Which one of the following is an example of a vector quantity it,*a. kg+nf 5uc hkm:/f3mzs?

  Which of the following oper-w jau2z3nm7uations will not change a vector?

  Which of the following is an accuratelsk3u.1p d -ei statement?

  The resultant of two vectors is the mgq0n1t/h4*/uy nsx( t rkjf3smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, n8 /gzkgef /0nnzw/y 8-vrwf6: m p2z) fh;pefrespectively. When these two vectors are added,nn0f/ ;6 k8fgzn e2pe8zmr- ) yg:z/fw fv/phw the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follow8 dcn..d j*+ro ktmhnbcan.r+je 0(n0ing is a possible answer for temt+0 car*rnj.0d(cbn. +dkn .8j hno he magnitude of the resultant?

  Three forces, each having a magnitude ofsb y,lhs4 6zj* 30 N, pull on an object in directions that bh*l,s46j szy are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowfj8r1-f -: mtso(b oiqs0(ahon vector is

  Ignoring air resistance, the horr pm vzqb0nll 5.ew1ij:;ha7*izontal component of a projectile's velocity

  A ball is thrown with a velo)y vyjli(3cf5city 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 agk fvvz;t:n4 wa0-am 9 projectile's acceleration0wvf :t avn k9;zag-4m

  A soccer ball is kicked with a velocity of .z5bsoj)pc o;ayg jgtl4u ).1 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 the velo*x7 u wi )xgk3zknjv/0city v7 3*ngwx/u ikxk )jz0vector,

  If the acceleration of an object is always directdifje+(ezq4 n 4lbb9 1ed perpendicular to its velocityf+ bjnei(914qb d zl4e,

  At what angle should a water-gun be aimed in order for the water to land w-oc0. cwfapw+f jg9ck56n oe0ith the greatest horizontal 5acgw 0e+knf9jpocwc-0f .o 6range?

  An Olympic athlete throws a javeq4 adb +nwh i0y,.lp.mlin at four different angles above the horizontal, each with the same mb ily 0h .dqp4n,aw.+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. req//d*yd az9:xbce 6 If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your firstra6 xzecd /*d eqby9:/ serve) would be

  A ball is thrown at an original speed of 8.0 m/s at and fm y,e2b;8p/mh3ql) x,glni 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 maximkxl* hcby5yw5/+lr)g um height, how does its speed c5c* x ylgyr/)khl5w+ bompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at)z .lt)cpaln 4x4 3ddm the same instant a ball is dropped vezdclna)4 lt4 .dp x)3mrtically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally p6nvy, w2cfxs7 d*/9qircit4, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of th76qi4cvn i,/ pstfdr 2*yx9wce two bullets.

  A plane flying horizontally at a speed of 66.6 m/s and at an elevatiob copf)1za-a0 x:r kvi1 av*i3n of 165 m drops a package. 4.5 seconds later it a1- ri p aa3vk0vizcf)b:ox1*drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a seco baxwyai7x k53i.* rg:nd package is dropped. Neglect3a bixi:.w*xy 7gar5king air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally awwrp-xuvd*5 oo15cu+t a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane xup- r5 +*ow5uwdv1ocwill

  The acceleration of gravity on the Moon is only one(ug vev9 nsjl ,)r7s s8zcci;0-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at vg snz ,;u9c 0sic (se7lvjr)8the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/bwm.f 69y7qlyh in the +x axis relative to a straight, level road and pass a car traveling aty f9bq7yl6w .m 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due sv-f*. gyu;(bew0 jx ,/vjou3 f ylzm8south with a strong current. You start out in your motorboat on the east bank desiring to-,jf fvlmg y 8 ozbv/xse3wu.*(ju;0y 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 takeg9fm2 4vx(ksxly1 jmp7j abdo 34u86 v you to move 12 km downstream, in a lsm 6m2g9 xyj1(jbxpfu3va4d 78v 4o kriver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 doc.t(xv 8d83 h np9a8kfxgxl*w0. re legrees below the +x axis. The y componenoe.x xlh 3ar*p.( v8k8 x9 8dctnflwg0t of A is

  If a ball is thrown with a v 166x7e ;ewbyjxit:rkelocity 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 eas 0fjgxk/v6r801 vh*c3 tqz adyt and you end up 2.0 km nvyjdc0z/8x *q30g v haf1kt 6rorth 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 98 2bjkx 9 b+/w l, vrb:orqcfgs1gc7kcomponent of its velocity is 8.00 m/s. The angle between the direction ofocgwr v2k q:1fb rskj,8/c9b b9x+7gl its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level grouni1or*8q dr : ao ;bz3hwc1--azn x+covd. At what angle is the Sun elevated above the horizon?+c :wr-z-cd3z xhvn 8o;a11oabqro *i

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.0+yhsji p +zb1 What are the components of the sum of these 1s0h+bp yz +jitwo vectors?

  Two vectors A and B have components (0u.-n2wds/q y 3jzlll:, 1) and (-1, 3), respectively. What is magnitude of the sum of twjqz.s ldl l/-2u:n3yhese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + 73zw dl e ox )05t,a2feiqq5goB . What is the magnitude7 ,fw g35a)lxo2itezeq0d o5q of C ?

  A car travels 20 km West,rrak4lvz-x vt6.+ s ba*en3 8rvr:;y a then 20 km South. What is the magnitude of its displacement?s.3rt b lavyk vz:nvr+x8 ;*e-ara4r 6

  Three vectors, expressed in Cartesian coordinates, ar c26galrx b :.g0wkv/ze
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 Cartesiang:b1*4abh* w + +0mocxi fwlmftkg1;v 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) cv d.e8 *1fvxvtl/y9jxqw*b) and vector B = (+3.0, -8.0), what is the magnitude of db 9txj8x*y) .vweq 1fvl/cv*vector C = A - B ?

  A runner runs halfway around a circulazx.+*fj ijxog-o/ l7 wr path of radius 10 m. What is the displacement of +7*ogwox ijj-zlxf . /the jogger?

  Two forces are acting on an off 1/6legkli yp yu464bject as shown in Fig. below. What is the magnitude of /yf4iuk6 f gpy4l 6el1the resultant force?

  Two forces are acting o;d/ pyhd4x. j-tufzx - kbo; 7t3adkt1n an object as shown in Fig. below. What is the direction of the resultant for.b x4f1hdzj ok3-t7tadx;p k u-dt y;/ce?

  Vector A is 5.5 cm long and points along the positive x axis. Vector B is 6.9 8q4 5ypa (cgmtcm long and points at cpyga8m t5q(4$+48^{\circ}$ 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 84 cm long dv*pme mss*) 2and points at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 45 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 215)bubz2jazt ( m/s from the edge of a cliff. A stop watch measures the zab2(tz5bj)u stone's trajectory time from the top of the cliff to the bottom to be 2.7 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, from :sqqf *oe )qd.dmx, f0-cd0rka bridge. It falls 29 m to the water below. How far does the rock travel horizontally before striking the*qcdrqm0 :fs0 ,)q-xfdd oke. water?

  A ball thrown horizontally from a point 20 m above the grounj hzfolhd+ p+7b3 +4afd, strikes the ground after tfzp++ fb+h7ho3ldaj 4 raveling horizontally a distance of 12 m. With what speed was it thrown?

  A jumper in the long-jump goes int.76 vl giir:vxo the jump with a speed of 12 m/s at an angle o:l v7 6xgvi.rif $20^{\circ}$ 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 8 m/s at a.4l+sdphfq z2aazr , ,n angle of l4 +dzz ,a2,.prsf ahq$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 59.7 m/s at an angle of87f5b)kgwc 54w/r (p-i mqjmhuowhn8 $20.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched woqsz zeirh5 v8(,(z8 x 2lcl5yith an initial velocity of 59.7 m/s at an angle of $33.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anumjrsf kb32u rq3p .:-gle 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 horizont2ozl8r(5d a2ts;tu rnally at 20.6 $m/s$ from the roof of a building 35.4 $m$ 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 win c2ib*5:;cxgy7m--1w qobyuzk l/f y7c )r vrth an initial speed of 55.6 m/s at an angle or 7ixrmo*7g2yn/5uvfy;qc zwb1 )-yc cl-b: kf $46.4^{\circ}$ 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 race at a velocity of 4.0 m/s.0ez,sz9im , b;l1 gdrp If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 msz1pb em z ,;0rl,g9di/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s ;ad*d ioajfifm 3 eni.:(p:o. due North, and is in a wind of 50.0 m/s to the West. The plane's speed relati*i.i md(.;a:poe3n ai:jff dove to the ground is

  A plane is flying due rgo-0* 3len csdl,,un b7sgg1South ($270^{\circ}$) 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 kb ly,8v/oe8c3 ipi q-zp* npr-m/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 a projectile with speed 50.07+6lge p)pxg1ugfkkro ki4+h 4 z4z-e m/s in a forward dire1g z+g6h)4 eoierzk gpkxf4puk 7-l+4ction $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in ,fo vumm s,8d5bk2qx* still water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is tqm,2m8x*bkfv5du, so he speed of the boat as it crosses the river?

  The driver of a motorboat that can mhgdnpr1- 1-gucxv k1 -a*nh)3. osaggove at 12 m/s in still water wishes to travel directly ac-u*.gh)sr3oav 1-x11d agnh-npggckross a river 0.5 km wide in which the current flows at 6.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in svva9p )5phjv9*xi.p still water wishes to travel directly across a narrow strait in which the current fxs.vjp5a)iv 99p *phvlows 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 th,o.b fhnf8qk8 ki *y4(wzj3jq e opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wat*8nzqw(fkjib f8 .3j4h kyq ,oer?

  A swimmer heading directly across a river 200 m wide r fphjkqa0 0dw(*)sw 5jeaches the opposite bank in 6 min 40 s. She is swept dowj w)hk(sq fda5p00*j wnstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.11 m/s, must aim upstream q1tsnl+lu/ zx8rse(8at an angle ofzeq1lu8t8x n rsl+ s(/ $29.2^{\circ}$ (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)  $m/s$