Which one of the following is an examzl1kk3 adz i5xs,k) t7ple of a vector quantity?

  Which of the following operat9je2* jn5z)nr h/ ytfuions will not change a vector?

  Which of the following 4;:5nq09i/cczg s qq(ax em pcis an accurate statement?

  The resultant of twou*aeiemnu 2g):f, iq5 vectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m a( bu*el xuzx((.ojkz. 2rby2j r/hsi1nd 7.0 m, respectively. When these two vectors are added, the magnixbb x(e2. *k(r .zo lr2 /hjsu(j1yuzitude of the sum

  Two vectors, of magnitudes 20 and 50, pe q6k ,7wri/ayy+ut wh:g* ot*/8lynare added. Which one of the following is a possible answer f*w y+l/t, e/ ygw*y 7pqo8iaknh6:tru or the magnitude of the resultant?

  Three forces, each having a magnitude c,tflh2 co +8aikj fi8)7,yiu m9ekz4of 30 N, pull on an object in directions t,hc4fu2 c9ikz y,o78kemil ja8)ft + ihat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the dt lv7wj y(1m4unknown vector is

  Ignoring air resistance, the horizontal component of a pro,fj 1layq) t4njectile's velocity

  A ball is thrown with a velocity of 20h/dhlulbe8sqj.bf 3)/ d2: vs 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 acc yh+em-1dt r0-qnl-o celerationynqo -+mdlht-e1 r-0c

  A soccer ball is kicked with a velocity of 25 m/s at an ajqn 04+swwuhz( gg /c7w)y of)ngle 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 is directed anti-parallel to theosn q7d;0-e jy velocity vecto7 - ;0qsnyejdor,

  If the acceleration of an object is always directed perpendicular(3e 9lm8xemor to its velocit83( xolem9mer y,

  At what angle should a water-gun be7ej. hhaw/fl 0 hj)+hc aimed in order for the water to land with the greatest horizontafhc. 0l hhe/ajh+ jw)7l range?

  An Olympic athlete throws a javelin at four different 6pxt8hds)1mo6k7ox g angles above the horizontal, each m1t8)o67dopsh x kg 6xwith 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 leaves yok7k *t yk s03w;wfkh-dj9(k orur hand with twice the velocity it had on your first throw, its horizontwk- (dk0rj9s*k kok h;3 7wftyal range R (compared to your first serve) would be

  A ball is thrown at an original speed ofcf- i:x )t wawd86,)n;dezskp 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 its maximum height, hon4wt)7q rdnb :w does its spee dqb7: tw)nn4rd compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant m:g.q ;e aklm/f/v j:ahcg3-ha ball is dropped vertically. Which object is traveling faster when q/3-;cgvf a gjame:m.h:/ lhkit hits the level ground below?

  A bullet is fired horizontnlcr)s:9a. qkbd g ob(z)bb,0ally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the timesr.:q,o(lbc zbab n d0 bks9g)) of fall of the two bullets.

  A plane flying horizontally at a speedrld/5h8ipkmgpm)gi 9o e al1fh7; 10v of 58.2 m/s and at an elevation of 184 m drops a package. 7.7 seconds later it drops a second package. How l1ka 9m7/5hvfhppgl;01 dori iem 8g) far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a secon; yd.o4duj/pqiy ; my(d package is dropped. N(d/umy4i;;.dqpyyj o eglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constan 0zg8u0mokips0okhd)47g6pne6b0;vhh; z k at speed. Neglectinv0);mou08hdse46;p ipbgz 0 k a0hgzohkk76ng air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Mo*-thh7n5c rm uon is only one-sixth of that on Earth. If yo mn*5hch-ut r7u hit a baseball 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 54rq(d 6.vq c0co:-nauukkx, q 5 mi/h in the +x axis relative to a straight, level road an6adruc:kqq4q, -n .(0vu kocx d 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 river that fvry-w,verbbxl/97 9m : r.kw elows due south with a strong current. You starte.yw7:vxb 9rm / rrle- 9v,bkw out in your motorboat on the east bank desiring to 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 waz5m 5lskjywhusqguc;o60.1 j* *- uv dter. How much time will it take you to move 12 km downstream, in a river flowing kv; qj6wz smsluogd.uhcu51 *j05* y- at 6.0 km/h?

  Vector A has magnitude 8.0 m at 2c65ag10 ibzizzvxi5 an angle of 30 degrees below the +x axis. The y compg615zvi0 zci2b zxa5i onent of A is

  If a ball is thrown with a 5t7l xvf(( q0- ugztyzszj3l.b+ 1mtsvelocity 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 linemk rddis,cv/f9 cd21/ in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees imc21f/ rdkvdd 9s,/cnorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x coms)xu3(e,llc fkm5)t3 rf/olg ponent of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must bgt/le(3 xo 5s ,fuckrl)m)l 3fe

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what a.li,h 8 q l/cu4uj.yh,l+vbw bngle is the Sun elevated above the vl/h. 4u.bjlb 8wh+,, lqcyiuhorizon?

  Two vectors A and B7w p/uq1- wige have components (0, 1) and (-1, 3), respectively. What are the components of -i/qpe w1ug7 wthe sum of these two vectors?

  Two vectors A and B have components (0, 1)ij,t*xj (h ,.mstb(wf and (-1, 3), respectively. What is magnitude of the sum of thei , wbj*(xjft,h. tms(se two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the 9oqh )w6ju(kx magnitude of(juq)h o6xkw9 C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of itex/+jgv 2z ef(aqin +4s displacemev qz/jfgax 2e+ +(ein4nt?

  Three vectors, expressed insn (y /6nk 6sip2jw+:uw m7nck Cartesian coordinates, 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, expres1 19:kvln qxhjsed in 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 magni( rd6q*zku; c3 ymbxb+sbi 2l0tude of vector C = A u+0ylrbq 6 km*3(szd2 bxi;cb- B ?

  A runner runs halfway around a circular path of radius 10 m. What is the disp8 uhx-vr ,jpv)e:5dnelacement of the joggerr )epxdnv-: 5uvj,e h8?

  Two forces are acting on an objex.p 4tmaaspb7f99 k )htuq6o/ ct as shown in Fig. below. What is the magnitude of the resultant force?p49 am)tb7okhuf s6xt/pqa9 .

  Two forces are acting on an object as shown in Fig. below. What xcwanu cf-/a/t 6x6.x is the direction/6f/.-ta aw 6nxc uxcx of the resultant force?

  Vector A is 3.7 cm long and points along the positiw6.fzt3jpn52 de n a4uve x axis. Vector B is 8.6 cm n6 w.z25nf u j3adt4eplong and points at $+52^{\circ}$ 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 73 cm long and p m ,ibfpa7a88:,bsqp hoints at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 31 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 29 m/s from the eg 2gk7ob;f;gt. q t/xcdge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.3g xb;f/qkc2.g;og7 tt s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 13 m/s82afj: cn x.k;h g*zo6 k(ozjt, from a bridge. It falls 27 m to the water* ;6jjh2ta8kz:ozk c(gf xo n. below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally 87s ,:*r d8coe huqmcufrom a point 21 m above the ground, strikes the ground after traveling horizontally a distance of 23 m. With what speed wa qsmch8ude7:c,or *8u s it thrown?

  A jumper in the long-jump goes into the jump ngggpn(w qoh55 5:j+kwith a speed of 12 m/s at an angle ofgh(wp5n 5qkgjnog: +5 $20^{\circ}$ 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 with atbdf-+*e 2bzn xk9g.n speed of 12 m/s at an angle of bf*zedgntk +x.9bn -2$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity 9e9a; 4uhptmav,w f3ty 4qn,vof 29.3 m/s at an angle of $15.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched mei)j3pn+e ojn)0l;+aumcw,o nq.,g,: o r ub with an initial velocity of 25.8 m/s at an angle of $48.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fit+o:zdf/jtchh 3qr 4+red 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 horiyeb,k x2/ 8bv.iyle6. ng /3 ogd1xwzvzontally at 20.2 $m/s$ from the roof of a building 57.0 $m$ 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 spkkj; s r)m42 e+vlm6roeed of 40.8 m/s at an anglee j) ;r +2mkv6lsmrk4o of $38.3^{\circ}$ 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 velocityj tl3+i8qw ta9 of 4.0 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, thq3aijtl t8w9+ e 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 winbg+lf *tbwxp6k1r t+ .d of 50.0 m/s to the West. The plane'kwb.tgxlt + 16* p+bfrs speed relative to the ground is

  A plane is flying due So h.vb5;+ij khmuth ($270^{\circ}$) 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 z*.dill2iurwh 4,mo32e qeh1dk-1 w ris 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 horizontally fires a proje) uxgji5 ;6qwbby,b u4ctile with speed 50.0 m/s in a forward directio4)qj,yx u;bubg 6i5wb n $30.0^{\circ}$ 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 acros nifeibty5 3(0s a river with a current of 6.0 m/s. What ib0ti3iyne 5( fs the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes t:izl8h2fl*(rguz wuhr*w6 . to travel directly across a river 1.0 kmuzthlr8:u *6wl2 *.rfwgh(zi wide in which the current flows at 4.8 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 tosrsqct2/4+lr)b cs-7p sg f,m travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driverqrr7+ sp)4 sbsl2gt,cc s -/fm head the boat?

  A swimmer heading directly across a river 200 m wide rm 9n;se v wu3w6xww5k-eaches the opposite bank in 6 min 40 s. She is swept downstream 48w;s3kwx m- 59vnw uew60 m. How fast can she swim in still water?

  A swimmer heading directly across a rivela;kck2fs lqup0 758 br 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream f7ks0p 8kl;l quc5b2a 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.87 m/s, must aim udx beut fy (o;)ayc ,(.vj/ykb8/r4y upstream at an angle ofcf/; bay8t(), y y4(bd/oj.eyuukvxr $24.6^{\circ}$ (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)  $m/s$