Which one of the follol,w-ky mf 83mdwing is an example of a vector quantity?

  Which of the following operations will not change a veubijykdm r7-y wf; 33+ctor?

  Which of the following cp . v(,mi(o,:yoa9kgbhh3 ex is an accurate statement?

  The resultant of two vectors is the smallest when the angle betweenp5-lbya 1 hbb )/z:6dqpau 3ck them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, r:crxw77o gznoyjw-g(0qz: 3l espectively. When these two vectors are added, the magnitude of theo lr-gy3 zcgx j70:(:zoww7nq sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follo,igg6gclbi0e q44ep 2 wing is a possible answer for the magnitude o44c6b2egg,gpqi ei0lf the resultant?

  Three forces, each having a magnitude of 30 N, pull oncdjmu r*: )(m5f(ra nz an object in directions thatz*f (rd5u mjcan:mr)( are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is 5my; ; 9p4du.9 axkbh1qbdgga

  Ignoring air resistance 8/dtf w0bnqog5- 70;fkamf**jlo we g, the horizontal component of a projectile's velocity

  A ball is thrown with a zqz5f1; + k2imuhb*aqb tfm9*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 componente0j 5y66+zvhcp k 3qnv of a projectile's accelerationp vz3qejnh+k6 65vcy0

  A soccer ball is kicked withb;w)/q8r fsma*mqr m2 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 is directed anti-parallek.an576+yws u my 6tmol to the velocit6y7 6m5w s. uyktanm+oy vector,

  If the acceleration of an object is alwaysue,vnq v43;hyiri +8cx ,d6xp directed perpendicular to its velocityndqcph64vx3vrxi8u e ;y+ i, ,,

  At what angle should a water-gun be aimed in orde.8h ny :+7hlqcsj 8cndr for the water to land with the greatest horizontal ran:h+8lqn8ccshj.7yd n ge?

  An Olympic athlete throws a javelin at four different angles above thmbc1 yosbk f;3a k95f6e horizontal, eacfkfmsa1bkby3oc5 6 ;9h 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 secf9yux 9 6szj 4fcc6s-qond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to ysfs9u xyc96j4c6- fzq our first serve) would be

  A ball is thrown at an original speekwnb -ce* 3v.cd 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 ooy /tvs.9vt(field goal attempt reaches its maximum height, how does its speed compare to its initial (9v o stoy/t.vspeed?

  A stone is thrown horizontally from the top of a tower at the same instant ns7 w f*5 pk tvch*so:veo4h5:a ball is dropped vertically. Which object is traveling faster when it hits the level o:vh5 onssc*45 kw:7phvfet*ground below?

  A bullet is fired horizontalld (zxm2uby-c.17gf qmy, and at the same instant a second bullet is dropped from the same height.7bc dx-21 ym.fmgz u(q Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 62.6 m/s and at an e-bw *cmkrn)5jlevation of 133 m drops a package. 2.9 seconds later it drops a second package. How far apart will the k5w rmbn)-*jctwo packages land on the ground?

  A package of supplies is dropped from a plane, and odka )f64lp* jpne second later a second package is dropped. Neglecting air resistance, the distance betwejf)46 kda pp*len the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. mr*h vx4;mns7bg /hw2 Neglecting air resistance, when the bomb hits the ground the horizontal;bxhg 2sr mwh/m4* 7vn location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. 8b avjqz d*/b.If you hit a baseball on the Moon with the same effort (and b d*v8.zq/bj aat 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 strai3dvw3kjng+zn 7w t(+n ght, level road and pass a car tw+g3v7k t wn3j+n(nzd raveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river thz,h y50 afzg1s6psoq*8ua)(pg i k n+rat flows due south with a strong current. You start out in your motorboat on the east bank desirr86*s p0oy+asfa5, z)ghig1 ( knup qzing 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 water. How much time will it jx+i x0b :es)rtake you to move 12 km dow:)+ xxb0 resijnstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angl9 l-uhf) 0x5 k7fsxtsce of 30 degrees below the +x axis. The y compo5x fh)fu0x9l st7-s cknent of A is

  If a ball is thrown with a velocity of 25 m/s ,he j e62e f6lv2c/ghei15ecw 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 directilgwqm x* a.+e 5gha-,von north of east and you end up 2.0 km north and several kilometers east. How m5w.x-qmv al+a,g*heg any degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/- fi7 c8ihq5bds. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and ic-ib q7d f5h8the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a le,3d1oohr( qn aj3: 6oi,f dskbvel ground. At what angle is the Sun elevated above ord 36: ( ,3k hndajq,bo1ifsothe horizon?

  Two vectors A and B have components (0, 1) and 0z ujh-q w(z9q(-1, 3), respectively. What are the components z( wj 9h0zqq-uof the sum of these two vectors?

  Two vectors A and B have components (04l t)szxfp)+ s, 1) and (-1, 3), respectively. What is magnitude of the sum of thfz)) s ls+4txpese two vectors?

  Vector A = (1, 3). (h nbva /)y*nnVector B = (3, 0). Vector C = A + B . What is the magnitudevnn/)b *yah(n of C ?

  A car travels 20 km West, then 20 km South. What is tfrzs;f* q+d g;he magnitude of its displacementsdf+q;gr f;z *?

  Three vectors, expressed in Cartesian coord hd3pi/w.q pn/inates, 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 Cartesian coor uh2p86r:n trm/kqbs 7dinates, 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 magnitud.a ops6f3pw.be of vector C =pa .3w.fp b6so A - B ?

  A runner runs halfway around a circular path of radius 10 m. Wl32df+ *l t,y he3zghnhat is the displacement of thet 2h gzlf3*+3h,ndlye jogger?

  Two forces are acting on at7c kx1t( c-7hzjad0s n object as shown in Fig. below. What is the magnitude 0-c7j czt th ksa7d1x(of the resultant force?

  Two forces are actingxpo(ww w+v./48wbkj m on an object as shown in Fig. below. What is the direction of the resultant force?k.xp /ww( bmwo4w v+j8

  Vector A is 3.4 cm long and points along the positive x axis. *y*l odg 1dqai27 (brwVector B is 10.0 cm lonwqd1dgo7air2 (** lb yg and points at $+24^{\circ}$ 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 70 cm long and poiij l,m(wy 5a 2 d/+2igoexpea/nts at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 46 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 horizou j7--na nbsfeb; m9pngl,h4;ntally with an initial speed of 20 m/s from the edge of anlb j 9,- fhu;-pebn7s4namg; cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock hgtd- unh7agr( z95k/s orizontally, with a velocity of 13 m/s, from a bridge. It falls 16 m to the water below. a nuksh7t rd/g(5 -gz9How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from e2tfxz6fq) )ja point 22 m above the ground, strikes the ground after traveling horizontally a distanc6xe j))f zqtf2e of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speqtuib0r3-l8lyf+g,oz gi 8 ; sed of 12 m/s at an angle l+qb8 i;,8tol igf0s3zu ry-gof $20^{\circ}$ 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:gw q7lz1ltp l rt(nox-7x3e, a speed of 10 m/s at an angle o wtln 7et(xp-r,:z x3l1l7qgof $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with anc;23p1fdrs y oqob.6wsmv *u. initial velocity of 45.2 m/s at an angle of $49.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 50.7z ,rea9 6wsnw7 m/s at an angle of $19.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an aon:c 3 .a blf/i9vcty/ngle 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 bz49r wbb6ywp/wk5 5+ noi3i4aaa.d 3pp ymm: 16.3 $m/s$ from the roof of a building 60.4 $m$ 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 inyzni+ulr14qw i77z8l27s san initial speed of 49.6 m/s at an ang2i7ns yrii 17l 7s+8qzw4 ulznle of $39.0^{\circ}$ 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 6 fdiz-8sig32jyiy* p) o yk2b1500-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 your speed by 2.0 m/s, thy* fsz)y8 o3-kj26bgdiii yp2 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 wind of 50.0 xo 4+v hmkmyrgta3ikto+5de ) e7j2c.cs3+,km/s to the West. The tsh i3+ y. mce 73av2,jxo5)kdk +or+ektgc4m plane's speed relative to the ground is

  A plane is flying dug /s)9zdhq g/ee 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 v3mvuyqm(16 bzl1 e h(is 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 horizontallz xk* 5m)han8dy fires a projectile with speed 50.0 m/s in a forward dire)ka zxn m*hd85ction $30.0^{\circ}$ 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 r x 2)47u7kelop qm2fqwiver with a current of 6.0 m/s. What is the speed of the boat as it crosses the 2xmq7p)k2l74 qoufew river?

  The driver of a motorboat that can move at 18 m/s in still water wishr6gh :er, ow1 qo,2dwoes to travel directly across ,oo2,g wqo1hwrd 6:era river 1.7 km wide in which the current flows at 7.8 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 tiinwx. -7tk+v u tq5c5c:gn*w 0 y,ojyo travel directly across a n:ix-.onnj v,wqtic5 +u ywk70g yc* 5tarrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches tho - f, 8*v :+nqaw-rhluclsmz-e opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still-f8z-s,l cwhqvm +ulora *-n: water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank *2+ 1pj ,wav,8vp aelorkj/d1v 5gkz ain 6 min 40 s. She is s*1ala ov/dv,rpwge kjp2j5ka1+8 z ,vwept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.14 m/s, must aim upstream at-gn*eahw(: wbe+ie *x,irt ks .78kin an angle ofwngi 7ex-*bhiier ( wk8*esk+,t.:an $28.8^{\circ}$ (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)  $m/s$