Which one of the followingf -+*c xwvbf,yofbuo*o; y 165hfp;r u is an example of a vector quantity?

  Which of the following operations wi0sm3ghg-wj/u5s bx e /ad3r3o.2y cazll not change a vector?

  Which of the following is an accurate statem xzpg)2+ hy:kfent?

  The resultant of two vectors is the smallest when the angle between them i+stkowww)t 6-s

  Two displacement vectors have magnitudes of 5.0 nu0y3ndo-g 8 -/1,ea ffcz nnmm and 7.0 m, respectively. When these two vectors are added, the magnitu-m,3 g/ ff a8o1n-d zennyn0ucde of the sum

  Two vectors, of magnitudes 20 and 50, are addydiwxbmm0 i /(7+ny:.eahgu8 gb) 3 kjed. Which one of the following is a possible answer for tbemb3a7h m.in) :yuy (xjg+kwi /g80dhe magnitude of the resultant?

  Three forces, each having a magnitude of 30 xuz*3*eb wmllpuu5b5kvf/ rm9b x., 7N, pull on an object in directions tha39*z w5ubvb,7l ukx*lpxe/5. u mfrmb t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the1tzr/z3jb- /mrjqtbek x()u ) unknown vector is

  Ignoring air resistance, the horizontal compdr2gp/e+m4 vj onent of a projectile's velocity

  A ball is thrown withc24;65ylm8 ewhlwraf 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's acceb xklxaib 0s3b(lxk0s s p-:6;hj56tblerationkbl3 6b lp6xbjsxs0b(hkti0ax;s 5:-

  A soccer ball is kicked with a velocity of 25 m/s a)1fn4d6grrh yblp /6jf;o a(yt 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 mif m*og/sq e)5c1wz9an object is directed anti-parallel to the velocity q ceswgm/im51*)9f oz vector,

  If the acceleration of an object is always directed perpzqfszc;2r xj ,7jeh8d* -,hj wendicular to its velocit-8hjs2,jzc; d j*q whf7 rxe,zy,

  At what angle should a water-gun be aimed in order for the water se;2jx+ 4 eafxto land with the greatest horizontalasexf; x4j 2+e range?

  An Olympic athlete throws a javelin at four different angles above th w mkgu(cq.9wz3 ygl.*e horizontal9*u .(3z.kwygw mclgq , each 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 for the second tj t.p4 ) 4y yfk;euuo7:;zaqsoime. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your firstjfy4:z) to7o sa;qukup;.ye 4 serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an ang pk3cz*e ko*,yle 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 gvsqt 99/ rcdbew90x*coal attempt reaches its maximum height, how does its speed compare to its 9s9cbx wvt *e/c90r dqinitial speed?

  A stone is thrown horizontally from the top of a tower at the sa b(qi3dy-qqrg/ / vc9ixg(uo:me instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground belowyiidq q-ug3x(o/:9gv /(qcbr ?

  A bullet is fired horizoq9a9ldl dw84ib0d 8ujntally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. qau8id49l0l 9j8d bwdCompare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 402al8qj:ej,o/ m;dewzaby cdqc:c 0 1).4 m/s and at an elevation of 180 m drops a package. 4.2 seconds later it drops a sec20czlwy d 8:aa),qc;o m1bq:j / djceeond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pacvaxlc7 / maf70kage is dl7 vxm/ 7cfa0aropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neglu,2 6vgt6 ynanectingn u6g2 yn,a6vt air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity ; 6h0n +gbuinsq6hq e(on the Moon 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) henh6; sgq +i u6q0(nbthat you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axispz-:ms pdn4x use t :j1ezb9-f r6,hp6 relative to a straight, level road and pass a car tra p6-4:pz ze- mthubx:6e9p1rsdj,n sfveling 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-erg . k.h7aje south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank ee.7kahgj .r -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 wi58u6t4x h/pp sxkgi9ibqg 8y+ll it take you to move 12 km downstream, in a rivepyx is69g+ ikp 8b5/8g4qxu htr flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 )ykic-q vq.;e degrees below the +x axis. The y componve)iq;y-qc .kent of A is

  If a ball is thrown with a veloci gw6v e5bw6bb,if+b l-ty 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 tu)+qarw:4l1)t ep 1tr(a hmn east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you walk1q+nt() :up 1 lrtwar4)a etmhed?

  A butterfly moves with a speed of 12.0 m/s. The x componenazhz;e)nx6vl : 9 /av a-irr5vt of its velocity is 8.00 m/s. 9z5 avl 6 rvnr)iaa-x/ hevz;: The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 60 xn((po h,jqwv:+cr8m0-m long shadow over a level ground. At what angle is the Sun elevated h ,cjp q+(rnw8 (xvom:above the horizon?

  Two vectors A and B have components (0, 1) and y nt+y/zekt6ue34o6v (-1, 3), respectively. What are the components of the st4z+ey/ et 6ukv3yn o6um of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), +ca7o5a 2jio1tjjv:)fs dcf j u08c+i respectively. What is magnitude of the sum of these two vecto++i:0djscj7j5au1 2j coc)i v8faoftrs?

  Vector A = (1, 3). Vk9kz.7vjz k1j ector B = (3, 0). Vector C = A + B . What is the magnitude of C ?9.z kzjj1k7v k

  A car travels 20 km West, then 20 kwfzzw9 +6 lde7m South. What is the magnitude of its displacemezfew9w7z6d+ l nt?

  Three vectors, expressed in Cartesian coordinates, arfva7 ;htfq9:agnscd( ag); ikbsi3)*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) m i(,z:nuvcd Cartesian 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), what is the magn ,e2eg3hgx)c0wr0hxvitude of vec0eh3e,0)xhvggwr 2xctor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the da9h-r c st9ppkdg,gt p0-(b(g isplacement of grbh-gcpsg -d(p 9 9 ,0pkt(atthe jogger?

  Two forces are acting on an object as shown)uh,d9 bz-ei h y-fnyvlo 9/z9 in Fig. below. What is the magnitude of the resultant force?9lezvio--zy9/ud)hfyb9h n ,

  Two forces are acting on an object as shown in Fig. below. p1z73ifyz2tcy 55cbeslh g( q:yi./q What is the direction ofycf:q g5lhq ysb2 pi/eci1z 3y7 5(t.z the resultant force?

  Vector A is 5.9 cm long and points along the positive x axis. Vector7:ri h fli/n)n.s fe+j B is 5.3 cm long r 7/ jsfne +i.nil):fhand points at $+20^{\circ}$ 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 76 cm long and poi 6j;/lo-cvb:y alspxa1b r8u8nts at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 36 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 10 m/s from 6q(u7gdmri2g the edge of a cliff. A stop watcd67igqgrm u( 2h measures the stone's trajectory time from the top of the cliff to the bottom to be 4.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge f0b0x:5ny hr ;att(nj0ej /vc n7vuc*. It falls 12 m to the water below.a07:v(c0nytnte;c /nj *rfbvj0 h ux5 How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the gro*0gqd; wd+g jgund, strikes the ground after traveling horizontally a distance of 16 m. Wigd0+ gwd j*;qgth what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12yb) -ggexr5a 2x 3s3ul m/s at an angle of - )y3a 5lr2xsbgue3xg $20^{\circ}$ 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 wi r lk4iuz4ig2 4wot5c-th a speed of 9 m/s at an angle of rlg4 o4wk-c24tiiz5 u $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wi-: tb)/ dteql21m bh1-5sgb. okn s)raxqmi/qth an initial velocity of 38.8 m/s at an angle of $17.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with anj+vanecbt7 dm77-n6s initial velocity of 35.4 m/s at an angle of $44.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angreu 7 m)6 q wxnlv.3cc i6mssth*ryd(ld b896(le 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 at 21.*.c( jmvrj e5l5 $m/s$ from the roof of a building 63.4 $m$ 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 55.9 m/s .:bjk)3scbnw at an angl.)bnk3:s cwjb e of $44.0^{\circ}$ 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 4.0xruhlgivag),i :2 0) z m/s. If you ran the same ra2ixg il g) zar:,h)0vuce on 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 20y:ygh2tyho f .p ;0d hf4;b7yenrgg440 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to2t0;rg.gyfhny4y hpeb :fh ;g yo47d4 the ground is

  A plane is flying due Soutf24hy gz eg/m9h ($270^{\circ}$) 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 head 0 (1 lnfi o*usm6csr4j5n/tan9xnji8 ed $30.0^{\circ}$ 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 fires3u.om+e 7whp 4j2scjr a projectile with speed 50.0 m/s in a forward directs pujo2m+.ec rw h743jion $30.0^{\circ}$ 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 across a river with na9u0 .wf d1jga current of 6.0 m/s. Whag0d anuf.jw9 1t is the speed of the boat as it crosses the river?

  The driver of a motorboat 7a ci(c13eeb fthat can move at 11 m/s in still water wishes to travel directly across a river 1.8 km wide in which the current flows at 3.0 m/s. e7 bfc3i( e1ac How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in sti8 udz) gsrcoykal oxcdt*u-) :zqg+h8-8f :/l ll water wishes to travel directly across a narrow strait in which the current fg 8ht du-rs/dc c :o+8oyzzl gkq8-a*u))fxl:lows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a rivez 2vudxx.*6 4ftlf0 fer 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. H x*xe0zf.tl46vf2du fow fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide g28/:mw- u5h v1wuvkooac)ck 9yw0cqreaches the opposite bank in 6 min 40 s. She is swept downst gqw5muyco1 ok-h0ckvw8:a2 w9u )c/vream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.57 m/s, must aim upstream at an anmb7*sq7ph) vagle of bph7aq * m)s7v$16.0^{\circ}$ (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)  $m/s$