Which one of the following is an example of a vector quantig-7e.k t;4w5u 7r(isci hyx vyty?

  Which of the following operations will not change 87 sqm-tgq n5fmlr(m0 a vector?

  Which of the following w9b(vl crl g:2 ol7l-q 5abwrzk+a (x(is an accurate statement?

  The resultant of two vectors is the smallest when the angle between themi 7g 3yf b7g(fbqm8vw,x7*bbh is

  Two displacement vectors have magnitudlnce7nja d *ys /ox-94es of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude eaj4 -*cxl7yod n 9n/sof the sum

  Two vectors, of magnitudes 20 and1 :rdh:l ovny, 50, are added. Which one of the following is a possible answer for the magnitude of thervy:ohd, l: 1n resultant?

  Three forces, each havin.kfmq*p6vwt:z 56k vpg a magnitude of 30 N, pull on an object in directions that are tw6q 6 :k*vp5zpk.fvm $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, ,du le /dmun6qrel72--xon3p the unknown vector is

  Ignoring air resistance, the horizontal component of a 1 ;(1dijo guz: r wonahes.-9aprojectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle owp2;v5iav :a+euqz q2 f $60^{\circ}$ 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 o7 dnk n8 /ztr5jw5fp2cf a projectile's accelerationp8j kf/5twd2 znc7rn5

  A soccer ball is kicke *4ydv-74ru n6 wso)e5saccmcr,fs1bb.m x 4v d with a velocity of 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 obje)h*vps g: d+miptq8 z-ct is directed anti-parallel to the velocity vectdpv-q)mh:g t*is8p +z or,

  If the acceleration of an object is always directed perpendicular to its vl5*uk0sv2 - npg-gdz relocity0p-zsug-2g* vl kd5rn ,

  At what angle should a water-gun be aimed in order +y -;gm0u qeyqfor the water to land with the greatest horizmy0-+g yqqu ;eontal range?

  An Olympic athlete throws a javelin at four different angles above the ho d5hq3ncc8b*f(4f l.(2wvwl fz -igixrizontal, each with the same sfqldc- n4*.5fi x3iw82 zw(v cgf(lbhpeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. ck8 u4b xs.1 apkmzda7;x:za) If the ball leaves your hand with twice the velocity it had on your first t1m.a 8aupds7kabz4);x:k czx hrow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spegk: o 6:sizkfpbq9:m(ed 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 att.mp-mdsvag+ o u+1bg uxj( 6-5-ankds empt reaches its maximum height, how does its speed compare to itd+m-mpua-ngs5x(oas -b6g.d + vu1kjs initial speed?

  A stone is thrown horizonta52o /abrq om:hlly from the top of a tower at the same instant a bal:5hobmr2/ao q l is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horirl7ru 1g/sa z5zontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bul grlusa57r/1zlets.

  A plane flying horizontally at a speed of 47.2 m/s and at an elev1 j 5 qls2ajg o4te9fuy7uv l*90imn:zation of 131 m drops a package. 4.2 seconds later it drops a second package. How far apart wil zljaef9 i90u usmvyq75no 42 :*ljtg1l the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a sec(.vt 2j3 ,2qenwul pfqond package is dropped. Neglectin22qv,tj ql ( .3wefupng air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally k4j3u,wilfiu 0;m ;biat a constant speed. Neglecting bi uk ljw,im3i;40u;f air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that od 18o0nju+dd hmlo;fjwa)g+/ n Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) thdg1lfwn u oo;8+m jjd+a)h/d0 at you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a dder zuaa) *em40 01sestraight, level road and pass a car traveling at 45 mi/h. The relative velocity of your 4em a01 *ede)sudar0zcar to the other car is

  You are trying to cross +)jhbij;40iconscc 5a river that flows due south with a strong current. You start out in your motorboat jc0i4s+j)n ocbhi 5c ;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 .1c, mw u)3q +sgegyfd2yw2jl still water. How much time will it take you to move 12 km downstream, in a river flowi3q,lcmd 2fw).gw+ 1jgu yey2sng at 6.0 km/h?

  Vector A has magnitude 8.0 m at ak-da ze ,2 ynviq(an/rh9a /.pn angle of 30 degrees below the +x axis. The y compydn zai/ na /-.9aq(h r,2ekpvonent of A is

  If a ball is thrown with a ve.lb7v ilbv;p;um u6-ac,e s/qlocity 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 directio;, )gvqjc7m ygbyl ;+tn north of east and you end up 2.0 km north and several kilometers east. How many degree,lqgytym 7;jc)g; v+b s north of east have you walked?

  A butterfly moves with a rk3kep pjd 7v)j1d-k zvx0 r)c-x/4ra speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x av4xddkzxpjpjr1/ ) 7ar30-rkc)ek -v xis must be

  A 400-m tall tower casts a 600-m long shadow over a level gdlpu homk+4*d,y.o ,l round. At what angle is the Sun elevated above the horizon+ okdpmdlu*lho y.,4,?

  Two vectors A and B have components (0, 1)l ya.;nsw3 pc+ and (-1, 3), respectively. What are the ccya3 pn+;lsw.omponents of the sum of these two vectors?

  Two vectors A and B have components (2ggtdp5tarbt1 9:b. . o6obly0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vect.tbap2g5td o6lbb. y9r 1t:goors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitukbrjk.t.noy ,4hfq ,m hicy j6e54* z3de of C jo *5b6y fkk.j4e n4,q3yri ,m .chthz?

  A car travels 20 km West, then 20 km South. What is the magnitudxgre oq0k,tr ft+((w+ t9szo3e of its displaces+ r(e tzf+3oq wgt o0r(t9x,kment?

  Three vectors, expressed in Cknp4 nhztr *3oc x4;1y2 q.ydaartesian 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 coord8l5v )pptkyl) inates, 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 i,9junf39ecf17al w9a gbi, m vecto937uf9igm w1a jb,ne laic, 9fr C = A - B ?

  A runner runs halfway around a circm6 jxnomhgrt3 *.7v 3lular path of radius 10 m. What is the displacement of the jogger6xmh mvjnt7g3 o l.*r3?

  Two forces are acting on-zx *2i nf+*-sbpxm ui an object as shown in Fig. below. What is the magnitude of the resultx2 -*u *bfxnizm+pis-ant force?

  Two forces are acting on an object as shown in Fig. beloo 8d- f6z1f8s(4aqehdnk z;onw. What is the direction ffkozqn8h-4n6 dzo ed1s( ;a8of the resultant force?

  Vector A is 4.0 cm long and points along the positive x axis. Vector B is uiw e;+ 5/ixxjrlm 36tv-jmy 7ylh2 p36.7 cm long and points aj;u35p /x3w jlit -im 6+2m7exvlyyhrt $+28^{\circ}$ 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 80 cm long and points s fvn5r*(h oqo;ib.c /r5svdnwq04 z,at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 30 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 oe,y ,bs5e )7;ruaj wwd57 kle5ao:idsf 12 m/s from the edge of a cliff. A stop watch measur 75k osb5eldds ru:ae 75w,)ij;y, weaes the stone's trajectory time from the top of the cliff to the bottom to be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 5 m/s, from a bridge.eg:w4 )xatk j) It falls 11e)xjw ka4:)gt m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 i.hdpa43**ni2g ek 40t m fwcdm above the ground, strikes the ground after traveling horizontally a distann*wip0a*4tidf.gceh k2 m d34ce of 12 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 ano37w ee,lq533lkfegi gle of 3 fo3k7 l,5gileeqw 3e$20^{\circ}$ 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 15 m/ 9ba5oifs8 up)s at an angle of pa 8fus9)b oi5$16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launch8ulu pnvm:z 3nqbsn,buq.j7;q-u4 ;med with an initial velocity of 52.5 m/s at an angle of $18.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 28.0 m(x-ya5po))f 3 ytswhf+ e c+hn/s at an angle of $45.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at a6;3vv v/pys- bwd .b)qe*8 qfai1wsqhn 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 +:k4 rx4gar,h,qss ofhorizontally at 18.7 $m/s$ from the roof of a building 48.3 $m$ 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 56.3 m/s.z/ eb33 rxiwx at an anglerxx3.b wz/ 3ie of $42.0^{\circ}$ 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,;i2l 1e68 it j.arq4csxxzti 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 majec q8lr1;ixz426x ts. ,iit/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 5di+ f+,zdx nnsqefb y202i.2v 0.0 m/s to the West. + dqy zxsn2+,efvf2 2idin0b .The plane's speed relative to the ground is

  A plane is flying due :3kza-vudqxqph byu5r,i1/ . 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 of 120,tp(*sqgbz.nf +jv 5x 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 horizontally fires a projectile wi8y ;7gy, x-0xlbaqv 0sbocpc6mt17z+w 3 p trqth speed 50.0 m/s in a forward dittblyzc7w01ps+b3c , or-q0vxp x qya6 m87;grection $30.0^{\circ}$ 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 wac9c.yy 7hvr7p5n6cshf t4p0uter is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the spety79v4y6cpc.h n phru 75scf0ed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still wate cn3y12w 5q n(y ;bix/ofbkgc1 s2u3gmr wishes to travel directly across a river 1.4g1nx1; gnq cofy2y5 2u3b c /(3bmkswi km wide in which the current flows at 4.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 1hpdj g5i3vo.df .)lbund:11 k1ab *n u0 m/s in still water wishes to travel directly across a narrow strait in which :1 pvb. dd5n *abuj u3)oig. lkf1ndh1the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acrosseyh)koalq,2y 7eo 66 d 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 e6h y7d6oaye2k )oql,?

  A swimmer heading directly across a river 200 m wide reaches p .nt0s0z v;ynthe opposite bank in 6 min 0 yv.tn0; zspn40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.15 :ycy e;igdz6b.s43 mym/s, must aim upstream at an angle of 6mcsygi. z 4dy;y 3be:$16.7^{\circ}$ (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)  $m/s$