Which one of the following is an example ofpb9:o5fsqy 3w dw tm*: a vector quantity?

  Which of the following operations will not cha :eg6g i94xdnm g00wpjnge a vector?

  Which of the following is an accurate sta ev5k)3:xao oa8gb(lotement?

  The resultant of two vectors is the smaoe2wdfm 5+iz -llest when the angle between them is

  Two displacement vectors h9;vkri i*hb, eave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, thvie* , ih;rbk9e magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of th4fwgb4qtdv9pmkjg b i2t-,gq(ap 22 * e following is a possible answer for the magnitude of the reskdqg (a-qgw42bifp *gtb4jm,9 2v2t pultant?

  Three forces, each having phozus60 )fi7 a magnitude of 30 N, pull on an object in directions that as7ih 6pf0uzo)re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown; hn+j/fgco rfx2c3ppj g2r/+ vector is

  Ignoring air resistance, the horizontal componenxhpd. qr266wv,qa kwdb4i;y) t of a projectile's velocity

  A ball is thrown with a velocity of kltg9 w2w1xj :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 oqs1 *( 0wqpafod 5ncr /i ;ogi4zhyh,9f a projectile's accelerationoqg0(, *da4 5 ri psq91fnho/cziw;yh

  A soccer ball is kicked with 2viwpfg2 st0rcn)63r mknj 98 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 object q( hl;vywr.eq.5 h6kl is directed anti-parallel to the velocity (lqh5qe y. ;vhkwrl6.vector,

  If the acceleration of an object is always direcn6u*k6tp2 mqr) kkg6 pted perpendicular to its velocity,*m u66kkkp6qtpr) gn2

  At what angle should a water-gun be aimed in order for the water to land wit:uok uc7y9zw;0 mzj*;a s3 ;wxvqneu:h the greatest horizontal x 9z0q3ko:uuac nwv:w;y s; ez7*j;umrange?

  An Olympic athlete throws a javelin at four different angles above the horizonta:s;4rh jq8*(bf/ y etawi6nhe l, each with the sh6 byie(4:*;hsqw nefar8t/ jame 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 ba mmfaa(g9c7i6b k65hrll for the second time. If the ball leaves your hand with twicegfhr c a66m9(7 kim5ba the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 mdrphgfw2) xj4-y h*4 r/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 maximum height, hofx47op gi:6)vq3lbj) m2 al gjw does its speed compare tjllgb :f6oxi 3jv)ap7 4mg q2)o its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a balf pp v :x0wj7l(dw9b-4kot *wil is dropped vertically. Which object iso97tpwxl0-v*4 j:f (bdwkwip traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet i+f q/j+:hjur/vpkebd9km 2m9 s dropped from the same height. Ignore air resistance. Compare the times of fall of the two bullfm9pe/qrubhmj +:/k 9d2 jv+ kets.

  A plane flying horizontally at +es*e:f p;ejxs4(r fga speed of 54.3 m/s and at an elevation of 136 m drops a package. 6.9 seconds later it drops a second package. How far apart will the two packages land*p4:e+ssfeg fj(; e xr on the ground?

  A package of supplies is dropped from a plane, and ox +m(/ tjd4xdsne second later a second package is dropped. Neglecting air resistance, the distance between jd/+4xsmx t d(the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a+eqr.pytfi 2 b/cw0x7 constant speed. Neglecting air resistance, when the bomb hit/ erbp7t+f2i.y c0xwq s the ground the horizontal location of the plane will

  The acceleration of gravi(d.2nn/lqu mwzu9k :u ty on the Moon is only one-sixth of that on Earth. If you hit a basqz lm(:nk9u d.nu/wu2eball on the Moon with 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, level road ar0x-d ouq 1xlbv3st *1nd pass a car traveling at 45 mi/h. The relaxl b0d u1- q13xorsv*ttive velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong currentw)-c: kf9 lhfr. You start out in your motorboat on the east bank desiring tr)f-w lk: ch9fo reach 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 times1li ui(a y8ts(8c e,v will it take you to move 12 km downstream, in a riv(sv(8y e ,csltai18uier flowing at 6.0 km/h?

  Vector A has magnitude 8mx:nf- jd- y 8;xyszyn h6+7vqe1.tmk.0 m at an angle of 30 degrees below the +x axis. The y qyny + e1h6 8f x:.k-j7y;mtn -xdmszvcomponent of A is

  If a ball is thrown wqr1dbgb 581;p7pnho gith a 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 east ani+u,jerb6)u9wk6 xw h d you end up 2.0 km north and several kilometers ea hxi9k6 wbjw)6ru e,+ust. How many degrees north of east have you walked?

  A butterfly moves with a speed .a5bzhln:4:9xntrk5wuud 5 wd8d;gnof 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of i;rd :w wlzdkd:hu 9nu. t8455 nxbna5gts motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what aeel l8 c1oir+k1gf4h(4-lfbua (ay )kngle is the Sun elevated abou4ye+fgofik1ce llar8)(khb(a -4l 1 ve the horizon?

  Two vectors A and B have components (0, 1) and (-1, :5j6-e ka6ev8iy w,o , rhrwoo3), respectively. What are the components of the sum of these eyvww6rk o6ir: -j58 e o,ho,atwo vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.vthfv 61a8c* u s, 5wzb83uzehdm* mr; What is mawf38c*aesvum dh,*1 rv tbzh ;z65m u8gnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, vi1(w rieq5* *qj ,z3lg egp(m0). Vector C = A + B . What is the magnitude of *ev e ji(qlig1 qwrg p*35m(,zC ?

  A car travels 20 km West, then 20 km South. What is the magnitude of itv fsz0qfrzew57mv 0 *0s displacem0vfrs0zzq0*5 f v e7wment?

  Three vectors, expressed in Cartesian coordinates, ax rbo-)r5r7b bre
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 coor5)sx( *k wxfpdv6(ibk dinates, 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 = (+3.0,55r fy 80:wvc8 jjcrcw -8.0), what is the magnitude of vector C = Afw85rc5j:0 w8cryv jc - B ?

  A runner runs halfway around a circular path of radius 10 m.kzeect g-.+6e What is the displacement ofztk+6g e- e.ce the jogger?

  Two forces are acting on an object as shown in Fig. below. W+*jcbl;(v :sfkl: bbh6 p 6dq8sgkzj;hat is the magnitude of the resultant for* pjfzgc j;68kb;:(llhs+:skqb 6bvdce?

  Two forces are acting on an object as shown in Fig. nz td5lel76zu3x*tt /below. What is the direction of thtd *ztlunx5e7 t36/ zle resultant force?

  Vector A is 5.6 cm long and points+gtcaboez:+ :.- l23uhrul d q along the positive x axis. Vector B is 6.5 cm long+.u rqz clahl-2 o:3+udb:teg and points at $+40^{\circ}$ 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 50 cm long an-qq+ f7 kb5x gs 0 sr(sd+smqhh/a.*ukd points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 32 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 wijxn (qh-,mrbi8dkm5.i6 hp yc/ u/v6 gth an initial speed of 29 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cli 6(,jnmdx6-y h. 8h5 /gcp ibumik/qrvff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity vbng m :m(p0yx)dk8)j3 o ccjv9g9 h;;e6mxl mof 5 m/s, from a bridge. It falls 14 m to the water below. How far doenvb8cjk)mh; (ojy g m09 ;m g3x9cpe:d6xlvm)s the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 18u:ar loho4- c2 m above the ground, strikes the ground after traveling horizontally a distance of 15 m. lc2uoa4 :-ro hWith what speed was it thrown?

  A jumper in the long-jumpzt/ z*znzn3,v onu c+* goes into the jump with a speed of 12 m/s at an angle o ,z*ntzn +o*uz/czvn3f $20^{\circ}$ 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 j )5j n;x56einh-g fxbgump with a speed of 9 m/s at an angle oxx ghgje;nfb5 5n-6i )f $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity lwj5wk +np k ):yy*mp9 r..psxof 46.3 m/s at an angle of $34.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an sdo (-m(rj*3zy8ld qfinitial velocity of 54.4 m/s at an angle of $27.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at (i)ingq oml/h)6e i .gan 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 horizontall 1; +2q+joti5xv k juyy0vfoe5y at 26.5 $m/s$ from the roof of a building 32.5 $m$ 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 levelshem2(v -ej4d with an initial speed of 43.2 m/s at an angle of vjshe2e d 4m(-$47.9^{\circ}$ 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 windoa8p w6fjsx5ly8x qvf;- o 58r), you can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows yoo pf f86owalr -85j xvx;5q8ysur 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/nkhuxe8 :* cb;n; fk-ws due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to thekh8fu :;e;wx-k cn*n b ground is

  A plane is flying due S xtn 3y6j+ssmh+3,kg touth ($270^{\circ}$) 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 headed qf5: z 0 kmot1 ,mmd001fuowcl$30.0^{\circ}$ 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 horizontas f my72* ua:qtv7ju.plly fires a projectile with speed 50.0 m/s in a forward directvt:7* uju. qf7p msa2yion $30.0^{\circ}$ 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 aci5-2d8 z-8eiy afpyh iross a river with a current of 6.0 m/s. What is the speed of the boat as it crossyi a fy8 zh8e-d-p2ii5es the river?

  The driver of a motorboat that can move at 14 m/s in still wag 6t* , z,a9;j fq)+ aucq((r)wyorz r7sefugjter wishes to travel directly across a river 0.7 km wide in which the curren,c+s9g ;wqf7o(ery r (j aq )tua6z,zru)gj*ft flows at 6.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in rj.yy :yav*n;still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver heajy; y.nr:v ay*d the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppos7 j),k sreoiere:8k b:4n o/nhite bank in 6 min 40 s. She is swept downstre4k)7,k8ei/oj:o : hnbresern am 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposd/kwb2 :7bi otq)bf (4kmn )giite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the curknmfqd47wotk( :ib g/2b i)b) rent?

  A boat, whose speed in /i f 5 vd6um-xmvkn4ixez(u4 1still water is 1.45 m/s, must aim upstream at an angle of /u4enku d(im5 61zxv ivm4-fx$16.1^{\circ}$ (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)  $m/s$