Which one of the following is an examdt*zl+ 7-xbn0wxr8ap vx5+p) dyr i n.ple of a vector quantity?

  Which of the followin)u*9 nizxk p)cb+g8nr g operations will not change a vector?

  Which of the followi980ig s0 2zj*sweiyb gng is an accurate statement?

  The resultant of two vectors is the smalles5g 9xa cci.np3t when the angle between them is

  Two displacement vectors have magni r qt8(7d(5kbtx8s5 (dlxahmitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude rx7 s mlk(xit 5d8(85ta(dbqh of the sum

  Two vectors, of magnitudes 20 .v wnr:xq34h jand 50, are added. Which one of the following is a possible 4jh3rw:qvx. n answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on ydji2sxps-4ji)zbjz2y. 5 j.an object in directions that are jsjz4 zy ..-jijd)5x2 py2b is$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown ve3ohuv(i1qnv3)qn7y p47pk g xctor is

  Ignoring air resistance, the horizontal component of a pro.1*kud 9 ifm5/4l8:4 muvzq yxguagab jectile's velocity

  A ball is thrown with a velocity oz2vb 7r( yll;arpbl m;h: 5w5djpi,d.f 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 horizon8v;su,/a/v2zryn5c tdj9cr5w g l lg,tal component of a projectile's acceleration/jcvv,s2l,w9 a ng5 u5crl ;rtydz g8/

  A soccer ball is kicked 6z;y w4mu- mlqwith 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 is directed anti-parallel to thuh ++v4clce.w e velocity vect4cuv+ l c+e.whor,

  If the acceleration of an object ism j 5wcziwom9n+-3g,k;sb /hwnj*x +s always directed perpendicular to its velocity-wi j9+o3m, wbc+ssg/xj; 5 n *whkznm,

  At what angle should a water-gun be aimed in order fo 6)7huu2 u ed:4mebjugr the water to land with the j d4:ebg2)hu euu u76mgreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above thx,cd9 mmv8x /te horizontal, each with the same spm,8 xxmc 9t/vdeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second 70 2*1qkwa6 ,rub bet.vo+dxlzx.ryj time. If the ball leaves your hand with twice the veloctkwlq1*od 0yru zj bv6.ae+2. 7xx r,bity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at *gk9 b upcg04wan 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 height, how does i*-3 wple dsn+g5)xbpd+f3g kdts speed compare to its initial speed sxgk-dddp3 p* lnf+ we35)+gb?

  A stone is thrown horizontally from the top of a tower at the sbx l.oq3qr +fb+xy:7clxp u5 ;ame instant a ball is dropped vertical pq :;5rxx+xc 7ofly.ubq3+ lbly. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullrjbx d/m*/0v dc tc-z.et is dropped from the same height. Ignobrj/.c0 xtvm-zcdd */re air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 56.3 m/s and at an elevation of 2tkte* eb:5n :y4 qu,ij77 m drops a package. 7.6 seconds later it drops a second package. How far apart will the two packages land on:ijy e t,:e4quk* tb5n the ground?

  A package of supplies is dropped from a l p3t;3oqrqu1xk3e ;.y,qlofo-p u3r plane, and one second later a second package is dropped. Ne y.f r ;ol3le3 uxo;1k rp33qptu,o-qqglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontalqfwie;)s fmo-,(sy p6 ly at a constant speed. Negle s 6,wfq -sm(fpe;)yiocting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-s4zqk5ycce w/v(y8)emixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you wouldk/8 )qcec4 5yy vmw(ez on Earth, the ball would land

  You are traveling at 55 mi/h nvy,kcvkluvqi -f,6f; 0cx5 t 75(e akin the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative ;x cykuan,5q0v ff(76kek,cvv l-it5velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong curre0r r8f ef0b-pe u,s-wfnt. You start out in your motorboat on the east f--,ru srfef0w80bepbank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at auih k,9k(b1q 30 km/h in still water. How much time will it take yokua ,ik(1h9b qu to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angl v nj8nn(qh0f4e of 30 degrees below the +x axis. The y component of A if nnn40j8qh (vs

  If a ball is thrown with a velocity of 25 m/s 5rqtcm,5e,o w 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 ;qpa sw 4s(yi;north of east and you end up 2.0 km north and several kilometers east. How many(sy s;;qw ipa4 degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 mavic)ls -3es*rp5j i 5/s. The x component of its velocity is 8e v*j3pi5 5sia)rcl -s.00 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what f ilzu/lfi29w4zk0o 4 angle is the Sun elevated af49flk0z uii/4 w2zl obove the horizon?

  Two vectors A and B have coamo;q*3u, y,pwv)+i 7p hjk atmponents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two v3h up;ak +tm)ya7,o*wj qip,vectors?

  Two vectors A and B have components (0, 1) and (-1, t ibei s4 .yjw b6(y*hk,-hb0y3), respectively. What is magnitude of the sum of th,i*tyseh6iyjh 4kb w.( b0 y-bese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B 4x1;fcmvb.vti ,tqgr;rnzs:y/yk* / . What is the magnitude of; 1.s/vrkx;bqv,r:tf/ iync *z4gt m y C ?

  A car travels 20 km W +xz;(7eshz ca tbk) z/.ycnblth8*1 qest, then 20 km South. What is the magnitude of its displacementl8t*hqb)c sb; x.hetnz 7/a zyz1(ck+?

  Three vectors, expressed in Ca-lt/f rk 7t3 t0dhx+quzmz;j4(dha l +rtesian 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 dvt(; p0v4l1bd 5yf ud98 yyhcCartesian 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 = q 1e7g -4s/+4to. dmyjvamohz (+3.0, -8.0), what is the magnitude of vecd1.z os 4 4vja/q-yehg7tom m+tor C = A - B ?

  A runner runs halfway around a circulaf3z w5a 9-rzjtr path of radius 10 m. What is the displacement of the jor wa-3fj5zz9 tgger?

  Two forces are acting on an object as ssypa/ldv 9)hk 2*r*a )kv, p/vs1pzikhown in Fig. below. What is the magnitude of sh l* //)v rsi9vyk,vkp21)zkd*appathe resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the 4yea (8pyx2yc direction of the resultant forcyypx2c ey (48ae?

  Vector A is 3.0 cm long and points along the positive x axis. Vector B v)uwq9;,sypnod xc(itxm w(r+)m/m, is 6.7 cm long and cd)i ,(sqn ,/vm wx+; 9xrpmoywtum) (points at $+44^{\circ}$ 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 74 cm long and pj yut6g1n nj8f29nh3jxx5z1 idv04 vfoints at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 49 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 horx er, :1g83zsevyud0pizontally with an initial speed of 15 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 bottom to be 4.2 s. What is the height of the cspzx8:ydr3ev gue10 , liff?

  A girl throws a rock horizontally, wnc: uyv /6h ;e2j5frhqith a velocity of 16 m/s, from a bridge. It falls 17 m to the water below. How far does the rock travel horizontally before striking t 6hh5veu :j;/2cqnfry he water?

  A ball thrown horizontally from a point 21 m above2d )mr:v90f sylzd.km the ground, strikes the ground after traveling horizontally a distance of 21 m. W)2dv9mkmy lrd0s f :z.ith what speed was it thrown?

  A jumper in the long-jump gp1gua:xq gr4hn/c) -8dj: rui oes into the jump with a speed of 12 m/s at an angle of i:x/1r:qgdc)j4 u gura8p-nh $20^{\circ}$ 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 of 13 m/s atzi +sfca2 b+;t an angle oaf2 t;b+zsic+ f $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velociwb28ex q8a gz;ty of 30.0 m/s at an angle of $15.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialru9mimn 2lh w/ g+41/n,ofwvd velocity of 21.7 m/s at an angle of $44.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle 7cvpjf .-fopc bu tpo m175,a7of $30^{\circ}$ 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 19. 7;i/ayxt gbn/o 2(wgom;uz/i/pcn6x 6 $m/s$ from the roof of a building 45.4 $m$ 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 an initial s4 tda;ja9rmu6 peed of 38.5 m/s at an angle of;m rdaa6t9 ju4 $43.6^{\circ}$ 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 150nm9) xtes(,tmcc h (vh8x,jl70-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 2lcm7m xt8vxhcn ,h 9,j()tes(.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s du.qq gvf : 2on3r/p3xj/g 6a5gs9vhcile North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to th/ r63v:sgo i.g 9xcq/2 3fnpgvlqah5je ground is

  A plane is flying due Sou w2vlfydjvk;*l2 e6l 5th ($270^{\circ}$) 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 spe0wpj;dl ry a78ed of 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 ohu5lp4 kf g::s9ht-wj v;l *hhorizontally fires a projectile with speed 50.0 m/s in a forward directi hhjg kplhvfsuo 4;t-lw:* 9:5on $30.0^{\circ}$ 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 w+ sm;qn+u7 g)igzp;kxater is 8.0 m/s, is directed across a river with a cur ms pnuki)+ 7xqzgg+;;rent of 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 16 m v0qd hn-r61tfz*vtx) /s in still water wishes to travel directly across a rivdr1vnzft-q *)v xt60 her 0.8 km wide in which the current flows at 5.8 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 trav o-alm-c6 vqi4j0 oz*tel directly across a narrow strait in which the current flows zc4 j6*a- -ol0tomi qvat 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a r8 ze ;uqz.epi, ge**nyk9ypcu5*e w x7iver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. gc kqze*p p, eyz*yxne5.;9*ue7wi8u How fast can she swim in still water?

  A swimmer heading directly ax1ak*e r.m)18uj /duz/pqvv across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept d e /)u/ q*kuxpdzj.amv 8arv11ownstream 480 m. What is the speed of the current?

  A boat, whose speed in still wat saj)nkpdj/s:jq:iz nb p.e0,+c b r02er is 2.09 m/s, must aim upstream at an angle of .be: da +,ps0n02ni:)crsjqjbkj/zp$19.8^{\circ}$ (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)  $m/s$