Which one of the following is an example of 3fovb fb8pgs3p: bvp :j5sk/*a vector quantity?

  Which of the following op(rvvpvg )o;r. erations will not change a vector?

  Which of the following is an accurategs .rt+,g xkpft9g: j7 statement?

  The resultant of two vectors is the smal o,g z)xju1/nelest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m an3udx a8 pblhd/9xfy 9kpt;3 ;bd 7.0 m, respectively. When these two vectors are adde;ltp p9 /3h8dabufk dx3;b9y xd, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whichjp4 j7vlnkqxwqso 228:-+ gs-da 7e4qm ,lrqw one of the following is a pos-qlq 4p- v+r7ma jwse,24: 7sk28 dnqjowx gqlsible answer for the magnitude of the resultant?

  Three forces, each having a magnitude osc2- p *pv1iir2kzr4r1sm e:of 30 N, pull on an object in directions that arezerocpv4mkis r:1 -i1pr*s2 2 $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector isj-r0fxi) pv )i

  Ignoring air resistance, the horizontal component of a projectile's velocig(r e4l/9rez b0 t(pkvty

  A ball is thrown with a velocity of 20 m/s at an angle0nqnjj3y 3 cn(xl4 j(1di cj p93p6kog of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistanjm +kn(n2wax,sa 4/omce, the horizontal component of a projectile's acceleration /ns4+m2 n a,mkxow(ja

  A soccer ball is kicked with a velocity of n zivppgvdi13;32sz/ 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 wbgp -d5z.7k xaz;o v2directed anti-parallel to the velocitz2 7o5kg bpd- xzw;.vay vector,

  If the acceleration of an object is always directjx+b7q tj937wwpw8l ; vnm7cked perpendicular to its velocity;wj c vbpm7 8q37x9k7w +nwjlt,

  At what angle should a water-gun be aimed in order for the water to land with tp3t/q/ xht(djov0o v0 he greatest horizoxhto / 0dtv0o3jp /vq(ntal range?

  An Olympic athlete throwsd tj tbozzk8 7h685d;i a javelin at four different angles above the horizontal,z t7jo688dbdktz;5hi each with 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 teoh(7+r2p3 i bu bj)rhhe second time. If the ball leaves your hand with twice the velocity it had on your first throw+2u7(b3rh eiphb )oj r, 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 ni-hb7*udo+g6xt7bin)-e aa 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 goalbd7tqren(7l * o6evr/t4 hkl. attempt reaches its maximum height, how does its speed compare to its initial l b64(drlhe/k .7*qn7 trtoevspeed?

  A stone is thrown horizontally from the top of ,heg im3/zgv ldjtz:sg;58bzk1/i,t a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground bel/bi, t gzv/h;8 g:ze1k3dltsz ,m ij5gow?

  A bullet is fired hori7i wjm7 u)ul,*wln ,gf 2ghc1czontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. gjclifu2 w7n*gc 1hm,, l)w 7u Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 55.0 m/s and at an elevation oraf hp+ )zaq a/i2srpkb*7+v. f 244 m drops a package. 6.8 seconds later it drops a second packagha.srq pb*kiv a2+7+pf/zr) a e. How far apart will the two packages land on the ground?

  A package of supplies is dropped from b34 fylxb9) jia plane, and one second later a second package is dropped. Negle9b3)jl4 fbixy cting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Negl5g s jgl3+mt, miqp3d*ecting air resistance, when the bomb hits the ground the horizo qtjl*m sgp3mi+d5 g3,ntal location of the plane will

  The acceleration of gravii7 apq+o vc(w /b60ccbty 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 ball would la+oq ib(a7c p 6/ccwbv0nd

  You are traveling at 55 mi/h in the +x axis relative to a straight, leve 7/taaj sn;7cil road and pass a car traveling at 45 mi/h. The relativ/inj7;tsa7ac e velocity of your car to the other car is

  You are trying to cross a river that flows due south with a stron i 2bu:6eukmf8g current. You start out in your motor u2m8eikb :6ufboat 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 still water. Horv+tnvl5/frv hw,/ f1w much time will it take yov/nf 1+l,rt/hrvv5w f u to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of wd o+:7g :8u 2rpdm,b-tafuo z30 degrees below the +x axis. The y component wb2:oodm, a u pz8d+tru7- gf:of A is

  If a ball is thrown with a velocity of 25 m/s at an (4tr9-jn95 lpuk,u ee ibh e3tangle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in omc60nu8pbkna ii7/pb) qpjqfx5 ::. a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees x i56p7 qj f:kqcopain08 /b pnubm):.north of east have you walked?

  A butterfly moves with a spee.toac 4+.gijfby6jk* h ii+4 zd of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of .gc .jitb iya6 ijo4 4hz*fk++its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what7 qfmuv ;(3)vft+cixs (zaz)d angle is v(fx)( c7+)ztdz3vufim; a sqthe Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivuf bm -a:f7b;rpv4 (ly x m789zf(wdyxely. What are the components of the sum of thesx;yuymw mfxd4 a(b pf7 :b8-fv r9l(7ze two vectors?

  Two vectors A and Bnf m5;.aw)j)p0plmw 6rw d iq/ have components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these nm6)a; dfwp) 0ipw mlqw.r5/jtwo vectors?

  Vector A = (1, 3). Vector B = (3, *p.i n wuzoa,1g6;yyhjfo 5q/0). Vector C = A + B . What is the magnitude oy if*6w. 1jz,oguaop5; n qy/hf C ?

  A car travels 20 km West, theb qo(gr;cou5z ww dg26e+)7 drn 20 km South. What is the magnitude of its displacement?rd6 +)uow g ;wb5c rdgzeq(o72

  Three vectors, expressed in Cartesian e1.q g +wvov.;hn:zoxs(,zn jcoordinates, 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 Cartesd.uy --5 cpwx1xe6tlq ian 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 vector B = (+3.0, -8.0), what:7bnogm /hf 0a65o5s .wn ezgr is the magnitude of vector C gmah n5b 7eso./0zgnor56: fw = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is npv8, dllqb5: the displacementpdqn, :b8l5 lv of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the ()ror 5l5clrz magnitude of(5 l5lcrzro) r the resultant force?

  Two forces are actingth/c v1 r7zex 2bx3/nj;fe,ef on an object as shown in Fig. below. What is the directionef ,r/t cv3fe/7z1x jx2e;nhb of the resultant force?

  Vector A is 5.5 cm long and points along the positive x axis. Vector B is 6.6 efz)yjas7 ch , p*; o*i9vxr/fcm long and points atepf*;)h ioc,sx f97 rzjav*/ y $+55^{\circ}$ 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 54 cm long and points ak* y6 aj//m8ryyz0:-zm, urio/zojb( p xm+qdt $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 35 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 spee8 lddyd3z31qma l;is euyjo3l. -*o g5t79ufm d of 21 m/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 *s.8a3f15douim9ed zqgulym 7lot;-3 d 3ylj be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 12 m/s, fr q.1fhkbp-pafh,i0)som a bridge. It falls 10 m to the water below. How far does the rock travel horizontallk-1ai p .h,fp fsqb)h0y before striking the water?

  A ball thrown horizontallp 6 w5sjs8(d wb3cye.jy from a point 18 m above the ground, strikes the ground after traveling horizontally a dis8(6b pec.sswwy d35jjtance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with azwf 9yhu )dtcgu-3qo al 03/un8k;t 7w speed of 12 m/s at an angle of dao3kuyuztwtf c 0;w lqn9uh8g/7-3) $20^{\circ}$ 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 j.kfw,-ewye7tl1 k t) oump with a speed of 9 m/s at an angle of k, tof1).e we-ky 7ltw$36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial x 7:n ;fnv6m*u,oy xsf/r+glevelocity of 37.9 m/s at an angle of $49.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initinsgcs:x4 vwz3y8 p )z 9lb5n*nal velocity of 43.8 m/s at an angle of $37.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired8( 5ynp ziv54p nh s:z4:nhyhp 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 horizo imtertm ds-(r64 *fp8l.oyp.ntally at 21.2 $m/s$ from the roof of a building 49.8 $m$ 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 fro.m ;wf nl mh9hpxg 9w7ooj-4l7m ground level with an initial speed of 53.2 m/s at an a7.;h of9 xgjml7wo9nwl-m 4 hpngle of $44.2^{\circ}$ 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), youib6wqgkk; v 9 kxvgo,5w, kvg ;j9tl:) can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day9g gj: ;kkq 6k,)95t ox;wikwv vlvb,g 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 m/s due N ebtt;kv 35ke 9lh9t-a10rj ztorth, and is in a wind of 50.0 m/s to the West. The plr ka tt0k 19e-tlezj5thb;93v ane's speed relative to the ground is

  A plane is flying due South x-:fza)z75l2q4t qtvg3 vhws($270^{\circ}$) 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 i7ur upaoqz) aiu,v 2vwb99x1 7s 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 1iw 03o) g4scv 96sf0vlytcjl50.0 m/s in a forward directiy9sl40 vjcl1)itsg v06cow3 fon $30.0^{\circ}$ 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 directed across a river w5q(rtadhe bnqg :593dith a current of 6.0 m/s. What is the speed of the boat asg:h55ddtan b q39eq(r it crosses the river?

  The driver of a motorboat that can move at 19 m/s ingkf;t0.gmxqkx3m (8 z/lh vm.(o36 k9smiba r still water wishes to travel directly across a river 1.4 km wide in which the current flows at 7.4 m/s. How long will it take tx/;3ogkqi0h( 6mk ( 9bm3 fmzkg. lsv.mxa r8to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wcbtch2n;3ui cpij (5 y5kyp.ou1 (5mlishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what tyck5h.2p1lb y5c3jpi nuoiu;5mc(( angle upstream should the driver head the boat?

  A swimmer heading directl643o pwlf8rg sy across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreapl36rg84fswo m 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bdpvrqhs.insdu8 (:5: fj5q:qank in 6 min 40 s. She i:i :(.r5:qs dqd8fnh5jpqusv s swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still8uxh 6nlp 52g1x/fzvs water is 0.88 m/s, must aim upstream at an angle ofp fv2zgl18nsx5h x6/u $13.0^{\circ}$ (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)  $m/s$