Which one of the following is an example of a vector quantity?yrhcz+3 y m+z/o6tu slgp,d:6

  Which of the following operations will 8q36fin6y; ux+ 3 :rmgaxauhyyc+ w (rnot change a vector?

  Which of the following is an accura /p)me-c(b5aqaux e s.te statement?

  The resultant of two vectors is the smallest when the angle between th aoybq0353.ar g/rh pbem is

  Two displacement vectors have magnitudes of 5.0 m andwo+f(zjcj w o ,0x;/lr 7.0 m, respectively. When tj+,z cx rw;o0ofj l(/whese two vectors are added, the magnitude of the sum

  Two vectors, of magnitu3iv8ipov4n; k1sq 93j sdmc.ydes 20 and 50, are added. Which one of the following is a poskn.mq 3ii4d981c3s jsy ;povv sible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, p0 hdeo.(.*dso nz c*bsull on an object in directions thanzsoeh dc*( *0.bd.s ot are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown3,hkk -:7a2 lgpn(9aljsx16iqg j; h:t stt tx, the unknown vector is

  Ignoring air resistance, the horizontal component o . mhhw w;;itg4 t;scui*f .iq7-bt9urf a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle 3.6uzn,/3hlhj cap)gy( qjz hof $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistaq/u8 ibu-lb s0bw5tn6+s+-f dhro pg/nce, the horizontal component of a projectile's accelerationub8h6-d/qu- n0rl tb /+sw+obi fs5gp

  A soccer ball is kicked with a velocity of 25 m/s at an angle ofehz e9d;jt(z1 f5tpy21 .x0cf /juko l $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of ane6mnz o)k/++8i) v tkzm4tvnv5w- uzc object is directed anti-parallel to the velocity vectwz+it6z+ v 5vm)k 8- ezvtuc)nomk4n/or,

  If the acceleration of an object is all:5 oby.g/q+qzdvmk7*z f7 zeways directed perpendicular to its velocity,*m /z. qkq:fdl e5v bz7y+7goz

  At what angle should a water-gun beih*qv:-8 bu dz85 1htb8od kxt aimed in order for the water to land with the greatest horizontal r18i*hv8hd-zb8ut qb x otkd5 :ange?

  An Olympic athlete throws a javelin at four difq. i vi-5e0iolferent angles above the horizontal, each with th0eq. 5ili vio-e 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. If the ball leaz922dsrog kh 5a bg52pves your hand with twice the velocity it had on your first throw, its horizontal range R d k2o22g95zparbh 5sg(compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an anmwx7rq:lhh8oj 7xhfb59 1 zl1gle 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 maximum hei fh3fzl9j1.u kght, how does its speed compare to its initial1z .9l fufhj3k speed?

  A stone is thrown horizontally from the top of a tower at the samexem 3hwyjx ; 3bq;0uycjj6(e* instant a ball is dropped vertically. Which object i(qebjj6 m*y 3 ;0hyjw3xuc xe;s traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and a h *e,jvveh*,pt the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of th veph ej*v,*,he two bullets.

  A plane flying horizontally at a speed of 110.4 m/s xzc,a x5hgm s0+ x6y,rand at an elevation of 238 m drops a package. 3.7 seconds later it drops a second package. How far apart will the two packages land on the g,,ar5 x0+gy6 xmszc hxround?

  A package of supplies is dropped from a plane, andtxti0 :b-v0sks 55vuk one second later a second package is dropped. N0v0 s bx:ks5-tuvit5keglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant sp)yi+v;j5f(; zbyp ep peed. Neglect +zpye p)jf5yp; b(i;ving 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 ,/vaim*yk j uifpc,+ u6w)ts;that on Earth. If you hit a baseball on the Moon with the samjp , ay+m/uvw *ifu;,6 stc)kie 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 relative to a straight, level6nni qnj. 2;nn road a2nqnn6 njn.; ind 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 r n u 67bm pvm8+e.dl/;ghcz9zkiver that flows due south with a strong current. You start out in your motorboat on 6d7ekz.pc;zbv m9 +m /gun hl8the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move ab)w.m2roqyrphl vu f v .6f1;,t 30 km/h in still water. How much time will it take you to mo, v6)q mrpfh;fo. bwy2ulrv.1ve 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 the ml(l*hd.-o mk +x axis. The y component ool(md .klh* -mf A is

  If a ball is thrown with afvdt49(c894b:pcrtv l1*ruyc9 yp gb 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 ey uhg59ii71uhuf 4s be9l9s 8tast and you end up 2.0 km north and seve shsilu u94eu5b79gfi9h yt1 8ral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component tu8cxq;9 f -frof its velocity is 8.00 m/s. The angle between the f 8qu ;rft9-cxdirection of its motion and the x axis must be

  A 400-m tall tower casts a 600-m yn2-hd(r t al3f6s,up long shadow over a level ground. At what angle is the Sun elevate-(ynpr,l2thfu6a s3dd above the horizon?

  Two vectors A and B have comn)rfrqfd fsb5lq nnb 008*-c2ponents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two ve0csd*28rf nq5r-nlfq 0f)bnb ctors?

  Two vectors A and B have components .5f(gy6amm a352jsquqnn rs +(0, 1) and (-1, 3), respectively. What is magnrqy s.sn5qmf6j2m +ng53au a (itude of the sum of these two vectors?

  Vector A = (1, 3). Veczx sax- :p)z4ftor B = (3, 0). Vector C = A + B . What is the magnitude ofp-zxa x:z4 sf) C ?

  A car travels 20 km West, then 20 km South. What i)/ y3m kebv2a9d)jxfh s the magnitude of its displaceme3a2)kvy xbjd 9me/ f)hnt?

  Three vectors, expressed in Cartesian coorn*3k;nbd8q 4ndlj*svdinates, 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 c.q1b1qfcj i 6i uu:2vnk- 1rkjoordinates, 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 isi5i ;p .roh.tau5 (ayrfdy 00i the magnitude of veciyu rta5;y. i 0(0ofa5.dih rptor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m.7 zqhhp*nc+h k)u ,:ny What is the displacy7, kh*hc+ un zh):qnpement of the jogger?

  Two forces are acting on an object as shown in Fig. i2 +ab5vxwupcb5 qio85x64le fysk r1qa-w-7below. What is the magnitude of the resultant forcoiy+au 2sw i4x -5cwkqx 5lfp8-b7aqe56r 1vbe?

  Two forces are acting on c8zf9 zv67eov an object as shown in Fig. below. What is the direction of th zevvz879 c6ofe resultant force?

  Vector A is 4.8 cm l6jw4:p7tx0y3m x3,zav m tqs song and points along the positive x axis. Vector B is 5.3 cm long and points at mtmq3p 60xxz7t4,ys 3a wsj:v $+32^{\circ}$ 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 67 cm lou1g to,lz9ew1z euc,rzr c0 95ng and points at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 27 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 17 muefo z wno 2.+g.b3op2/s from the edge of a cliff. A stop bfp .gz3o.o2nw+2o eu watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 1rpc2hx /nf ,c-6yv o:t0 m/s, from a bridge. It falls 22 m to the water below. How far does the roct2,vnfh/coypc6-: r xk travel horizontally before striking the water?

  A ball thrown horizo/4brzhaz2 xs42y5oy 0b waad- kb39hbntally from a point 23 m above the ground, strikes the ground afterz x/92w4basdyha40kb3 hrbb-o z2a 5y traveling horizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/so rmpr80 gf8z2;lh-a0qx:vb .m qg+ hu at an angle oqr2;+p- m xomz88hqubg v .0rgf0:alhf $20^{\circ}$ 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 w1 ng w*13tf pbvy1 uiidrb.6hpd4 r(b2ith a speed of 12 m/s at an angle of v6rr3n fppdy ihtd 4b g11.*( iub12wb$35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with 0whqe(f +xa gq kb)6/qan initial velocity of 45.6 m/s at an angle of $46.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 39.9 m/sa:mayt -g2 /px at an angle of $10.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angs iia8eq /0ls- /+corhle 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 horizvr: 07d4yi),mau (qi19 q) k s-genddigb-ijrontally at 21.9 $m/s$ from the roof of a building 39.8 $m$ 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 65.5 m/s at ans)a89a p (ndnd angle nsaa(p dd8 9n)of $41.8^{\circ}$ 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 veloci9p2o:z ,lndq ce);xx6rhoq . ltk-tc1ty of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your t6 k)-l x 2, px;qtc1odqhlc:n.9ro zespeed 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 due North, and is in a wind of 50.0 6b9yba0y 2oysm/s to the West. The plane's spe6obsayy y9b02ed relative to the ground is

  A plane is flying due Sw+jefm8(2b c2uh .ukyouth ($270^{\circ}$) 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 )/qunfhv22mkqaeb7 7 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 horizontallurke*n: dkfoi:y z, ..y fires a projectile with speed 50.0 m/s in a forward direcr .d:efonky uk.i,*: ztion $30.0^{\circ}$ 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 diz2 mhii l1x *cs8qm72crected across a river with a current of 6 *8qcsm1z 7x m22iihcl.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 8 m/s in stil9-s ,xu d5bhudl water wishes to travel directly across a river 1.5 km wide in whsx,b d 5uu9-dhich the current flows at 7.4 m/s. How long will it take to cross the river?

  The driver of a motorboat thab1 c 8fv/qc3)s q;dpwqmxt5 n2t can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. vd5)sp/m ;qwq fcbct 1q28n3x At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reachej87g g-;vy.pgqr xju( s the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wate8y.up7j-g;gvr (qgj xr?

  A swimmer heading directly acro0uy7x4u k bfg;om z f4l2m/r1pss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 4 /7l41uyx frf;zbu0km2gm po480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.08 m/s, must aim upstreajm1cyyd5z65b m at an angle of c61j5ymd5 zby $23.8^{\circ}$ (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)  $m/s$