Which one of the following is an example of a vector90.//a-a uyukpj8e k ve*)hy*ns ohk r quantity?

  Which of the following operatior3k v w;fho,/ tsb6r .dflzwp)cm -7a*ns will not change a vector?

  Which of the following is an accu ens3d-e/w2 gz,vy+w4prs0et rate statement?

  The resultant of two vectors is the(so iu(qfd4 eli mu-2. smallest when the angle between them is

  Two displacement vectors have magnitudes ofgc f,19hm u;i 2p 0;khchwddu0 5.0 m and 7.0 m, respectively. When these two vectorschfk g, 9 i;p;hd2w0u1 0cudmh are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following is /3)0)bcfbkp* 0r*u i/vw :lep1.bjgkfbz c zu a possible answer for the magnitude of the resultanpz*ebc.)uc) v/0kb 3f :b0jpu* w/ki1zgf lrb t?

  Three forces, each having a magnitud8h4xlr jcp4r 86bc cs-e of 30 N, pull on an object in directions th4cbr4 c h68jprl-x8c sat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectorm1ewy16,h g gy is

  Ignoring air resistance, the horizontal component of a pj 4f)uvhz )l-oy:.qaorojectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angl8nn2r2ej-1p /ilc wr )u:yhwoe 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 horizon26,ltxm+j(9q av3c zndt,gwdt9uz -wtal component of a projectile's acceleration(+zwvt6n2dlwj ax,zcu3-q, ttm 9 dg9

  A soccer ball is kicked with a velocity of 25 m/s at an anc0p o3dybw4d+ gle 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 objectpzsx96 mx en di6/0ce9 is directed anti-parallel to the velocity vectornxi966 ecems 0/p9xdz ,

  If the acceleration of anb+d:8qmg-/h,2jbz p5xxx b vd object is always directed perpendicular to its velocitvmdzjb- q2d x/ 8gx :+,bxb5hpy,

  At what angle should a water-gun be aimed in order forkaot +qv)s4 7foeivr b(j.0np-cv.7i the water to land with the greatest hori krp+tj47i( 0 n i.fqo. )aeb-o7vscvvzontal range?

  An Olympic athlete throws a javelin at four d7smna1sw 7 u*5m :uirnifferent angles above the horizontal,s7m :w7um1n *runsia5 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 ba/oy /to 0ji62fi kux/ugjl. 5i)q*gb)xgy k i3ll for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal rf2yqgty gji x.*63iul/i koku) b)5j/x i/go0ange R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at and h7a2 yf-l84id urwx/ 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 at )b,cjume14 2cxp+v kvtempt reaches its maximum height, how does its spc cb2 kpux),+1jvmv4e eed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the,rv2jk vo.,wy same instant a ball isovw ,jky2,r .v dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a su y76ni2cfuiyq k: gvj s:n;,:econd bullet is dropped from the same height. Ignore air resistanv:g :nj6ni2 fqcusi yy:ku;7,ce. Compare the times of fall of the two bullets.

  A plane flying horizontalloee80owl6gzo fg 0n +jh;l +6by at a speed of 95.0 m/s and at an elevation of 245 m drops a package. 6.0 seconds later it drops a second package. Howol eewo0+j;gf+8l0 hbz6n g o6 far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one sec4- o1,el,h8d8fsav7qbve ty vond later a second package is dropped. Neglecting air resistance, the distance between the falling pa4qb ,,8v8fe d-levsvhy1 ot7ackages will

  A pilot drops a bomb from a plane flying horizontally at a 3uho xy1l nc50constant speed. Neglecting air resistance, when the 1u0x3 hco5ylnbomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moonfki0g7w a rv3b 0feyu.s* ;we, 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 isy g wwarfe;e,fuk *3v700b. would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, le1nhoi(u,ia + *q,whc/y+w nx3rly(lgvel road and pass a car traveling at 45 mi/h. The relative velocity of your ch,wwr+qiox +hn/1 ,ly iy (*g3ucan(lar to the other car is

  You are trying to cross a river that flows due south with a str(idud4 2+hj e,ha.bsaong current. You start out in your motorboat on the east bank desiringsaih,a eh+4 .du2jbd( to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 w51vgmg 8)b x9:dly gqkm/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 kmgl):9x1 vbgq g d8yw5m/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below elv q:ez zi0i6 nvw*i ,z2tx*vl;(cm0the +x axis. The y component of 2zl l60twq(:inxmiz *z0civv* ; ,ve e A is

  If a ball is thrown with a velocity of 25 m/s at 3u5 -;z 2 s-xkq1krsdknm,wew-i yfkz 0u3bs8an 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 ri*+)6piq(9g lneju0d7nnm70kb zpkoz m3-iin a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have yoom(nr ib )kg9- nzj*ed q0kiz+p 6n0m7liu3p7u walked?

  A butterfly moves with a speed ofe 7md: ufp z9q2t 8./tiy,lx7;ttetbt 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion ezp,qtlbm e2x .79 tud7:ttf/tti ;y8and the x axis must be

  A 400-m tall tower casts a 600-m long shadown.9pyx, ym* /ccucd7w bgsm2)kq8 h 3g over a level ground. At what angle is the Sun elevated abq/).7,w nc m23ubk9gysh*dxg cym 8cpove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectich5 2crxpg c7ab*1e*pvely. What are the components of the sum of these two vectorsrccp7p *b52c1h e g*ax?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whtyjc uw *(azvo6 *tv03at is magnitude of the o(*zv 3v*jcwy0tuta 6 sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = gyt uem8s uiq(9n5w 61A + B . What is the magnitude ofei6n 1 gm9(q ust5uw8y C ?

  A car travels 20 km West, then 20 /+yfa*n diln-egc) t; km South. What is the magnitude of its displae n) -tnl;y+i/fg*dac cement?

  Three vectors, expressed in Cartesian coor a6o 6tb qsgn7i.4+ayzdinates, 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 Cartesiau2p*fc j- c:xsn 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 = ( fioh71rl+ctux . :2iu+3.0, -8.0), what is the magnitude of vector C = Au21xoi.rtc:hf l +i u7 - B ?

  A runner runs halfway around a circular pauvu.8wurdbbj yf3-h7 l(o 14lth of radius 10 m. What is the displacement of lfu lr o-8.1h(u jbu7bv4ydw3 the jogger?

  Two forces are acting on an object axl( 5 c:, s;ix* suuze5cdaa6 ,vb7ypcs shown in Fig. below. What is the magnitude of the resultant force?u;s dpx(y: cxa5,uceba 6*,zv 7 sli5c

  Two forces are acting on an /ol+tg cg /5ufobject as shown in Fig. below. What is the direction /g+c5 golut/fof the resultant force?

  Vector A is 4.8 cm long and points along the posf.n-tap a)uw) oefdd7i (* 6w1f+zatmitive x axis. Vector B is 6.9 cm long and dw)(t-nzt1m f d*+po. a7uaae f)i fw6points at $+36^{\circ}$ 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 61 cm lo x os(qzjl(v6j*l9bs .ng and points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 23 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 16 mtk b6c l*e:s.l9; mjda/s from the edge of a cliff. A stop watch measures the ston td9el cl6ks.;a*: mbje's trajectory time from the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontall4v 8nzb,blr2j y, with a velocity of 9 m/s, from a bridge. It falls 12 m to the water below. How far doe284v,rj bl zbns the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes the grz9bnnnq1o i87 ound after t 1o978niqznnbraveling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 rf8bwfel*y k4r8)4mwp 9 6u khm/s at an angle of4mbw kr 488kf6lp)r eh *w9yuf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into thl of+6m-uy64cc. j*(kg rkfime jump with a speed of 13 m/s at an angle of+c ou.-4 6fgclm*rm6jkk(i yf $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 45.0 m/s at an angle zp;ee:i+f6c n5 yhh(jof $46.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 316k6- ;j. hmwr 6legfx7pe: j.g cc2wsx.6 m/s at an angle of $29.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedut+s6kt jhz *8 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 horizontallj wdyt6s 9*ks, .5cmfiso ,/qhy at 17.5 $m/s$ from the roof of a building 67.1 $m$ 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 with an inith6bypph n8bgfd2 so:: yh 2-fak47;vtial speed of 55.1 m/s at an ah87 f:yyh:f 2- 2s dgt;hknpvpabb64ongle of $41.3^{\circ}$ 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 u d nhmfx7fq j7gakq.kub*qh1+ b5:p877 aar4.0 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 it would take you to finra7f7 7n1 fd 8qg a hjk*qu5akx7:h+bbump4q. ish would be

  A plane has an air spee 40p.2r8onvxljjvn 4yd of 200 m/s due North, and is in a wind of 50.0 m/s to the West. They 4 nljvj0428pn. xovr plane's speed relative to the ground is

  A plane is flying due South,i1ckx 9tha2 u ($270^{\circ}$) 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 azl)k(;/gll:- g2l dk+ga jywheaded $30.0^{\circ}$ 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 horizontaly.y1a oqp5m.c ly fires a projectile with speed 50.0 m/s in a p 5c1q.yamo. yforward 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 stillb)o 4k4bigf4l water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. Whg lif4) 4kob4bat is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 187)t:lt k w8zox m/s in still water wishes to travel directly across a river 0.6 km wide in which the curtk:tlo) 87zwxrent flows at 6.4 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 w5nszc 5;me i5rd4y n)fishes to travel directly across a narrow strait in which the current flows acder; nmy) s 545zi5fnt 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 72bd ;m/tg u0z8hhv xfm wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim ifhvh butgm;0x82 dz/7 n still water?

  A swimmer heading di9 pyu(sf )uyot*eg /z*rectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m.t9( yuypg f/*)szo ue* What is the speed of the current?

  A boat, whose speed in still wx q2.8+zdfz1 dw6kp ruater is 1.79 m/s, must aim upstream at an angle ofd1+2zkx.86zpu fwq d r $22.9^{\circ}$ (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)  $m/s$