Which one of the followi(hqhspvja72e 3x ( w*jng is an example of a vector quantity?

  Which of the followinwiws 2dj8*l8fwlx47c g operations will not change a vector?

  Which of the followin a5*uu v;-)oa1o dvcwxg is an accurate statement?

  The resultant of two vectors is the smallest:sjhy/j h;mzq r+ ;s9 igac/ a*6d-dbg)q trz3 when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m,aesfmk .z 4o8:merf,tk: t b49 respectively. When these two vectors are added, the f. tet zbkr9fmmk4,s8e 4a:o:magnitude of the sum

  Two vectors, of magnitu.*w yf xyokmf:y.l a, 70rql-+mb/s zwq6x 3wqdes 20 and 50, are added. Which one of the following is a possible answer for the mysbx,-7yw.yqa+ lr6w3.fxf lq/*o :m 0qkzmwagnitude of the resultant?

  Three forces, each havinl g 3// m0ogxbtvt5e2m +e/mkag a magnitude of 30 N, pull on an object in directions th/am0 k5t3gm+t lgv/bo mex e2/at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown i 1h kej10q wv*l) nhs2zrt-4dvector is

  Ignoring air resistance, the horizontal component of a projectile's vy qg.cb.6q0gg 2vbuhrl ;q:w)t ovxue+;sv, 7elocity

  A ball is thrown with a velocity of ,l 7bi xb ezde1b(7ih420 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 horizonw ):.n;uxy)x)u9xgi j rl:gjntal component of a projectile's accelerationxlwury 9xnun. ));ixjj: :gg)

  A soccer ball is kicked withx z-i4bm132xvt v* qpun7: fel 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 alt73i9 ,yx-j5l g28uppkl wpwn object is directed anti-parallel to the velocity vectktw 7 gyxlil9up5 3jw8,2p pl-or,

  If the acceleration of an object is always directed perpendinf 8na7tg +li6rb,by tv 96gf6cular to its velocit6 g fbatinnyfgv l+tr98766,b y,

  At what angle should a water-gun be aimed in order fon 7k35oht po,vr the water to land with the greatest horizontal h35tnkvo7 p,orange?

  An Olympic athlete throws a javelin at four different angles,8;kkwh9ynsx above the horizontal, each with the x hwn ksy9k,;8same 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. If the ball l.rennnlo4(m 7r jv- 2beaves your hand with twice the velocity itrl4nb(rn ovje.2nm- 7 had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speen*o7dg- 7 ukixd 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 h-l+vfuo mtn4 ;eight, how does its speen;tm+-u lofv 4d compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant aj v.v;f88i uf x)fue u.itc3r3 ball is dropped vertically. Which object is traveliu3 uef.tvicri fxvj83 )8u.f;ng faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is ,syse9 sqsj )+dropped from the same height,j s+ys9 q)ses. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 81.5 m/s and at an elevation of 17nu )uhjca805tsmw u 68; z9fhh3 m drops a pajusn9huhu86 ma)85ht0 f zc;wckage. 4.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a 2ee 35mt;6ctj ):hzu jpc iv1yplane, and one second later a second package is dropped. Neglecting air rest mj3cpu zve;i c :1jhyte2)65istance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizont kjigb8 u9x5k8g7fvws: 3ra z2ally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontga2iuxbw kg kv78f 3z58rs j:9al location of the plane will

  The acceleration of gravity on the 3kbkni.:e6t d Moon is only one-sixth of that on Earth. If youk 6deb .n:k3ti hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h k.yf e9ji+ vk2/rprk1spj 1 5 rhsev08in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to i pvk.h p r5+ fs1 jr8e201yk/esjk9vrthe other car is

  You are trying to cross a river that fl2 mjkfuw2ut/diq42 x /ows due south with a strong current. You start out in your motorbowumufq2t2i2x/4k jd/at 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 stil;m qcd3p; osy9cwd:+7xx /a5aiw w+y ul water. How much time will it take you to move 12 km downstream, in a river flowinsaq+yxm 5pow37;wdiy u/xdwc+c9a;:g at 6.0 km/h?

  Vector A has magnitude 8.0 giy2 -zq b5l7u(zq) sjm at an angle of 30 degrees below the +x axis. The y)-jqz2z(ubq75yli sg component of A is

  If a ball is thrown weaxrzo*jks uqw*(1*5.ny 19bei cu7aith 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 eas*6fny1h6jkg pknek0 , t and you end up 2.0 km north and several kilometers east. How many degrees , 0nj6ep fgk6hy1*knknorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component ohty 43gg g roqha.6 5d6pv- t3dibw4k2f its velocity is 8.00 m/s. The angle between the dire.53h 6bghtqragg4i3-v ykp owd2d t64ction of its motion and the x axis must be

  A 400-m tall tower c5. xfgedo;10k0mo6oipyp qf z (2n/ oaasts a 600-m long shadow over a level ground. At what angle is the Sun elevated above tikfmzp qyaox0(;e1go/f5o62 donp0.he horizon?

  Two vectors A and B have compo/ir33v q bnes(nents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two vectors?(vseqr/ 3bin3

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wf7h36pwq 1mye4 b5qwihat is magnitude of the sumq76imyehb1fww34q p5 of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magn16 - adt:vkz)zc3 xupqctx/8aitudea-t8z p:a3dck qu)zcvx1 /6 tx of C ?

  A car travels 20 km West, then 20 kfnp:726og qac m South. What is the magnitude of its displacemennpaq2 c:o7f6g t?

  Three vectors, expressed in Cartesian cok9iv*lx38u3n 4r sz0 aq/o ksnordinates, 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, expresse3yi: b j ndch4lhh,/wvj6heo l93i33gd 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 vecd zs p09-nvyv(lwo0) jtor B = (+3.0, -8.0), what is the magnitude of vector C =vozy- 0(p dlvs9)0 wnj A - B ?

  A runner runs halfway around a circular path of radius 10 m. Whuqbi, rq.;;g/pba ycy7)r(v z at is the displacement of the joa uqpb)br;qy(c/yvi. g ;7r,zgger?

  Two forces are actinlejjafpupet5d*un.3is,m)7e de 23( g on an object as shown in Fig. below. What is the magnitude of 52t uu*ep3)s,e ed3 ij pejl7.nmdfa (the resultant force?

  Two forces are acting onq34 x ;ipb cd4uswuulk8f8;emyf96m5 an object as shown in Fig. below. What is the direction ofuflq5f s;mybc36x8 9ke4 ;84pud wu im the resultant force?

  Vector A is 3.8 cm long and points along the positiv8)9qf4lxa3di lft ) 2 ds3ustze x axis. Vector B is 5.4 cm long and points a 4d3s23qt)lsft8df az 9uxl)it $+24^{\circ}$ 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 85 cm long and point f5uxn:mh9im6 s at $30^{\circ}$ above the positive x axis. Vector B is 17 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 izm1fw+-r nhw irj28wra 2i+uw c5-b 7qnitial speed of 19 m/s from the edge of a cliff. A stop watch measur2r5r+wm-jfz7rcw+awii- 1hb 2wqn8 u es the stone's trajectory time from the top of the cliff to the bottom to be 4.0 s. What is the height of the cliff?

  A girl throws a rock horizhok v*8i3ijr)sl,aq ou4 e( p7ontally, with a velocity of 12 m/s, from a bridge. It falls 28 m to the water below. How far does the rock ti( l eh7jo8ar3 kqo sivp4)*,uravel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above thjm( v 9ne *5)ns+7i-qn.+np ppe+ cy 1zjporwhe ground, strikes the ground after traveling horizontally a diseny h-ope)7pnpi s95vprnqw(jm cj.+ +nz1+*tance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into yphw*aa1x 3is-l, zg0the jump with a speed of 12 m/s at an angle of i h1l3x,* azap- sygw0$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goesaz8gm*sot* e lqr (w54wo.w3c into the jump with a speed of 10 m/s at an angle oom8ze q 45lg*cwr3 t(*.wowasf $18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wit** 9qcmdxz9*nll1s 9 ayern y6uk- :oyh an initial velocity of 45.1 m/s at an angle of $18.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 54.4 m/s at an angle ,zh qwki6) dr* /tp1mkof $41.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle qz *ni9 0z.e-muni8yw,3qkhy 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 horizyjm*-ypw-l3stv/ kr : ontally at 18.9 $m/s$ from the roof of a building 55.0 $m$ 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 51apox8)1ig qix9 d73ln .5 m/s at an angle xl79oi i3a)n1 dxpgq8of $40.3^{\circ}$ 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 15 n .f690wjfjqg/+,pc xk;k w-w7 fxuuz00-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-u9k7x xpnw.w/f 6 zj ugk;jcq,+ff w0 slows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s to bcon/x/uuy;1. pzdf-.ynhs 2the West. The plane's speed relative to the groc- x.oz./f h2yn1usb;n yd u/pund is

  A plane is flying due South (u uemakt5(/+o*e;wpr $270^{\circ}$) 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 is head mzzh9aw uy gxi+c9(k 8(8/nnsed $30.0^{\circ}$ 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/e9.crv-si5ii7k4 faxs horizontally fires a projectile with speed 50.0 m/s in. 5rv7 xfe-49aisii kc a forward 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 still wa*h;0 hzwwxe.w, 3uobwter is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What,e wzo.bw; hu3hw0* xw is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/z 0o twim0.cy0+lvz 5es in still water wishes to travel directly across a river 1.8 km wide in which the current flovzy+5m c toiel00. 0zwws at 4.2 m/s. How long will it take to cross the river?

  The driver of a motorboat that casv x u1*8zsryjlw95- 4 kesuc9n 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 angle upstrea4ywsu *cs9jxeku 9lsv-8z51rm should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reacbh9g( *w ube m3vc;n)nr.m, klhes the opposite bank in n;)mvghuw3crm.9n(e *l,kbb 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the gpqt85 58d eanopposite bank in 6 min 40 s. She is swept downstrea5ea8 td8p 5nqgm 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.82 m/s, must aim upwaolbf6: -fwe /,yg;fflp6p9stream at an angle of -al:96/f ,;e fpg bf fl6ywowp$14.7^{\circ}$ (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)  $m/s$