Which one of the following is an exyxzgk 3*, *mqeample of a vector quantity?

  Which of the following oper(o(. fc t8ljeh;p q1vvations will not change a vector?

  Which of the following isvtzenjd8a *.a9oq /osh ,vs52 an accurate statement?

  The resultant of two vectors is the smallest when the angle between o0 cpti)d j 44z9 j6dzojw6xd1them is

  Two displacement vectors have ma7dnt9giv2r3aurn g o6w+ )gw8gnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are ad rv)wt 93gndw72i86o ar+ nuggded, the magnitude of the sum

  Two vectors, of magni4.- *xszdeb;d)y7at/zfs dbvtudes 20 and 50, are added. Which one of the following is a poss zvda z 4t/b.s;e)-xddybfs7*ible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pul(.m1h lj k.kzzef.u9i5yj j85bni,gwl on an object in directions that am 8ih uj.j.lnjfkwi(9kz5,5y ezb1 .gre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecto e xpawswisu2c-9(ln4 71f kdy6))kkpr is

  Ignoring air resistance, the pyuv oa6g-y 7:horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 mbwuiem6;3ozl jk6qu1 5cw w21/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 projectile4zz vh5 y;*fhhumb)hn s;wd:4's acceleration ;f wz*)hn45vmzsbhuh;4d y:h

  A soccer ball is kicked with a velocity of 25 m/s (v+nyq 40lb/o /m 1 s vxbjmnj70l2oaiat 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 objeco a*jy0t;ib3 ly5acart7(e* gt is directed anti-parallel to the velocity vector,b;y*j ci tlye30r 57 oa*ata(g

  If the acceleration of an object is alwaysz3o b *lrn;c(g,iwi/q directed perpendicular to its velocity, wz;/lcnrqib3i(, g *o

  At what angle should a w03z6npfnfee n/7b 6 hfater-gun be aimed in order for the water to land with theh76fnb03enz fp nf/e 6 greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizou(3ox6r xz0q ontal, each with theo(x6qro0z3x u 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. 6g-34i94m*c j he/yz aoc.aoqe kq7aj If the ball leaves your hand with twice the velocity it c/6eae.ajik9 *yqqjom a34zh7- co4ghad on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spe)4bi7qqg)q( ao3ak mk /6wde med 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 +uq m6a12 x w(pk7iliymaximum height, how does its speed compare to its initialy(7a l wm2+i6kx puiq1 speed?

  A stone is thrown hori53xq8 0syrcocpp q, ww2zch f3 n 1y(5udx6cx+zontally from the top of a tower at the same instant a ball is dropped vertically. Whh 3+uypcccsxf8 xyz,wo 32 5 0xwn65(pcrd1qqich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a seconde8) d1w/ruqw,mw 5i2(nnsng hi96nm f bullet is dropped from the same height. Ignore air resistai dmwqnf9wgir (m5w, 6) 8en2n uh1ns/nce. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 77.0 m/s and at an 2mj eo5tr+q/d elevation of 290 m drops a package. 2.6 seconds late2oq+tjedr/ m 5r it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is drocwq h 4en:.y 3zxs3 d,j,pz0wqpped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance bec p:w yqq,z.e,dnj zh3w30s x4tween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at .:u5 k5l.phizd4f5j hv-ajh x a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane w-.hjad5k5 5lz 4hu f:xh.j vipill

  The acceleration of gravity on the Moon is only one-sixth of that on t6ar7kqe8rq,r c:( cq Earth. If you hit a bas 8t7:(cq6, cekq arqrreball 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 in the +x axis re*4 l+jpsx-6w azxwlheag+(( *5bgnizlative to a straight, level road and pass a car traveling at 45 mi/h. Th*e64*5al g bz+a-gx ( w+sipnzlhwx(je relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong c3(bq0- .0d jgvzjinhno 7zc:iurrent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from y bnvd 3ji i-qgcz.(n7hj0z0: oour starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Ho. fivlt/(8v:a yjtzf00bz5gnw much time will it take you to move 12 km downstreafzb0 g aij 8.tn/ty5 :vlz0(fvm, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at tadiucs, 1 (oe(w:k,d czc/c1 v9u +kzan angle of 30 degrees below the +x axis. The y component w ,a1kcc k/dut1di:z(u cz(c,voe9 +sof A is

  If a ball is thrown with 0c*v jzz nlh9c(l*:ura 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 east and yxf+17joa6h1talw7e d ou end uxa7o tahdwl6 7f+11 jep 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. Thefbm5n/-m; 062vakdhmhmiq3/ ;nt u2kexv e- a x component of its velocity is 8h vu/ie35kb;qa- exnkm v n/t h;f ma022m-d6m.00 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 sk o nu;b1i7)lxhadow over a level ground. At what angle is the Sun elevated above the horizo n1ku7obix l;)n?

  Two vectors A and B have components (0, 1) and (-1, j)(y en.yc x.m3), respectively. What are the components of t .m)nxyj(e yc.he sum of these two vectors?

  Two vectors A and B have compx* vuc f,h9ur0onents (0, 1) and (-1, 3), respectively. What is magnitude , vcr*09f xuhuof the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What )4g2( z9i.apdp m nrvna(ml/lis the magnitude of C /.r)lam94zv(apind gn l2p(m?

  A car travels 20 km West, then 20 km Souep.7qt2l rw0k, olu w+th. What is the magnitude of its displacemen02u , r k7lpwlqo+t.ewt?

  Three vectors, expressed in Cartesian coordip547r7c vevth;x69edwku,1evcwr(q yo t)8 j nates, 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, expresset rj zpbwmi)(419p fzu dv14(zd 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 vector B ;yb l3xoy6mtup3 7. nhhsq 9n:= (+3.0, -8.0), what is the magnitude of vector C = A - B ?l 63t yyxh uso37;np:qm9.nh b

  A runner runs halfway around a circular path of radius 10 m. ; v udsd+(p9/zjzad9j What is the displacement of thu(;dzap9z/v+jj d 9 sde jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitud szc5d6sj;x s4- )fxkde ofcsxz 5s-;f) kdd46sx j the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the ditk*h,r8+n wsy6 xc-ftrection of the resultantk*hscw- yx8f ,6tnrt+ force?

  Vector A is 5.7 cm lonki+yuz ;)rp(* gx7 aydvoyr4- g and points along the positive x axis. Vector B is 9.8 cm lon *y xo+dpry-r4yk7vuiz g();ag and points at $+23^{\circ}$ 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 71 cm long and jrvk .bi. -r na12k5cybifv5nu w0-i3points at $30^{\circ}$ above the positive x axis. Vector B is 23 cm long
and points along the negative x axis. Vector C is 44 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 w; 6plf .f lz /*fabuww:*1 qpvja;zr+rith an initial speed of 15 m/s from the edge of a cliff. A stop watch measures the :6 1rlfaz;+u; plrz/w vaw.b*qf f j*pstone'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 h; -+ yycsur5;fy.qsmc: yssh+orizontally, with a velocity of 16 m/s, from a bridge. It falls 13 m to the water below. How far does the rock travel horizontally b+s:ssymuycqy5 .r- +y;s ;hcf efore striking the water?

  A ball thrown horizontally from a point 18 m above the q5+ .knk(pq,m. y0ouzi ;aix 8pmw*rh ground, strikes the ground after;uiy,m5q(i q *+k 0kpnpoaw mxz.. 8rh traveling horizontally a distance of 24 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a;i(mst,p )dzg speed of 12 m/s at an angle of,pd m; )g(zsti $20^{\circ}$ 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 8 m/s at an anglel2srf mi a/7r; s.c/1g iswna6 o glw ii7/2m6;ssa.f1rsa /c rnf $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launqb ,+-jew4o 2e )stn.:tj mfkached with an initial velocity of 25.2 m/s at an angle of $47.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched wck9l;/aabpjixj py9*b3sg -(ith an initial velocity of 32.4 m/s at an angle of $29.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an7 dlv5p/hq5r xk:emx+gle 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 shotd6npc4.q1b r9y1 fpws horizontally at 27.4 $m/s$ from the roof of a building 49.2 $m$ 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 fromx5f(qwna a1+n e3f2dm ground level with an initial speed of 56.3 m/s at an anglf13+ qd xw2 aaf5nen(me of $44.1^{\circ}$ 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 v ydkzr:)4 *eas91a5zg zuz/l gt /s)vfzcv )*1500-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 slows your speed by 2.0 m/s, the tzv*v 9)e5 )gzl*t :s g /aa/srvzzy4kc)uf dz1ime it would take you to finish would be

  A plane has an air speed of 200 m/s due Nortfy+it) z1cb 5eh, and is in a wind of 50.0 m/s to t)eiy51 bct zf+he West. The plane's speed relative to the ground is

  A plane is flying due Sou72c wtye+bhs8th ($270^{\circ}$) 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 h5tl xux5u ku d4de8m;6eaded $30.0^{\circ}$ 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/4ndfc9j /iwx yv+29sms horizontally fires a projectile with speed 50.0 m/s in a forw/mwxy9f c4+sv9ijdn2 ard 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 q00jqa yi)qw- m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat asq-a qijy)0wq0 it crosses the river?

  The driver of a motorboat that can move at 18 m/s in still water wishes k s8z rn 83kekg8vg- ed5y.f;hto travel directly across a river 1.9 km wide in which the current flows at 6.4 m/s. How long will it take to cy 3khdsg e8 r8ngv; kzk8-.e5fross the river?

  The driver of a motorboat that can move at 10 m/s i4 v(hu5b8 dqz m*)xugtn still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the dri zu 8*hbxq(u5gd )mt4vver head the boat?

  A swimmer heading directly across a river 200 m wid7nvbyd( *xr - t.xmlu2e reaches the opposite bank in t- (xmud2 *vnrxl .7yb6 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 vp mhlmkj,0,,len ;e-the opposite bank in 6 min 40 nl v k,,m-,0hpelm;ejs. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.46 m/s, must63lo tr.xsnkhf. ,2qdt6-su p aim upstream at an angle of ts,xquntkh- ro62.63. dlsfp $26.8^{\circ}$ (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)  $m/s$