Which one of the following is) er r4dyqb*(q an example of a vector quantity?

  Which of the followin yj/*c: wmwa)0d jl6vf utt-n1g operations will not change a vector?

  Which of the following is an, wiuxy7jqp v(zvr911 accurate statement?

  The resultant of two vectors is the smallest whwp8w + j*bsw,csbdf0 (4jak,jen the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0d-ccd1 al8,o1m cj+ e:a.uyaqi5zkz+sv ;o)z m, respectively. When these two vectors are added, the magnitudj )ecdy -osa+5.kz;oca 1iamdq ucv8: z+,l1 ze of the sum

  Two vectors, of magnitux0blb8sb. 5w6aw cxt-(o ,dbgdes 20 and 50, are added. Which one of the following is a possible answerb g5,86.sob0x(bwx td-lawb c for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull onoew f2li bh7 s:z9zp); an object in directions that arwe7zi:9 zl)b2s hopf ;e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec a ro iboj1ewo24js02*)x; umctor is

  Ignoring air resistance, the horpuw0c(bdwgzu ) w+p40uhn1o ;izontal component of a projectile's velocity

  A ball is thrown with a velocity ofc(k r4an/3yz z 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 arz ,8 suqq7,uuk*7c0 pxxnathc1cx*5 cceleration* xt c ,qcqxn8cr1075u hau7,kz*s xpu

  A soccer ball is kicked with a velocity of 25 m/s at an axwn:j,o)p,ug.2h evz 0 wm *gdngle 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 thvqz 6wt23 ny n;rin4f9zl1hi. e velocityq rv4 znfi1z ; l.3ht6in2wny9 vector,

  If the acceleration of an objjfiivq-lpsitb( n6lu*o/x 9- sym721ect is always directed perpendicular to its velocity,lxsi mquby27l- (f po/*n9j1stiiv 6-

  At what angle should a water-gun be aimed in order for the waterjz/m(bynxk+9b fn73 r to land with thebmz3x njb/r y7+9nk( f greatest horizontal range?

  An Olympic athlete throws a javelkonl h)e4,i6 +qp lj -kl2ldh0fl o,i8in at four different angles above the horizontal, each with the same speed + nifol ,k)llkho e8qli dl,h40-p6j2: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secon fn.c8 le3lsp(d time. If the ball leaves your hand with twice the velocity it had on your firstef38p. ls(lnc 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 an angle bl*y8 /i /p)oz9 kjooqof $35^{\circ}$ 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 rea,)ypawuxkn,,p5cn6yc-l s;a+r,u a q ches its maximum height, how does its spe )asuax c urn lwp +5qp,yc;6-,y,an,ked compare to its initial speed?

  A stone is thrown horizontally from the top of a u9 2wzsojs35:bfh0ru tower at the same instant a ball is dropped ve2 rzus3buoh09:j5fwsrtically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a s r5uh dw1hx0lxm 94h6d5t6vhyecond bullet is dropped from the same height. Ignore air resistance. Compare the times of fa0h9yd wulh6x5h rv56ht4 1m xdll of the two bullets.

  A plane flying horizontally at a speed ofrrvk60 m -meb3 96.6 m/s and at an elevation of 292 m drops a package. 4.7 seconds later it drops a second package. How far apart will the two packages l rmk036b-re mvand on the ground?

  A package of supplies is dropped from a plane, w ta5v3q xg*+wand one second later a second package is dropped. Neglecting air resistance, the distance between t5gv+t*qwxw 3 ahe falling packages will

  A pilot drops a bomb from a plane flying horizontally at a const )u8ejk+ hicv,gyqv (.ant speed. Neglecting air ).v8,(vcqhu +ekjiy gresistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of thaii :3l. w5evomf1o,qf t on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would offml,e1i:qw . vi3 o5land

  You are traveling at 55 mi/h in the +x d)v-1b m qmwnb,+4beg axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other e-vwb+d) bmgqb1 4m, ncar is

  You are trying to cross a river thg,zlt 17kw+ m5v ig)msat 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 startis1vm,5tlw +mk7gz )igng point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take yvqr:ccl ,( j ym04(cncou to move 12m cr4: (c0cnqj,yc(vl km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees bel(i,rlwg n0a 6bow the +x axis. The y component of A (6iwl0 ,b nargis

  If a ball is thrown with a velocity of 25 m/s at an aw ,f /9(ba4cl1 olqiiqngle 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 aizt1* :2 wvlu.ul8 6 zgl,crpe direction north of east and you end up 26llug*t r ,l e:1wui2pvzc.z8 .0 km north 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 c e+e9lly ,hz-of its velocity is 8.00 m/s. The anl+ c9,yz-he legle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a*k j+if4xplcjpp o4nlq4/oqeo(+zm 1we 9:/v 600-m long shadow over a level ground. At what angle is the Sun elevatlve+q*9(m/qozj l1xpjpiwc k4 4fop+: /ne o4ed above the horizon?

  Two vectors A and B have componene0*un 7mrwd*u+wvn 0fts (0, 1) and (-1, 3), respectively. What are the cwwnmr*ud 0n+v7u 0 *feomponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respjguzn,ehhz5xy u*-p(cq ht1;e 9;s.rectively. What is magnitude of the sum of these ttqg h-h, ;nu15je(u.9*hcrz szx;e yp wo vectors?

  Vector A = (1, 3). Vector B = (3, 0). Ve yw9ez r hxnbt-5:8y+k5u 64b:g chvwactor C = A + B . What is the magnitude ofwzbxyy aertw5k:9vh+h:-5 g n8c b u64 C ?

  A car travels 20 km West, then 20 nk adr)/q,4 xzw9mv1ekm South. What is the magnitude of its displacementve k/9xq wn dr)ma1z,4?

  Three vectors, expressed in Cartesian coordin)w9x mdr75h mnates, 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 coo d: gw 6qq esb2gq1:5:xg)uvwjrdinates, 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) af2k0so3b 7bkem7 by7z nd vector B = (+3.0, -8.0), what is the magnitude of zbs k70b237f beom7kyvector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What id ,2sc4t)xv7nj . hnrigr p.1.t,fgoos the displacement of the jogger nx.o g p,)ri4vsf.oj t dc,ghn17.tr2?

  Two forces are acting on an object as shown in 8slk mb57x7;ekr c z b34:wcen*du4maFig. below. What is the magnitude of theed4ma; 5xmb 8c7ks*k l7nu:e w3br zc4 resultant force?

  Two forces are acting on an object as shown in Fig. below.8y sh/ebjf1,k,5* 1x: nzsqajorg +q a What is the direction of the resultag ro+sabes ,,hz*q:1fq8yj15/xjn aknt force?

  Vector A is 3.7 cm long and points along the positive x axis. Vector B is 8e -h/a)i8mg(rb6k7euk oxh,u .2 cm long and points ohkkx , )meu87(g/ba ur6ieh-at $+59^{\circ}$ 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 79 cm long and poiq/sv3ak -6f3m ya zmqwqhw3 :6nts at $30^{\circ}$ above the positive x axis. Vector B is 23 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 horizontally with an initial speed of 19 m/vzqrgmk7gljdd2/n+9*g: qg* s from the edge of a cl9 gdjq*q/m :zg2dnvggr+7* kliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 11 m/s, f*-ycc k:o x)rtrom a bridge. It falls 21 m to the water below. How far does the rock traveyrtxoc)k *-c:l horizontally before striking the water?

  A ball thrown horizoxhvzwfey x6+ h + +54tt7ednm2ntally from a point 26 m above the ground, strikes the ground after traveling horizontally a distance of 16 m. Witt6dwe hv5fnz2 +++txy4h exm 7h what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speeda.n g6y(*d qr1po*dw df74 kkq of 12 m/s at an angle w.fyd ad6g* po(q74 1k*ndrkqof $20^{\circ}$ 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 ( :,cge82lj z+aam.d parvebf 7oi38za speed of 9 m/s at an angle offl i3egm2.z vo:z jb 7e dac8+rp8(,aa $38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 22.7 m/s at an angle ofrwq:i qs n99*pmlb,8i $23.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial2c+,xtm 7 dlmx velocity of 45.5 m/s at an angle of $45.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fige h vl6vz13fa9 s;uh,red at an angle 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 horizontall38 06gts 8pyowdab8fqy at 26.8 $m/s$ from the roof of a building 40.4 $m$ 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 speed of 62.9 m/svddui /vz)*r uid ,16d at an angle of 1ddr)uiu6 v*di, / zdv$46.4^{\circ}$ 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 1500-m rac; lu;shu+jseu-u227 yw ib z0fe at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slowsissj ly;+2w-27 zfuuubeuh;0 your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 2(+h coq+no0r7t*tlp t6zc, fd00 m/s due North, and is in a wind of 50.0 m/s to the Wet 0 ,rq7on ctpl o(6htz+cf*d+st. The plane's speed relative to the ground is

  A plane is flying due +f o30ae1r bmqtt(f9u 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 i/ir:aa7:gr:yux * eehs 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/o+zpe 4h t zj8zvw44wr *d+y+ms horizontally fires a projectile with speed 50.0 m/s in a forward directio r z8 4oj+p+4dtw+ m*v4yhzzwen $30.0^{\circ}$ 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 di*tsl 1pomc z u5+0mxwjfje+tic ) p:82rected across a river with a current of 6.0 m/s zp*j:5cm)+ti8t0cw1 om2 x+ pjelsfu. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/s in still water wishes to tr;m u9nq3*c4qdq - ro4ne t5hujavel directly across a river 1.2 km wide in which the current flows4mtq dc3 4uq 5 n;o9unrj-q*eh at 4.8 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stillp.c60j tr6zh-5 vt5 lgr y.x iays6rp8 water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should htt5 x 6yzvrr.60ga68jpis.rlpc 5 -ythe driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bskd6 mt5w9nbzkm47s 5ank in 6 min 40 s. She is swept downstream 480 m. How fadbts m9 5mn 6k7sk5w4zst can she swim in still water?

  A swimmer heading directly across a river9q8xc/i- d uy3f3ax jv 200 m wide reaches the opposite bank in 6 min 40 s. Shex xi3-ay93c/ud f8j qv is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.96 m/s, must aim upst5 u rfnl rcra8sa1,4 *j1de4esmb8o6rream at an angle ofe8*546ljdrfa sr1 u41o m, rbs8nare c $26.8^{\circ}$ (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)  $m/s$