Which one of the foll00p m4 w1luy0pj ihnr6owing is an example of a vector quantity?

  Which of the following operations wi8r,wr.et so,h (a th;ill not change a vector?

  Which of the following is an/)au bx,zo;lw ;9ic lh.wxs6o accurate statement?

  The resultant of two vectors is the smallest qw +s +k25xlqwwhen the angle between them is

  Two displacement vec3hhwv4 ifz8h )gyb4-p,g o g:etors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of zhvhwi)e:,4 y g-8gghfp3bo 4 the sum

  Two vectors, of magnitudes 20 and 50, are c0gm /l.t k,etqtcu)6 added. Which one of the following is a possible answer for the magtl q)t 0cuet/gk.6 cm,nitude of the resultant?

  Three forces, each hap5ny e67h5(ahcmlbr/r5zd mw d10) vpving a magnitude of 30 N, pull on an object in directions th6bvp m(n7hr1 ldw5hep)a ym/50cr 5zdat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thee, b);z f)fzgu unknown vector is

  Ignoring air resistance, the 7aoz0,1rb tjuxj gcmf44/z i4 horizontal component of a projectile's velocity

  A ball is thrown witwjn,5 p9c y: r5ulb3uh ul-)tch a velocity of 20 m/s 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 component of a projectile'tbdx* g) 4iy2obp zb)+s accelerationtxyo4 )bdbi2 *+gb)pz

  A soccer ball is kickedg;veic1kw4;w ; pxqa/0.pmhs 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 ob :8sj5idp(btulhg8 f ;ject is directed anti-parallel to the velocity vi ;bltj d8 h:(spf85ugector,

  If the acceleration of an object is always directed perpendiculari+lt d:e ,qivt1ky*s, to its velocit1id ,tsyelti+:qv *,ky,

  At what angle should a water-gun be aimed in order for the water to land zwkbcv6q5n(hb o t 8c35c.rdt(6tg)dwith the greatest horizontac6z tb5)g bvcwtt5. 3o6 d(hrq( 8cndkl range?

  An Olympic athlete throws a javelin at four different angles abovracalm/grblp y 4(.* 5e the horizontal, each wi cba5g(lra.*y4 /rpm lth 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. If the ball ledlz06f -(ilil aves your hand with twice the velocity it had on your fll-lif0(i dz 6irst throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an origiz+y z*a q2gcm/nal 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 i4opix582o zcq ts maximum height, how does its speed compare to82xpz45q c ooi its initial speed?

  A stone is thrown ho- hhttebp)d0s-*su+w rizontally from the top of a tower at the same instant a ball is dropped vertically. Which oth+et)0d h pw*s--b usbject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bulqc9o qy3t* xc9q+v m/olet is dropped from the same height. Ignore air resistance. Compare the times ofq t cc q/v9xooy+9qm3* fall of the two bullets.

  A plane flying horizlggph scq31 78ontally at a speed of 78.2 m/s and at an elevation of 292 m drops a package. 5.8 seconds later it drops a second package. How far apart will the two packages land on thhp 8cqg7g l13se ground?

  A package of supplies is dropped from a plane, and one second later a second pac1 uwv /9opqnh*kage is dropped. Neglectih9 1/n*qpou vwng air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed.6nf6e5wu 8/ pqnxp) mx)l:azi Neglecting air resistance, when the bomb hits the ground the horizontal location lep xq /x56npfm6n8)z aiw:u) of the plane will

  The acceleration of gravity on the Moon is only one-sixth odcql f6 t,ci1-f that on Earth. If you hit a baseball on the Moon widl- c6qc, tif1th the same 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, o v6 wm(:xk/.b srnzy,level road and pass a car trav:mk b ry(.oz6xvn,/ wseling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows d-9q s5y3o hdcaue south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboatao- ys 3cd5q9h

  Your motorboat can move at 30 km/h in still water. How much time will601fq:l oaf,gq pyt * ay79kji it take yo1 ya,g*l:67q affityp qo09kju 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 the +x axis.assaut83e 8wjr82-yo The y compone32sjwse aay8out -8r8nt of A is

  If a ball is thrown with a velocity of 25 m/:l -zq *:3lzvm0nsmpdhbv ;g5s 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 direc8bhp;u/ rx9mis/ .lldtion north of east and you end up 2.0 km north and several kilometers east. How many degrees north of .;/msbr9 l xlhup/id8east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its va /yqb89)+upaqqrt svu9 ;wuu60 u7bi elocity is 8.00 m/s. The angle between the direction of its motion a) ;b9w9 0au7qyr qq8pibu+u6aus/utvnd the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At c( 0ya;5d3chg9crfdowhat angle is tgrh3dccc9o;f0 ya( 5dhe Sun elevated above the horizon?

  Two vectors A and B have components (0, zg,++*/r oxv,bw n mto1) and (-1, 3), respectively. What are the components of the sum of these two vectorsm+b+ ,xo g/*w vt,nroz?

  Two vectors A and B have components (0, 1) and (-1, 3), respe6hqlivl a: hhcc- ;:hgky.ip:zy9w 2+ctively. What is magnituvphc i:h ylhgikl :a q:c; h9z.2-6+ywde of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0t3my)p5dil8a ). Vector C = A + B . What is the magnitude of C p3ya)5d 8 mtil?

  A car travels 20 km West, then 20 km South. What is5h41(pdd4hcfqj (jro the magnitude of its displaceme45pd ho( d(q4rjcjf h1nt?

  Three vectors, expressed in Cartesian coordinates, arb+ ld:-2ctxbb)hlp;ksh b) e.e
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 Carts9 wxh-k,) txaesian 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 qzixi(24+kx* z wim0pzud fldt ,-0w5 vector B = (+3.0, -8.0), what is the magnitude of vectoril45 0-q+wzid kz ,umxzx0d *(pi2 ftw C = A - B ?

  A runner runs halfway aro5n5 s r one:fv3hy 3th6ke+wp,und a circular path of radius 10 m. What is the displacement of the :ev,3 row35fn h+ s6hkpt5neyjogger?

  Two forces are acting on an object as shown in j28;rl gen(liFig. below. What is the magnitude of the resr (li8;e gl2njultant force?

  Two forces are acting;0 ufc 6rta hfk*o0pn9 on an object as shown in Fig. below. What is the direction of the resulta*6uo; 0fc0tpna r9k hfnt force?

  Vector A is 5.8 cm long and points along the positive x bg uibsdzqcs9c0/,;r 2 v8.eq rtz*z3axis. Vector B is 5.3 cm long andz g/uzi9q r*sc30b te r z2.q,c8bsdv; points at $+38^{\circ}$ 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 88 cm long and points ats8 s21dr(0jvg1qn4rqi(rkhp x;iwc2 $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 44 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 od-vqj 1zdv(yl2ga9bj p . ow3;;y2le jf 23 m/s from the edge of a cliff. A stop watchjyvj;;( b9lad e.13jlzvgod q2p yw2- measures the stone's trajectory time from the top of the cliff to the bottom to be 2.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, froeol;)0sj gqm 0m a bridge. It falls 21 m to the water below. How far does the rock tr 0qg 0;esjol)mavel horizontally before striking the water?

  A ball thrown horizontally from a point 30 m above the ground, stri: ag8iq f7m.qb 3+rmgha s fx3u8f,1pkkes the ground after traveling horizontally a distance of 19 m. With what speed was i,hpqfi3ur8fa 3 .:g7 f sm1kg+b8aqxmt thrown?

  A jumper in the long-jump goes inte;.oe6)+ woiibsb (vdo the jump with a speed of 12 m/s at an angle o (ewoesii) +v ;.db6bof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump q ;9mi9pe+ d0aqik8a 3 hhkp1lgoes into the jump with a speed of 13 m/s at an angle of e p qm3k89;1i9+ailphh0 qakd$32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velm/i69nw rq2 nz 9:frvd:yv*xf ocity of 37.6 m/s at an angle of $39.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with q94:a bdx 7ycfdf-hh3 an initial velocity of 33.8 m/s at an angle of $18.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofhb2 3a3j /fwcr $30^{\circ}$ 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 horizonta2c) ny8d ns.kjpz-0g hsb9t k-lly at 22.5 $m/s$ from the roof of a building 59.9 $m$ 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 spehz 8u6 aqt2:hae;dd 5qlop1td;k5 n;bonjg9 ,ed of 54.6 m/s at an angle ofq 5h8b;pad1zn9tano 2gd u tj; ;h,q5o6e: kld $38.1^{\circ}$ 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 oyki*bq; m,e9mp c qjo,y 0+af1i)(tma 1500-m race at a velocity of 4.0 m/s. If you ran the same race o c,b) o kqq,y tm 90fepmoia1*m(;j+iyn a 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 due wk*87dzp btc t3b15rsNorth, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground is7szcw5 1b3tktp 8db* r

  A plane is flying due b+a6(yz8;re1-orie j*f;1gleq aqqj 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 km/h is cf323 x2e j*zzxz:hfmheaded $30.0^{\circ}$ 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 horizonr2 )*ikmy (so qsgvoj0 ;7mt;htally fires a projectile with speed 50.0 m/s in as v7jqrg) mh0* m;;t2siooky( 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 k emyd27v1 7vtdirected across a river with a current of 6.0 v7yktd7evm 21 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 12 m/s in still water wishes to t(y729krm4mteaf9i x t1d4wil ravel directly across a river 1.9 km wide in which the ramkx2fl1t(ei my4d4t9i 9 7w current flows at 3.4 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 (7rbrs-au8 ld .zlw4dtravel directly acroz8rsa ur-(. wlld7bd 4ss 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 directlyypgy 4 e.2 (yzss.rm+e across 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 wateye+zr4 .sy ym(2 gps.er?

  A swimmer heading directly across a river 200 m wide reaches the opposi oahbam y095gdyc;.9f te bank in 6 min 40 s. She is s. om cd5hfg0 a9byya;9wept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.23 m/cbs4my 4z, pp7s, must aim upstream at an angle of 7p mzbycs,4p4 $15.1^{\circ}$ (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)  $m/s$