Which one of the following is an example of a vector quankaa:op u-l)4i)xr )qq tity?

  Which of the following opzs-opwe prk,j* :x/w6.bd 4xherations will not change a vector?

  Which of the following is an accurate sta9s( a. q0l-ws 5hswpsetement?

  The resultant of two vectors is the smallest when the anglevfw1pq;o3w/d :zv r8n between them is

  Two displacement vectors ha sr)p(at(a+xm ve magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude +at(rps)(xmaof the sum

  Two vectors, of magnitudes 20 9c5fbr06epw oli4, cl and 50, are added. Which one of the following is a possible answer for the magnitude of the resuc4 co, fl0il9be56pwrltant?

  Three forces, each having a magnitude of 30 N, pulr 7x2kgr 2g,e8fi4rgcl on an object in directions that a rxr27,f28r 4kggigecre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, t+ 9c axrlq,9/0sklgx . jdbc/mhe unknown vector is

  Ignoring air resistance, the horizontal component of a projectile 1j/imal,rpv8b ss p6;'s velocity

  A ball is thrown with a velocity of 20 m/x e9cl+ /xxk. hjf(ktg:9js; 7ye o1xps 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 comporm6pj3) ovjt8b rv3,inent of a projectile's acceleration)rmt , b j3io68vpv3jr

  A soccer ball is kicked with a velocity of 25qou8qeqro p ml(;t.8 w1n;1yg 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 directed anti-parallel to the v/4y 0.- elk a9qmecvwxelocityv-4e y/el0x9m wac .qk vector,

  If the acceleration of an object is always directed pvw t rka 9 n3 re2ink-d,fv*sh5q m,n,vau/,1merpendicular to its velocity,nvkn5 sur,*w eh ,ta m i3, 1-vdmr/ka9fnqv2,

  At what angle should a water-gun be aimewrum3bwp2( : ad in order for the water to land with the greatest hw arw: 2p(ub3morizontal range?

  An Olympic athlete throws a javelin atc8 tl1qru -74iyg nbz ;y148od5e lwcler,)bd four different angles above the horizontal, each with the scz;ruw d548e8lir)e1 b17l4l nb -, qdyg tcyoame 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. If the ball i3q1,e c3s tt l)x(de6m -timlleaves your hand with twice the velocity it had on your first throw, its hori e,i( xl3titem l)ms6qd1 3t-czontal range R (compared to your first serve) would be

  A ball is thrown at anesic -3-mfora5s:/mh original speed 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 maximum0uqju+/xvt x3 /zntd4 up)q4h height, how does its speed compare to its initiah tq4jd qunup3 t+xv/ 4xu0z/)l speed?

  A stone is thrown horizontally from the top of a tower at -qx jr)r c+f9dthe same instant a ball is drop+ 9crx)rjd f-qped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizk0ivb/2awv :contally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of thv bw/vci2 0k:ae two bullets.

  A plane flying horizontally at a speed of 41.7 m/s and at an elevatiuma t(gzu2(+ /o3b ebjon of 283 m drops a package. 4.9 seconds later it drops a second package. How far apart will the two packages land on the g oe+ju m(2but/gz(3a bround?

  A package of supplies is dropped from a 6xp,00be5z 8oof(fsam o -uyjplane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packo0a u0fe8mb fxzp(s5 ,oy o6j-ages will

  A pilot drops a bomb from a plane flying horizk66ka b2ry2h:zl6qf s ontally at a constant speed. Neglecting s6z rhl62aqk:b 6kfy2air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only oapqbrzgal/ 91oe 935r m g*;mqne-sixth of that on Earth. If you hit a baseball on the Moon with the samb3qagm*9o9 5paz/m q1grlre ;e 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 ret/va u.bvdy-58pojnlc9 / i:glative to a straight, level road abpo8yv j l/ct.5g/ia d uvn:9-nd pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong current. Y r9 .oiifr0 pk3bnax;+ou start out in your motorboat on the east bank desiring to re+09niao brp;rikf 3 x.ach 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. How much time will it takehw;c4y f.n(ers )xcb pl0/w o/ you to move 1;p/bhw4(lf xrcn0s w.o c)ey/2 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x aj.6 shs6ot(si)h fc z7xis. The y ctsji6z.ho7 s c6s)f h(omponent of A is

  If a ball is thrown with a velocity of 25 m,ia6 p /luis - w:8ih-bcvi8hrj82 yse/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 and0dggzi 0tz2c 1uvkn 35 you end up 2.0 km north and several kilome3ctg z5gdu100 2kzi vnters east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component .ffur;7n ry*/1k v k28ll4aouvqon*vof its velocity is 8.00 m/s. The angle between the direction of its mon7 *vr;y.*/uuonkl f8f rvo 1v ka2ql4tion and the x axis must be

  A 400-m tall tower casts g lpp6hbi:k.j x0 71uea 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizonugx7jh6p0. :1kpil b e?

  Two vectors A and B have components (0, 1) and (-1, 3q5ja2.xpjs ,bi(s ;y n), respectively. What are the components.ibns5yjx s2pqja ;,( of the sum of these two vectors?

  Two vectors A and B have components (0, 4mz8 dohp5e2cz6 fcu11) and (-1, 3), respectively. What is magnitude of the sum of thesez4 2 z5c1 cufpo8ehmd6 two vectors?

  Vector A = (1, 3). , z8si8dhs.2 -nsdzqkVector B = (3, 0). Vector C = A + B . What is the magnitude skq-d.ishnz s882z,d of C ?

  A car travels 20 km West tc7:f6* .2ll yrmanlb, then 20 km South. What is the magnitude of its displacementmtc la*.lf:ln2y6br7 ?

  Three vectors, expressed h1 pt69vugw n(in Cartesian 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 Cartesil guh hsxb8*3pg.qzb/;bd : ,fan 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), whx2 x6 9aix)panpt6)ha at is the magnitude of vector C = A - Bxh)2)aiap9 6xpt a 6nx ?

  A runner runs halfway around a u xcq2 l+clu1y fy971rcircular path of radius 10 m. What is the displacement of the jogge7 2ux9 rfyllcq1u +1cyr?

  Two forces are acting on an object as shown in Fig. below. What is the ma)6b 1f3mp60a ok-m:lhep hulzgnitude of the resultanz61hmemo ):- ubkhp36lfpl 0at force?

  Two forces are acting on an object as shown in Fig. bel4k:uf4l (fna2zsw(* xv: uyv oow. What is the direction of the ressuu4(y kox: :zvn2f (* 4lafvwultant force?

  Vector A is 3.3 cm long and bvw;mv u; +f0npoints along the positive x axis. Vector B is 9.5 cm long a nb;wuv+ m0vf;nd points at $+21^{\circ}$ 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 w) 3omu9po n3*/mwuavpoints at $30^{\circ}$ above the positive x axis. Vector B is 23 cm long
and points along the negative x axis. Vector C is 48 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 29 m/s from the edge pvtp,iv b bm2gkp(xy)+ +;brcxu 9*b(of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.4 s. ++v92t* pvby m ripp(;gbx (bbku,cx)What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 6 m/s, from ytynq, mw/j9ku4 n-d9a bridge. It falls 13 m to the water below. How far does the rock travel horizontally befnyy,und9j t 9k/qw4-m ore striking the water?

  A ball thrown horizontally from a psy3u3j9upf c )q;uy 9.ten x1xoint 20 m above the ground, strikes the ground after t3 ft991;3c.xusn yepjq x u)yuraveling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed 0 mczfb s(wc:c,eq (7ppwoon(u1 . ie9of 12 m/s at an angle opf0 n ow(ue7 z mecq((b1p:,wcs.coi 9f $20^{\circ}$ 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 jjjd6xdqu3+ pi g 8;3(j xjmhi3ump with a speed of 13 m/s at an angle of+36(gijjxpid38ujm 3 jqhd x; $30^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 26.7 m/s at an abbf11g y9ok ict l)1z.ngle of $36.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with 1j6i8kowop(9+ a lem.c y1eqean initial velocity of 21.7 m/s at an angle of $24.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang67 )pz5 textcsy5bsj:1 j:i ojle 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 horizontnvkdxb*ab0 yy/r +8 8nally at 25.2 $m/s$ from the roof of a building 59.0 $m$ 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 ferlq4+y2kdh/ p xz6c-rom ground level with an initial speed of 45.0 m/s at an anglkpc d/r el4z 6q2h+x-ye of $46.6^{\circ}$ 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 run a 1500-m race at a vqdnlw)8pgfqhs0jb)l*d q(2 ( elocity of 4.0 m/s. If you ran the same race on a day when you had a constq (qlfqp2sb(0)j h 8dlgwnd)*ant 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 iyizgwcb u p)r9 -,/q1w8p9 aqm/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative gw-p1q98b 9i zpraq,/)u iyc wto the ground is

  A plane is flying due Soun9. iyf;zb3g ra;u0ueth ($270^{\circ}$) 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 v.u 2ocj(rf*i2 : wocsis 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 projectilel:gti.f ,r0hw2ja83 et 0lhpv2xib : w with speed 50.0 m/s in a forward direction hte .lliwf3v,pt b wxh2:8:g0ia20rj$30.0^{\circ}$ 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/sm.phcw(cl(d nikx:p/k;p6 .i j1 (im m, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it croshj:( ;c6imp m.wkm 1(i /lxicknp.pd(ses the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trsj )/o6ryibvkyd2 b- ,r2 rox6avel directly across a river 1.6 km wide in which the current 2br) kr oo6bd ysr,v6- i2xjy/flows at 3.4 m/s. How long will it take to cross the river?

  The driver of a motorboal 0/uxk: yvhwacn(0*vt 37jr l)k+wmk t that can move at 10 m/s in still water wishes to travel directly across a narrow strait in0tw l: 0+vxju 7h)rv kk mkly/3a(n*cw which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reac k.o2zk.a q,sfxx.8a uhes the opposite bank in 6 min 40 s. She is swept downst2skxu8ko.aq za..f , xream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m p3 w srh bew82ctl de.+mn -0c/63)rhqchxd)xwide reaches the opposite bank in 6 min 40 s. She is swept downstch - xn)rw8 c2bh63 r q0/de+e.pwxht l3c)dmsream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.17 m/s, must aim up+o jkof; gi577:g8uut*3 - +ljb -jjfkb ivmlkstream at an angle oflik8*f+3fblj 7uogb:t ;j uj + 75--mko gvkij $26.8^{\circ}$ (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)  $m/s$