Which one of the following is an exjx o9f21 :fuuq +cj8d frswu*6ample of a vector quantity?

  Which of the following operations e t3*u+nv p9cdwill not change a vector?

  Which of the following is an accurate statemenzdtuw- l.k7xxi:,o) v t?

  The resultant of two -7xim) 3dmrsn2 rhx5mvectors is the smallest when the angle between them is

  Two displacement vectors hrb t -tq64l; o/.wkohl) w1nylave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude ofk bo /.1 ltnlhqotly) ;rww46- the sum

  Two vectors, of magni;pj1pg;d nalt.) m z1vtudes 20 and 50, are added. Which one of the following is a possible answer for the map.jng1pm)lz ;;1t dav gnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull onmr+g pgcg n798 an object in directions that argg8p9 c+gr7nm e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkn9ah2lum0ah6 sown vector is

  Ignoring air resistance, the horizontal compon)ree9 k39fnlml3,uchdb6r ahk 6t5)j ent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle ofts h.i2wwo 1k. $60^{\circ}$ 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 of06/hign fcc b)+my-cl a projectile's accelerationc-hybclmn)/fci g 06+

  A soccer ball is kicked with a velocity of 25 m/s at an angle ofg-wk/fyq.dy 9p x ky*( $45^{\circ}$ 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 direna2zs r3bkn*l vs.t-, cted anti-parallel to the velocity vetz*nb,3vlsk.- rs2anctor,

  If the acceleration of an object is always directed perpendilj-4nfbnc55 x . 6 .d)fuohpnhcular to its velocity,.f.hchn j6n -f)4odx5 5bnl pu

  At what angle should a wate4d pi( cln-z /6u(. clpmdsml+r-gun be aimed in order for the water to land with the greatest horizontal rml/-.+p6n zdicc( up(ld 4 lsmange?

  An Olympic athlete throws a javelin at four different angles above the jdpm 4h 1on jbc.i.r9-y0mb:6k) txychorizontal, each with the same y) rb ..th:4nopmy d1bm6i-cx 0k9jcj 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 tieigbwlm e/+7mm:y81m f 6 potb-gq4 j9me. If the ball leaves your hand with twice the velocity it had on your first thr b1 f - 4temgigjy7m/o:mwlebp86 +q9mow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s q8msop c+tm ;(+8(deccb1jomfe: ju7ry 0 wg/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 her( lyqf-6k 22 iy-wdu(ne.rxjight, how does its sdk22njr(- eqwf-rx6 (u.lyy ipeed compare to its initial speed?

  A stone is thrown horizontally froa xmx9+m 3cm5cgr6 0dzm the top of a tower at the same instant a ball is dropped vertically. Whichm5m0d+gzr3x9c6caxm object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally,)z g9cvo+bxsfn dx4wi-p:(8 i and at the same instant a second bullet is dropped from the same heig cdxb pi:x+nzsw 9ig()v4o 8f-ht. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 62.0 m/s ane6sk 4 ddsbmjkc2aw;d0g v944 d at an elevation of 219 m drops a package. 3.5 seconds later it drops a 6wa4k mb sv4e;dckdg92 s04djsecond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from fm 0ee/7e.xhz a plane, and one second later a second package is dropped. Neglecting air resistance, the distance betweeh eze7xf./m 0en the falling packages will

  A pilot drops a bomb from a plane flying hor n ecog+i36e ja.op3h9izontally at a constant speed. Neglect c oh6j.g i39oenpea+3ing air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravio exd2jf oq-2/ty on the Moon is only one-sixth of that 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 bef/jx-qod22 o all would land

  You are traveling at 55.rph/nbs - n:+fqnv 9b mi/h in the +x axis relative to a straight, level road and pass a car travelnr +-bh.s: /fv9bqnpn ing at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due southci88vg0hr7fgqtp+ kv ebq 2pg74q9f 4 with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly we7 gqcv2bftpi +4evkgf48q7rqg 9 0ph8st from your starting point. You should head your motorboat

  Your motorboat can move at 30 hax0)2.nke w7 dxq h,8/qrkhf km/h in still water. How much time will it take you to move 12 n8 0dxfkhk h/2.rh exqqa,w7)km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belogm;/gnij pu( 6w the +x axis. The y component of A iu (ni /gg6jp;ms

  If a ball is thrown with a v+q8p* hpo 3narjmq0d1elocity 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 east and you eds el 1. )m,2+p6sozfq a.wnecnd up 2.0 km nor z )aemcs26pq o,.f esln.1dw+th 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 of it+ yn2o*/0cqykq59mgz y;dggb e m5aj8s velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must badbj8+oky0 ecn/y*g5my 95g;g2qm zqe

  A 400-m tall tower casts a 600-txy7,aapo 50 hg((il 4crm ujo3nic. ,m long shadow over a level ground. At what angle is the Sun eleviyhpa(, , 4xolt g3jc5(ai0o7 cm.ru nated above the horizon?

  Two vectors A and B5,lg bse(i(x d have components (0, 1) and (-1, 3), respectively. What are the components of the s(b( ldeg, x5isum of these two vectors?

  Two vectors A and B have compo5i5(+on t *0eibgzb93 5 3oyufnazkjj nents (0, 1) and (-1, 3), respectively. What is 3ztjuby(j*n5o3g0 5a bk +infzoie5 9 magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + xf gg.b0wo- 3 d h*pa,rha9g-vB . What is the magnitude of C ?p-rfoxah* ,b0 da . g9v-ghg3w

  A car travels 20 km West, then 20 km South. What is th+hfg.op8qn u6pp eu .5e magnitude of its displacep.uq 6 pe5.u+nfh8opgment?

  Three vectors, expressexix ia (vgst;bq3rt1tty82 62 d in Cartesian 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 Cartesianxq0/pf e+()phv kede1 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):bmieui;m0c;yh9 3 /w pso+ui and vector B = (+3.0, -8.0), what is the magnitude of vectocuyi;h p09i i /+o3:msebumw;r C = A - B ?

  A runner runs halfway around a circus94wfgdfu2*k/h6ds zd 6h 9rz lar path of radius 10 m. What is the displace2 g99d4dzsz6dkru/wh*6ffsh ment of the jogger?

  Two forces are acting on an object as shown cha s(z4*/oxm6o0c v+ v0 jtzcin Fig. below. What is the magnitude of ttv x (6*scczc+oaomv 4/ h0z0jhe resultant force?

  Two forces are acting on an object as shown in Fig. below. What is qduj :cu,jl/:irr5 g2ln o/f 4n-kun:the direction of the resultant forcj/ ud4 g cnjuqill2/5r:,urk onf-:n:e?

  Vector A is 4.5 cm long and points along the positiv7/fs yetx:a 4ke x axis. Vector B is 9.0 cm ls47: eafk/xtyong and points at $+20^{\circ}$ 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 axlk1m874c+ wyau+ gx uxq0cy) t $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 21 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 12 gt)r, g9hvbn2m/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 3.9 s. What is the heith g)9,g nvrb2ght of the cliff?

  A girl throws a rock horizontally, wit: olkj g ya slhl68rc -g34f+m/vg*8pqh a velocity of 10 m/s, from a bridge. It falls 14 m to the water below. How far does the rock travel horizontally before st8k3y /gcl rv+pl:ofg gs8 jl mq46-ha*riking the water?

  A ball thrown horizontally from a point 28 m above thel fbcjt634ovin r60e + ground, strikes the ground after travelc6nv0rtlji3f6 obe 4+ing horizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an awm;:t c7+i1e+ uwrf dnngle om7 dr; un1+ :wi+cwftef $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumhuzz-( o 8sny )bbr)o.1jph/g p goes into the jump with a speed of 12 m/s at an angle ofo hu.zr /gyzbb j)o)(1- hspn8 $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 58.9 m/s at an angle ohl*dzg e1 n:; cuddz;e01kj5s f $17.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched withc5dpf( za8 vmidec9se*- 88oz an initial velocity of 24.5 m/s at an angle of $28.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofg(a0p1b0 *nm y;gbohrk+w8 kh $30^{\circ}$ 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 24 n3z0jbzo5 7/r ,njltu.1 $m/s$ from the roof of a building 50.7 $m$ 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 63.8 m/s a4;jd,ummc /msj xn1n;t an angle sjmn m ;j4/c1u dn;m,xof $39.9^{\circ}$ 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 449fdv cz:c0w b0,yq/ vzrp fzsgx ;4,y.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the tvwsvc/rcyd q ;09xfb44:fzzz gy,0 p,ime it would take you to finish would be

  A plane has an air speed of 200 m/ es/7x 5eog0izrb1mg1v6we :i ev8x)fs due North, and is in a wind of 50.0 m/s to the West.i5e:fmvesw1 )b8 xgxe og/6r7 vez10i The plane's speed relative to the ground is

  A plane is flying due Soutpfw5d7lz i/ z8h ($270^{\circ}$) 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/hkqa 4-6 )szxk-c7z xfs 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 mf :/zs*fvv; 7sk.lle2is( ttb /s horizontally fires a projectile with speed 50.0 m/s in a forward d/s:v2l z*;.s(ibelt skvt 7ffirection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in sti*2ptp hfo9 kw7ll water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the river?pf9*2 hwt7op k

  The driver of a motorboat that can move at 18 m/s in still water wishes to tras.3qpx3 djk hxka m(;4vel directly across a river 1.hxskmax p3(;q.3j4d k5 km wide in which the current flows at 5.6 m/s. How long will it take to cross the river?

  The driver of a motorboat t.i.lv -ja0 qam 82mrmphat can move at 10 m/s in still water wishes to travel directly across a narrow strait mp8-aj0ilvr2m am.q . 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 2o42z v2lfukavf+ pn(v)cmj4m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can slvfjv24cmu4zv na(2 2f kp+ )ohe swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite l2y9d r/o41y p+(ug la cgfsy-bank in 6 min 40 s. She is swept downstream 480 ldyca1y( f4s+p -r g/9 uolyg2m. What is the speed of the current?

  A boat, whose speed in still water is 2.06 m/s, must aim upstreampe0ryiv,or7 86ss.oifnl -6lt2cg u 1 at an angle of1o7-s8n6sloyv t f.0 g2 priuer c6li, $17.4^{\circ}$ (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)  $m/s$