Which one of the following -rgq*o7 ro)nh qs,b cupxh80w:3lw9iis an example of a vector quantity?

  Which of the following operationxf :mmbn gl;og aj7-*;s will not change a vector?

  Which of the following is an accurate c6ikng0 ef + w k6bz)0ea(q8/y-bzsyjt40ut ostatement?

  The resultant of two vectors is the smallest when tha 8i)mcc. su-1m*trs( clu vb5e angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7gs tlb *0n;:fd.0 m, respectively. When these two vectors are added, the gb;ds0l* :ftnmagnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the *ctjdfv3md8t8 :dki6,geyn -t sgh. 4 following is a possibl 8ggd, 83dn*ttt hk m4scj ye:fv-i.d6e answer for the magnitude of the resultant?

  Three forces, each having a magnitude ofp+q adzcc1zqc*f:n .2,o2gy9 pouc a 0 30 N, pull on an object in directions that are zc .aocn, 2pq fg20z:+c9ua*1opydcq $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown 7pearv, h6hqguy ,9x5vector is

  Ignoring air resistance, the horizontal component of a projectile's velolr)85)ty l pw nz.rytcxx23r xzy++ owv9vw/,city

  A ball is thrown with a velv8+xr9tl8p j3*s t4-z iurqmmocity 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 *:cbx a3 dd++h3j qebm)eh+fvcomponent of a projectile's acceleration)ha m: +bd3vcj3f*hdeqe++ x b

  A soccer ball is kicked with a velocity of 25 m/33t g.k i0ne *hm: -bvhmr,tuvs 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 directe)/7 7 1y,imq qf x1vasdg-vdskd anti-parallel to the velocity vectqd)vmai sd1q-kx/ s ,y 717vgfor,

  If the acceleration ofhw:z uvyx/3.ad kr/;r an object is always directed perpendicular to its velocity,uw d/yr/3vz:.;xrkh a

  At what angle should a water-gun be aimed in or )tfz.lb*8u,qr /a:85; ttonj jbqxc gder for the water to land with the greatest horcuqq8t g*bf:; j bt lraoz,tx8n /.5)jizontal range?

  An Olympic athlete throws a3ebv/b+ug gm k:q 63kj javelin at four different angles above the horizontal, each wite3ub:mb+g qkvg36/k jh 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 4 cgcy/grp 1a-for the second time. If the ball leaves your hand with twice the velocity it had-pggyar 1c4c / on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed ). pdtzki 2:zrof 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 aj.1t qwyqu1r -/zp is- field goal attempt reaches its maximum height, how does its speed rqu 1tsp -1y./j- zwiqcompare to its initial speed?

  A stone is thrown horizontallyprkj+ k2djq ks 32us 2092m6i-xbzzke from the top of a tower at the same instant a ball i2 pr uz dq2kes2kxki 6j0b- 39+kz2mjss dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same ine/ad .w +jfur8stant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall ofju er+/8 a.fwd the two bullets.

  A plane flying horizontally at a speed of 101.4 m/s and at an ep (rh;i0b1krf *9szfdlevation of 242 mbf0k zpr*isr1(; 9fh d drops a package. 2.8 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 p aiye/ 3d ahnki)0y d0gc7o6+blane, and one second later a second package is dropped. Neglecting air resistance, the distance betweeco60 3kiahdy)gba y/0in ed7+n the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spea/b6.m7zkfr8i3v z3h kyid 3hed. Neglecting air resistav6 fh.i3/ydb k3ha38kzzim 7r nce, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on tik 4y7f iq q8z7po+: uwd(gg-;4oqi zdhe Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon4w qq7gq ozd(id;yo z- 8k:g+f7pi iu4 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 in the +x axis relative to a straight, levebwouw+ e yu;p p9um .t:s,knuov2q5 57l road and pass a car traveling at 45 mi/h. Tho5tw:52ve;y ,+k.9 uumoq pbpus n7uwe relative velocity of your car to the other car is

  You are trying to crosmkf/ mp *t-wv,s a river that flows due south with a strong current. You start out in your fw ,m-kv*mt/pmotorboat 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 k.wit*4c 4bdnylahz 56pt) w/ om/h in still water. How much time will it take you to move 12 km downstream, in a river flowity .lb wnh45w 4 z/i*t6p)daocng at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +xr 5,v, t/wl9 3dzhakmz axis. The y componem, avk, 3wd lhz95zr/tnt of A is

  If a ball is thrown with a v yqh, o8:f1(h-uq adgtelocity 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 linegq05s2h0*. nvgezlgdt d7: rd in a direction north of east and you end up 2.0 km north and several kilometers east. How mg dgl*ns0e:5d7 hq0r.dg zt v2any degrees north of east have you walked?

  A butterfly moves with a spoaxh p 3;lw,rk w535moeed of 12.0 m/s. The x component of its velocity is 8.0hwp w ;l55k,o3omra3x0 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 kh;*zwev2q4foim9 m4 shadow over a level ground. At what angle is the Sun elmvo2z 4fqk w 9ih*e4;mevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), resh*ytd9 )o,w+ y0 nemrhpectively. What arm +ht ryd*h0wn ,9)oeye the components of the sum of these two vectors?

  Two vectors A and B ham mp-lw*p ivo2l5y01w8 aq,e lve components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of tl lwe21, i*pl0 -avwm5pm8oqyhese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the maj- to.q55:ywh d6 akxmgnitud-5hamdt :ow xy.5jk6qe of C ?

  A car travels 20 km West, then 20 km South. What is the ,xh (g69hrzy smagnitude of its displacement,gs( r6hyx9h z?

  Three vectors, expressed in Cartesian ihzu. 23h /toj;jneh-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 f:s q7b wvk36i8,hjxi 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), whar 4 a)lsq/5idd 9rc(jrfd 1:e+ 5xosiot is the magnitude of vec )id9+r4cfqj / 1e oi5ds r(xo:asrl5dtor C = A - B ?

  A runner runs halfway around a circular path of rad7i68rl( i.mjv+3qui/im qv+ s1 ynn nyius 10 m. What is the displaceiun+v7r.i jqyl6qv is+i3mnm1( / 8ny ment of the jogger?

  Two forces are acting on an object as shown in Fia*xgv3 qe -qk4lclih*.z.ks)g. below. What is the magnitude of the resultaalk ) ve. hlz *cgq*s.k4qi3-xnt force?

  Two forces are acting on an objecthlw- w akdrn(2)4p3wi: uhxf ; as shown in Fig. below. What is the direction ofaxiw 4hl(p: w;)fh2 uwdk r-n3 the resultant force?

  Vector A is 3.2 cm long and points along the positive x axis. Vector Bs 1j)a77 fsem jeu z5cr6vk52m is 6.6 cma75 cjfv)s6skmrj2e u 7ez15m long and points at $+28^{\circ}$ 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 68 cm long and pointj;mlkz f d 4sgoqg ;+)jrfb.0*s at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 41 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 ho1 vehcoezg249 rizontally with an initial speed of 30 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 t o2c9zhee4g1v o be 4.6 s. What is the height of the cliff?

  A girl throws a rock horizoe p-57 aw0 )pmfvq ase;s:c //2aimvhtntally, with a velocity of 11 m/s, from a bridge. It falls 19 m to the water bel e tmv/paw:cpeq0a-v) s hm;7i25as f/ow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, strikes the groung;0 uo6dvia(lcz00 u pd after trapcdgvl00a0(6oi u ; zuveling horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the longphw8k w vgaqz, o51 .yof:.pj4-jump goes into the jump with a speed of 12 m/s at an angle of8. j 14ovkg:woh,5faw. ppqyz $20^{\circ}$ 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 10 m/s wmyi0n9 23k7w bzsss z*jol,,at an angle ofmkw*zi,l9n,j3 sbyo 02w ss z7 $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is laun0rx+bqq/8kh r ched with an initial velocity of 34.0 m/s at an angle of $14.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launc2h3)/6+fk xo4;prt i sw crkg5n ib yr/3agn2uhed with an initial velocity of 22.9 m/s at an angle of $30.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at al( zb 2v5zxtgz+ t j9356daivtn 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 hor6-nb:vs- ici;-;gg y ,hghsvto pv 93vizontally at 24.0 $m/s$ from the roof of a building 53.5 $m$ 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 init wen. x)ig7uf5ial speed of 57.0 m/s at an angle onfx7w )5ug.ei f $40.8^{\circ}$ 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 d,/c8x9rrpxjzh hqt 5 n d+/j/at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows yo9/z/ 5jrj/d8nhrtc ,dphqxx+ur speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air sp4c:9p j l,brgxeed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relat9glc:r4, p jbxive to the ground is

  A plane is flying due Sou- nl1,l(qoe crth ($270^{\circ}$) 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 y h)of)p) lhm7m,*7lkpi y vi4cgg-:w120 km/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 horizontjukgd9 u.7sf-m 75qmd ally fires a projectile with speed 50.0 m/s in a forward directionm.jgdf k5u 7m-udq9 7s $30.0^{\circ}$ 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 dqw.q(aku c lkjfr(n1/2(ve:lj b +(l directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses thbl( ja1(ed(nqkw(.u/l:+ kv2 fq ljc re river?

  The driver of a motorboat that can mrwa-d 1 oqe0l*ove at 19 m/s in still water wishes to travel directly across a river -le0qr aw1o* d1.3 km wide in which the current flows at 7.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that hf8(f zll)l4w can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the curr8)l(hl4fwlf zent flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly aceor28 q uk*w l1dv;mw1ross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?m*v d;eqo8u11 wrl 2kw

  A swimmer heading directly across a cf,2-4xmoh 15,x b al5lbav r 0 xoqt262srepsriver 200 m wide reaches the opposite bank in 6 min 40 s. She is smfesa q62x 2a po-524 0b,hlxxtb,cl5vrr1so wept downstream 480 m. What is the speed of the current?

  A boat, whose speed in h+nuo uvcwg qbykw6(/+3) 5w2u/ne3hv.eg n e still water is 1.34 m/s, must aim upstream at an angle of 2 w6kgq(whnceu++uyv)gone5 3/e.nv3wbuh/ $21.9^{\circ}$ (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)  $m/s$