at an angle of $46.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launchyt7d7 6,wkkjx kqg,2 oed with an initial velocity of 41.7 m/s at an angle of $42.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle 8h2e u,ww4o96ycysdssnq2k4 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 at 26.2 3onam b4w-h . aid(n-f$m/s$ from the roof of a building 31.1 $m$ 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 speed of 56.7 jx+1/y ay:vnv1vd1pl m/s at an angle +1alvyy1vjv/ :dn1pxof $46.2^{\circ}$ 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 run a 1500-m race a 1bg sxo (dnhpr- 1l428rpdc:qt 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 time it would take podnrl:21b8 hr -(cq1pg4x sd you to finish would be

  A plane has an air spe qck 9n)+bn(2 zs(l,b13xi jjgn w,lened of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed rbq jzb,w xnjc)1s2k(,en+gnl9(il n3elative to the ground is

  A plane is flying due ibq (llfg(w;;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 ofkfbc c d u5a7ath-m8ti:kv- pc6ow413 120 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 h3p:i eveku-7t)xx;al orizontally fires a projectile with speed 50.0 m/s in a forward 3txa7 )ev ue lxk-p;:idirection $30.0^{\circ}$ 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 widd3z5re6ds,k / s/zvpth a current of 6.0 m/s. What is the speed of the boat as it crosses s/dres d63/pdzzkv5 ,the river?

  The driver of a motorboat that can move at 17 m/s in still wq :5u:,)f 73zxms- nbdq gkk8uuvqmag8 q4o3hater wishes to travel directly across a river 1.7 km wide in which the cqso:quam)g,q3m4x- fdq3 zuh8nb :58vkku g 7urrent flows at 5.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that * c zt ajzl1c;uec:8i)can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angl z l*)atj8eucc1i:z;c e upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bajmtu 2o 4to5g2nk in 6 min 40 s. St 2guto 25m4johe is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly 1u6z uqvn )xv(across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the spquv 6) n(vuzx1eed of the current?

  A boat, whose speed in still water p-l xfni8s5e+ is 1.81 m/s, must aim upstream at an angle of nf8-liep 5 xs+$23.5^{\circ}$ (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)  $m/s$