Which one of the followi3t5 l c- 1xonpvusb1t*ng is an example of a vector quantity?

  Which of the followit9i4qx r55uoc ub(ax 8ng operations will not change a vector?

  Which of the following is an ad3enj/1io7i okw-tl, ccurate statement?

  The resultant of two vectors is the smcf4,9yidq qb;cahz; .allest when the angle between them is

  Two displacement vectors have mag7eb* v(fyce0wno -+tynitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitud7yne(y+ tbc0e - v*wofe of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followii cqga3n m(g8j;x(c f)e,haw, ng is a possible answer for the magni,a(w jec mf,hncg 3qai; )x(8gtude of the resultant?

  Three forces, each havin ) 9yhe/6 ht1h4vuf-gwodjrdps sd;46g a magnitude of 30 N, pull on an object in directions that are u ; 6dh1w rdh jsf/tdyph9)o4v-se46g$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector isbrn4j7 4chyl bl5.c;k

  Ignoring air resistance, the horizontal comfk7x2oj78v9o n)cra4b n rer.ponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an a pk2ey0iu,jj /ngle 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 y (f 9v. u2xjilko md5pa*a52xot48wz)euf0lhorizontal component of a projectile's accelerationjf8 ivot52wkoxl2m 9u(a5x4ul yea 0) pd *z.f

  A soccer ball is kicked gc7n79 ln oxq4with 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 v;*cbp,u8 a2 0n7 tplup gr9bbwector of an object is directed anti-parallel to the velocity vectorpc;8ln, bpu9 au *wtrg2 bbp07,

  If the acceleration of an object is alwaysy 6penq2tfh/j,w7 ht2.onv a7 directed perpendicular to its velocityhnq7 h ,jwa2v 2 n67.po/yetft,

  At what angle should a water-gun be aimed in order for the water to la:rnd bu6 s+srubj,hrbm(q65 5 nd with the gm+ r6sb:u(dus5h r6rbqbj n5, reatest horizontal range?

  An Olympic athlete throws a javelin at four dif:h5gnt ln1rx8qljenx; ).jg( o90z etferent angles above the horizontal, eaz.j:q8x (0jt9l; 51l ogee ngn)x nthrch 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 2 ofs:oe6rb1t for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would bsebr6f 2o:t 1oe

  A ball is thrown at an original speed of 8.0 m/s at an angajx tsz/uy*yl2 be.) f2*wbfbi 5bn* -le 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 fiel-.4/kqr kyspb u. :qnxd goal attempt reaches its maximum height, how does its speed cok 4ru-/qxkp. :q n.ybsmpare to its initial speed?

  A stone is thrown horizontally from the topp5c0u3t;g ttqid8 mr,gvn)2c of a tower at the same instant a ball is dropped vertically. Which object is travelqtpg02t8g,;nvd)rcu m cti 5 3ing faster when it hits the level ground below?

  A bullet is fired horizontally, and atmut+ybr a :6iuw65fe5 the same instant a second bullet is dropped from the same height. Ignore air resistance. Comparu am:65t +5 ri6bewufye the times of fall of the two bullets.

  A plane flying horizontally at a speed of 71.8 m/s and atvgvj4y j(/hz w-lhk,: an elevation of 132 m drops a package. 6.4 seconds later it drops a second package. How fa :(vgjwjv-yzhh /k,4 lr apart will the two packages land on the ground?

  A package of supplies is i e1 kd6v4j2f40ky zlq/)zzbtdropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance betweenf b4ke1 l)4z zqk0iyv/6dz2tj the falling packages will

  A pilot drops a bomb from 3qz +1)rlhmdt h107i ; ufvazc:m3kmka plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal loih1zf 73z;1 mr3ahml+:ckt q)ukmd0 vcation of the plane will

  The acceleration of gravity on the .n) v6fc nft+/ flm8wnMoon 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 wou/ n8+ 6cwn.ftfm)flvn ld on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, levew)y.ieqgzgw r-x+q3 yk ua ;4,l road and pass a car traveling ayg.qg rie qau- + xk)ww3,y;z4t 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows kxb+nyc 7j2j sfa (.db(uo9,qo- xs 0cdue south with a strong current. You start out in your motorboat on the east bank desiring to reach th2c axdn-s.jcuxf(0b ksoq(9by7o, j+e west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still-tce6weawu /. water. How much time will it take yot6 u.w c-ae/ewu to move 12 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 th8gs+oeztl 6xii 7 xm6 pxy7.7de +x axis. The y component ofx7gi+ z dly76oe8xmpsit .7x6 A is

  If a ball is thrown with a velocity of 25 m/s at an ang/tu,kep/5 m)-te- jw qjhu,)t 2qs3 lb 0jbgbgle 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 o v9j8gazpbh7x+mb 823 od*n ijf east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you w m7oa8jd* jb9pvbniz8 32gxh+alked?

  A butterfly moves with a speed of 12.jgup1 u8y+d,z3 *v ajp0 m/s. The x component of its velocity is 8.00 m/s.z3uvd* g8,+yjjpu1 ap The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m locmqgxei:vcy*,xd/j+ j- )p /ong shadow over a level ground. At what angle ixy )x-e ojc, jgcm/vq+pd:*/is the Sun elevated above the horizon?

  Two vectors A and B have componzl3,jy6y jh i;ents (0, 1) and (-1, 3), respectively. What are the components of the sum oz jjh,36ylyi; f these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What ) wkkzhknon29hdmjb.4 m (w(d /8hd+ vis magnitude o9 h(/dndh mz2m4hb8ww. kvo+ jn kdk()f the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . 6ir7d 4ppba t2What is the magnitude of p7dtp ba6 24riC ?

  A car travels 20 km West, t:sceh5ms*a k ti 0.e.zhen 20 km South. What is the magnitude of its displaceahet0ms k. .*z: sc5eiment?

  Three vectors, expressed in u,zsv. vr:dkv0mew0 8 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 Cartesian coordinad, ac 7m(4gp2:fc8 hqthoh xy,tes, 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 vect 2 ;hx)z* dt(n00 1buo , mj7rdywati,of)wnsbor B = (+3.0, -8.0), what is the magnitude of vector 0ni7 a0stjx ;,)todh )oubnzy21,bm *(rdwwfC = A - B ?

  A runner runs halfwayb7xjj .oi, 2s*tf i/on around a circular path of radius 10 m. What is the displaceme ,b/ i*i.nxst2o7jjfont of the jogger?

  Two forces are acting on an objectylynkp8a6(i:y*:.yfy+ znjipz h gdi tj 423) as shown in Fig. below. What is the magnitude of the resultant f(iiplh: jityny46dn8* fyza.) 3pyy j+ zgk2:orce?

  Two forces are acting on an obj0vd5 3 gfzn(xuect as shown in Fig. below. What is the direction of the resultant force vd0nx5ufzg (3?

  Vector A is 3.9 cm long and points along the posi+u 8nw3gmk8p qb ia9p0tive x axis. Vector B is 9.3 cm loga+pipu 988q0mwk n3 bng and points at $+57^{\circ}$ 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 90 cm long and points at cj-bt8r n-an xi7;gn5 $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 33 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 12 m/s from thvbt, 6t-at/pk e edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.8 s. -a/tb6 ,t pvktWhat is the height of the cliff?

  A girl throws a rock horizontss2dtb0b 0f )v* 2ubwask i693otz bxyz p26)yally, with a velocity of 18 m/s, from a bridge. It falls 23 m to the water below. How far does the rock travel horizontally )b)6iv 22*z ks3 6zs sxb9byta d2u0by0powftbefore striking the water?

  A ball thrown horizontally from a point 22 m above yg;zd mzx/+iq5r-dcw+a4ay , the ground, strikes the ground after traveling horizontally a distance of 16 m. With what speed was it thro+qga-m za rd y/x c5zyw,+4d;iwn?

  A jumper in the long-jump goes into the jump dfa96/k h5lxuwith a speed of 12 m/s at an angle dkf 9/u lax65hof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes int 42:qoa2mwhhf2cb.9 viw dt)do the jump with a speed of 11 m/s at an angle of v :2.om2b4iwwqf9 h hd2t acd)$31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velo7h+:0wo k*mj e:a dutacity of 51.1 m/s at an angle of $30.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloc g7jf1 4 k,(m:1uen ajk,rjmnvity of 45.1 m/s at an angle of $42.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired:fosf u 6pn;:o,r5i 6 do)dmmf3xxw9 n at an 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 horizontally j2 tf n nrwccbl9(k 99u(i2:soat 22.1 $m/s$ from the roof of a building 59.1 $m$ 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 1 +msa, a6zfz*z(fe1wk;hg cuwith an initial speed of 49.3 m/s at an angl(hw gz6+1z ffsm1aa c,ez;uk *e of $46.8^{\circ}$ 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 at a velocity of gwbvmm b1en3a7e+ w16jv16g s4.0 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 time g3 1vwm6en7jvegw6m1sba +1b it would take you to finish would be

  A plane has an air speed of 200 m/s due North,f (a ,n3g4dv29 n)n(oay3my+ bvmhkz*j(ltnd and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground is la (v*,3d4(vnkyhmfn3mo2nna+ )bg jy(zdt9

  A plane is flying due Sowl-9seaom1 6u uth ($270^{\circ}$) 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 spee*,n5 j6 ab 5,qzt rgdeism07zld of 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 200 m/s horizontally fires a projectile with spe6;h)be62ys )qhwdcxied 50.0 m/s in a forward direction ib )h)6 eh2cw dqys;x6$30.0^{\circ}$ 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 ac5mi2br4ql exg46,px5goof :i ross a river with a current of 6.0 m/s. What is the speed of the boat as it 6qfbmi5g,4o p xxer4g2l5:i ocrosses the river?

  The driver of a motorboat that can move at 16 m/s in still water wishes to trav ;dx,x erl:t2(rhg.beb(ee.cel directly across a river 1.8 km wide in which the current flows at 7.6 m/s. How long will it take to crosebeder,.c l x. 2;gb(t(rhxe:s the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trt.on0a iu37ncmy7r4 gavel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head th c3i yr0.aogutnnm747e boat?

  A swimmer heading directly across a river 200 m wide reaches thh +y26x7/qgenq t)wmk+ay m+u e opposite bank in 6 y nx/)hgkmmq++6a q72ue yw+t 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 z 6lp(8kaslhh3j8 9c bwide reaches the opposite bank is 83(hlzjhb9 alck6p8n 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.67 m/s, must aim upstream at a12 jc:x o+ guukhi) /if*plte.n angle of l/gte*c+)k:2 h ojuxuf i.ip1$18.5^{\circ}$ (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)  $m/s$