Which one of the foll)hc :6jx ttrz )jo-*kvowing is an example of a vector quantity?

  Which of the following operations will not change a v9yl( f.tz,skvector?

  Which of the following is an accurat,,tt:ye2u w/o sffkv+e statement?

  The resultant of two vectors is t,:hhs1uplo )t he smallest when the angle between them is

  Two displacement vectors have magnituyf2e)8ps/pszm .mhx 6ccu 5.e des of 5.0 m and 7.0 m, respectively. When these two vector.zcme.esppu c) f6m/ y582hsxs are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are advxfot+1 )4kwe ded. Which one of the following is a possible answer for the magnitude of ove1t4)x+f kwthe resultant?

  Three forces, each having a pr33vvup7f ui,w))wsmagnitude of 30 N, pull on an object in directions that 3)r3vw uvw,p7u)s f piare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is0s2kfi s,qbdw a7fzm1x d(k4-

  Ignoring air resistance, the horizontal component of a projectile's v;b lrkho9a3 * wwwv;1yelocity

  A ball is thrown with a velocity of 20 m/s at an ang0d.g fz/r-ym rgn2 b-wle 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 ka+2rz-c/k iyst9w qn89co91mvaim5 horizontal component of a projectile's accelerationt2k/9s8-w5oiarc n+z mc1m 9aviy9k q

  A soccer ball is kicked with a velocity of 25 m/s at an angl6 clevuk6.5k le 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 directed anti-paros/qtz;0wqqp/ h5r6 uymucu ;o d)l2 5allel to the velocity sqpclo 0wd h o5zymt/uq/ 2 56)u;;urqvector,

  If the acceleration of srr ,7gso 6ae; cxw8ipm370hnan object is always directed perpendicular to its velocityc 0p7;gih7oes,sa8 xrmn rw36,

  At what angle should co81sdu ,jb8u2xrbq9e63dli a water-gun be aimed in order for the water to land with the greatest horizoiu8ql2,jb d89 36eru scx1bdontal range?

  An Olympic athlete throws a javelin at eno-kq b l3qysk9b b-e1 hh,i-(9 jf)rfour different angles above the horizontal, 9,--jbkbl hf31k(e eqisrbq oy)nh-9each 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 the second time. , qrv(0 dmz +ikjfr/s2 If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compari,/ z+skrj2dv f (mqr0ed to your first serve) would be

  A ball is thrown at an original spb0 2,pzleahag3*h..zriiy3u eed 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 maxi7* ukxg.7l0yd c xn-xcs4o:ummum height, how does its speed c*0xk4 c:x .yugcdmnosl7 x-7u ompare to its initial speed?

  A stone is thrown horizontally from the top exqf4 yep/ p6y-7uzx fa q)03/g jrip:of a tower at the same instant a ball is droppex 0 xy-ye3az)/67pgie/prfjqpqu:4 fd vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizonf wahpx9 wt,1wqkw(*- i fm5,ktally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the timqi fpwk- h(1m *xw5w,,af t9wkes of fall of the two bullets.

  A plane flying horizontally at a speed ofs:un;a4-(hnk s f gr5j 6rp:lz 83.6 m/s and at an elevation of 221 m drops a package. 5.5 seconds later it drops a second ukfls; 6-grja z5(::rpnns 4hpackage. How far apart will the two packages land on the ground?

  A package of supplies is dropped fyj)jd2d0x:p from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance betw0)pfj2xdj yd: een the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant xhn (m7pmih) +0 6s(crmnj 8m3uxdrs8speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the pm mh 3r7pm+(dix(8x8 hnnmu)0sc6 s rjlane will

  The acceleration of gravity on th 1t-dq:8tn 2ua f5hsfwe 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 wouldts d fnft-2u1wh5 qa:8 on Earth, the ball would land

  You are traveling at 55 mi1yvkboec/1( s3 .gs9s uc/ety/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relats1sek9occ/ (.1eb/y3uvg s tyive velocity of your car to the other car is

  You are trying to cross a qht+o :n*zj7v.l3 iebzq:7 wqriver that flows due south with a strong current. You start o +ze7 q :lz*o v:t3bw7nqijqh.ut in your motorboat 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. H w.tj 2hp1b+5z lcuj.9np,a bsow much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/h1.+pupbh9n,5 ws jl c.zatjb2?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below:,y lvkxb 6i*fp8bq68 ahp4a+.ysnky the +x axis. The y component o. h*4l:ifv6ky+ bx qn6 yy8 apka,spb8f A is

  If a ball is thrown withs:7zaer1u /n)4cjr lb a 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 line6p th xdqsx695j7ch*d in a direction north of east and you end up 2.0 km north and several kilometers east. 9ht x6q xc5 d*76sjdph How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is ng*j;ba;ya7j 8.00 m/s. The angle between theg an*jb; 7;ayj direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At k b jh1dgkrp- a6,z9g1what angle is the Sun elevated above the horizk-j1zbgd,h k 9p6ga r1on?

  Two vectors A and B have components (0, 1) and (-1m,i1gg )e0nnv, 3), respectively. What are the compo,n )v igg1m0nenents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivel mz(3ehvilhh( n9*rtm 4;ao(7 nhme /jy. What is magnitude of the jh4mon(alitvmr hhz3( 7; (e/*he9 nmsum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What ix6vy agw1 ozt3 0lp);s (ztqr;s the magnitude of Crtz gt;0lqway vx;63poz ()s1 ?

  A car travels 20 km West, then 2 ky*.6j 81 6 mzqkvpd.baigg(p0 km South. What is the magnitude of its displaceme 6dpb8gv g.y6ja mp(i .qkkz1*nt?

  Three vectors, expressed in Cartesian coordina fnr2n1q,t big7+u fh3u,f+z ites, 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 Cartesiaf c,s /v(9qw:iy6cj 5nbuzz-fn 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 is the magnitude of k*,hpi/ims 2.;fjv 5c vgc8ar vector C = A - B ?pc*8ahi v gfis2 k;crv,.5jm/

  A runner runs halfway around a circular path of radius 10 m. What is the d/x ;dmww:+5nrn hjo ss/f6i b2isplacementi5f ;/snbwj+rms :hxnw62do/ of the jogger?

  Two forces are acting on anw3.rb v.3 qa robokg(8 object as shown in Fig. below. What is the magnitude of the regk.qabr rw 3o(v8o.b3sultant force?

  Two forces are acting on an ob j0q63sf:vto lt+b n1bject as shown in Fig. below. What is the direction s tt0q ofbn1v6:blj+3of the resultant force?

  Vector A is 4.5 cm long and points along the positive x axx8 gamz h: sa254t(egc08hwr xis. Vector B is 9.4 cm long 5r8xwagscm0ah eh : 2gz4x8(t and points at $+31^{\circ}$ 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 points atau 7k. z2w 3/3quqrqrn $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 36 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 15 /y:c/ pl4ce9kv94+txmki nj,pi p4a bm/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.be, :cvn 9ppixm4 j/l4 t/aik c4k9py+9 s. What is the height of the cliff?

  A girl throws a rock horizontally, withy my+3ko(iplv k7l(8 r 5s:jl )bgodz6 a velocity of 10 m/s, from a bridge. It falls 27 m to the water below. How far does the rock travel horizontallylp y )kbd o:+s3y7lvk8z5mj (irg6ol( before striking the water?

  A ball thrown horizontally from a point 26 m above the ground, strikes the gr vbka ;g4g3+aoound after traveling horizontally a distance of 15 m. With what speed was it 4avao+;3ggkb thrown?

  A jumper in the long-jump goes i0vxv*lp-penez e1 ;.gnto the jump with a speed of 12 m/s at an angle ofe0 vpl-;p.*1z g xevne $20^{\circ}$ 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 12 m/s at aok7p5ewh p:8 z4 qp:ajn angle jk:7 4o8:zpp eqh5p waof $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched w mcilv4 .c*b7ki-us3 tith an initial velocity of 45.3 m/s at an angle of $22.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity o,nctt0-k*jhs/;rls w f 25.5 m/s at an angle of $39.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at a sp9 /q+qu3dckn 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 hngx*r;s7f:kx / (x srborizontally at 23.7 $m/s$ from the roof of a building 35.0 $m$ 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 xpl1 2ms6q0.iw+csx cground level with an initial speed of 50.8 m/s at an ang0.+2x1sx6mc qipswlcle of $39.6^{\circ}$ 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 r :i8vxpcv r+bl.*bh6w un a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on *xh .bpwlb+ cv rvi:68a 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 m/s e po7j*; 4xn8s2.0myyttsnry xjs18s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relativeyex 10t xs74jso8n*r .j 8ys;tsyp2nm to the ground is

  A plane is flying duz0z 2 l:xr 1d.h1ayrvx nll1i9e South ($270^{\circ}$) 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 ofm1r t-tar5x3q 6) x1e blyn/lw 120 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 200j ssz)1g i.)hn m/s horizontally fires a projectile with speed 50.0 m/s in s) ng.1 jhi)zsa 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, is directed across a ekc;*bbggi3. river with a current of 6.0 m/s. Whe*bcgik; 3. gbat is the speed of the boat as it crosses the river?

  The driver of a motorboatnt 2ow jzr+k obn2l :5 69+,fvxguwn-d that can move at 13 m/s in still water wishes to travel directly across a river 1.82of ,x olgnt -w:9knwbn+vrzd 2j+56 u km wide in which the current flows at 6.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to tr(3jqv4 o: h/;jupmh lsavel d:m3(hlv4hqj u osp;/jirectly 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 ngn-: 2-svz vge 5iy1iacross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is-geyiniz 5n:1gsv2 v- swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 2y two:di)y +o300 m wide reaches the opposite bank in 6 min 40 wy+3 :t )odyois. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.81 m/s, must aim upstrea:8g wn m5av -w)9b:0ehmwls pkm at an angle ofl5w0s)a: v9e p-wwhm mg:n8bk $20.1^{\circ}$ (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)  $m/s$