Which one of the following is an examplel l)-d8n e0m9mebhv0f of a vector quantity?

  Which of the following operations wni t qttvv0 .8uh(q),zill not change a vector?

  Which of the following is an accurate statemennfdy0+ 2 5xpjzt?

  The resultant of two vectors is the smallest when g01pohi qfjg) mv*.m33 lka(ethe angle between them is

  Two displacement vectors have magnitudes of 5.0 m and1eaa t0sq c85zy fonxm56 wg/5 7.0 m, respectively. When these two vectors are added, the magnitude of the/afa ng1q58 5sxz0y tmo6wce 5 sum

  Two vectors, of magn )r6ny dubq.i*itudes 20 and 50, are added. Which one of the following is a possible answer for the ibn6rqd yu).*magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objectsf+n-b q//g ls in directions th -bs/nf /qlgs+at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown zb7g 9-mfy5; mgy ph)w;0wbduvector is

  Ignoring air resistance, the horizontal component of a projectile's velocit*d97t: v)3bu otlm j6eo,smjgy

  A ball is thrown with a veloci72 d,gle.a(py+ c askzty 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 a psjq5be 5 9e 0pn+s:jfgpiv21orojectile's acceleration0sgvejijqb e2o+f59 spn5:1 p

  A soccer ball is kickea vez;ii 9aeb+-cqt+:dxxfuo ) pq( 53d with 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 vectuo72(cajm 7ts xui.e1gfg-y)2: m a nfor of an object is directed anti-parallel to the velocit:27 fyjug2of nc-7 tsi)a(mmg.xe1au y vector,

  If the acceleration of an object is always d pobw -d25zp6bv, ,glmirected perpendicular to its velocit5w2g6, pmpblov d-b,zy,

  At what angle should a water-gun be aimed i :i52n9 2vft- ayo fjg/9mxswun order for the water to land with the greatest hori2g5 nf92t i 9xv/ afsw:-ymoujzontal range?

  An Olympic athlete throws a javelin :.lgcyi+ z b/nat four different angles above the horizontal, each with:izgy+/n.c l b 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 ball for the second time.ehjveh9r7-uzczti / a;4xz9*2 ku sg2 If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal ruz ;i-e9u7*/ czav9 g2th2 4hjsexkz range R (compared to your first serve) would be

  A ball is thrown at an original speed +x) p3c gu:mbeof 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 height, how does b;c/zyk h op2:its speed compare to its inipc:ybo2/; zhk tial speed?

  A stone is thrown horizontally from the t xwocmy2j:p2/x(y,sj op of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground below?,j/2xop yx2:w y(scjm

  A bullet is fired horizontally, and at the same instant a5c* opqvxj.+( )qvtz*nqpub ) second bullet is dropped from the same height. Ignore air resistance. Compare th.q)q)jc t 5+nquzxv* *vpob(pe times of fall of the two bullets.

  A plane flying horizontally at a speed of 107.3 m/s and at an elevation of 150 q2fc aa)41vmac:8vbpm drops a package. 7.4 seconds fm2 caaqv1ca 8)4v bp: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 plane, and one second latl+m irysol +xvj+2-0ber a second package is dropped. Neglecting air resistance, the distanc+oyb rl-xsi+m2v+jl 0e between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at bsz w7qo l7z5u:p5purp01ms ( a constant speed. Neglecting air resistance, when the bomb hits the mw zob057rqsupupl1:7p ( 5z sground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixeulqu w4bo5)wi 8omt (:h a,3kth of that on Earth. If you hit a baseball on the Moon with the same effort (and at t uo,( 8a th 345mqolu)bwwk:eihe speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road nkar /snrd73stgc b/q* f12-m and pass a car traveling at 45 mi/h. The relative velocity of your car to the other ca1 d/g* 3ct-kr 7n2s/aqmbsfnrr is

  You are trying to cross a river that flows due south with a strong current. Yo* ;)dq; ,k.fkjxvc:v*cwlkcf u start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorbovfk v :c)f k, q*.xjklcw;;*dcat

  Your motorboat can move at 30 km/h in still watep.g t3rbqog ++9ui a,kr. How much time will it take you to move 12 km dokp9 ti ., +b3ug+qaorgwnstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 ksnk/k)6b48g4 hjzil degrees below the +x axis. The y component o8bis g4ln6kk /kj 4h)zf A is

  If a ball is thrown with a velocity of 25 m/s at an angler6n8nfj;9z:0o edi.x lo4ivt 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 direxrp ,y(se 77dection north of east and you end up 2.0 km north and several kilometers east. How many degrees norr ,d( xey7sep7th of east have you walked?

  A butterfly moves with a speed 6myq,zk2h k)wc4dc x 7of 12.0 m/s. The x component of its velocity is 8.00h64cd ,wqycz)k2m7xk 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 grijtdf q.j g 7g4x3h)v9ound. At what angle is the Sun ele93vxdq gfh7j g jit.)4vated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3),3 a2mvk 2uya(n respectively. What are the components of the sum of these 2kvma3a(u n2ytwo vectors?

  Two vectors A and B ha;xhnar 5dpb.a;ynw k2 6uun)4ve components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of thesedx2kub n6h); rnw4a5; nuay. p two vectors?

  Vector A = (1, 3). Vectoq v-ckels:n,v7 ( 8amcr B = (3, 0). Vector C = A + B . What is the magnitude of v-( n, a78:vcscqemlk C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its rwmxr ).q)1xg qj7hafv tv;9vw85 2f ydisplacefq.aw9jmhvx)g r5f7 qx vyr)81v; t2w ment?

  Three vectors, expressed in Carteg098 (*giim(rm 5imprr l-moxsian 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 Cartesian coordinati8b os 0;z )sssd sd12tojin/;es, 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), what is the magnitudenxbhf5uj *2l - of2u5 - *bnhjlfx vector C = A - B ?

  A runner runs halfway around a circular 8t xnp k f2jftz*pu xy/c3:nw1/jxm+;8re s.qpath of radius 10 m. What is the displacement o12:8.w8q +;x fn*zpt jn/xuxfm/ y 3krptc esjf the jogger?

  Two forces are acting on an obbr ptt 0g;c(7sject as shown in Fig. below. What is the magnitude of the resstpg;b r( 7tc0ultant force?

  Two forces are acting on an object as shown in Fig. bel,mkg8lm+fb :9txp - n1qg3sgrow. What is the directiol, gxm:b83s9 q+fgkmprngt -1 n of the resultant force?

  Vector A is 4.2 cm l 63ukn/jaf be9igz6)2m jgtc:ong and points along the positive x axis. Vector B is 7.7 cmigzfc n2:jj m/tguk6a )9e6b3 long and points at $+32^{\circ}$ 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 62 cm long and points at97gldq+p kkcba7x0.c4 .gpa/wdigl6 $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 30 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 horizontall 5r ):7falrxsi4s -hxfy with an initial speed of 26 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the )fa7ri4:srlh- xx5s f cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, withr:z3x7o5 ckkm a velocity of 10 m/s, from a bridge. It falls 22 m to the water below. How far does the rock trav k7xz:ock3mr5 el horizontally before striking the water?

  A ball thrown horizontally from a point 24 m abovef4zgdra3 2z2r the ground, strikes the ground after traveling horizontally a distance of 16 m. With what speed was it thrzf3d4zga2rr 2own?

  A jumper in the long-jump goes into the jumpbuh ep,gpk() dhc 0u8( with a speed of 12 m/s at an angle edhu0h8g)(pu ,c( b kpof $20^{\circ}$ 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 mq- tm+ og12lh-lvuc,speed of 14 m/s at an angle omv1l+-, umqg t-oc2 lhf $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an ine/( rbc(fu*9yzc qm-jitial velocity of 32.8 m/s at an angle of $27.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vel5k0de3ealmr- ocity of 21.6 m/s at an angle of $25.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an ;x+zi s3rzqy2gle 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 17.9 +dmeh wqwh(39s9) l hegxy./ i$m/s$ from the roof of a building 40.3 $m$ 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 44.2 bd1fm ujrmpel /zhjsu:br(340 cjm9o/x/ .+j m/s at an anjp r0z m:1/rxcbj h+bjfo/4u (djme.s/3u 9lmgle of $47.5^{\circ}$ 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 amuup ,q6se:oc4r- a6m 1500-m race at a velocity of 4.0 m/s. If you ou6-pe4: mqas r6,ucm 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 you to finish would be

  A plane has an air speed of 200 mikl ;hxr4j+y-w b+3dd/s due North, and is in a wind of 50.0 m/s to the West.y wdj;4h+rlki +3bdx- The plane's speed relative to the ground is

  A plane is flying due South0kb6pcy c nm16 ($270^{\circ}$) 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 heade h-wcuq;pf2l; d $30.0^{\circ}$ 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 horizlc z4ctfs6a(w kp8n4k89-dicontally fires a projectile with speed 50.0 m/s in(8n6 z4lc-4ads98cwk tf icp k 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 water is 8.0 m/s, it:z 6w*h)epep(r o3-tgv,j kds directed across a river with a current of 6.0 m/s. What is the speed of the e6vo etgj ():pt-d3 *wph,kzr boat as it crosses the river?

  The driver of a motorboat (a gr,1*dmftpn x(z+ othat can move at 17 m/s in still water wishes to travel directly across a river 0.8 km wide in which the current flows at 7.9 m/s. How long will it take to cross the x d fat 1(n+,(ogr*mpzriver?

  The driver of a motorboat that c-+af heh9g5r. bvxf)han move at 10 m/s in still water wishes to travel dhhb f5re-gvf+.xah 9 )irectly across a narrow strait in which the current flows 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 the opposib*5ii+, xo-cyxo 1ax yte bank in 6 min 40 s. She is swept downstream 480 m. Ho*x,5 xbcxy-i1i+ yoaow fast can she swim in still water?

  A swimmer heading directly across a rga4e; x1m,a h9o 1rr larnv8p2iver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the 8oa941hr mxl ;r,naae2rg1vpcurrent?

  A boat, whose speed in still water is 1.56 m/s, must aim rny,q/y.l ) wnh08vpcxzmvhh 6c - w(,upstream at an angle of y(6-/p mynccwv8vh.hxnq,h )rz,w 0 l $14.3^{\circ}$ (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)  $m/s$