Which one of the followingc p) rngsamigy8i6p5sys;l *jx4g1+9iy d) .l is an example of a vector quantity?

  Which of the following operations wiloha):j ,jye .2gga(( obhvzi;v )e(kjl not change a vector?

  Which of the following is an accurate statemenm ktw-w2 sk3+drgz*y 9t?

  The resultant of two vectors is the smallest when the anhh vd)8/sx4 st45k jp-hayvx )gle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivelyttaa d9+f3b)/qr u,) f)u oqct. When these two vectors are added, th qr)) aqbt+f9fta t,3uo)duc/e magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whh*1cus 8qc5r n6 eodwy(3/ yyuich one of the following is a possible answer for t 6s8e rynucq w3y5cy(1duh/*o he magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions t8gg.i+q j -**cx/xe(ugukuj p+g/ gpqx* u xc.ku(u8 *-gjeijhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkno -gqk7dgq ad)pi gz7 s1zp3f4:wn vector is

  Ignoring air resistance, the xp:3 zdr urvne80iv6dj-v : nwit90j+ horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 sfxy7 .qqa vzn.w)*sitg/s / (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 no0ati(4bs q ia1ejnu.4kk (jb0 j( q0of a projectile's acceleration(. (aiob n4jaqi104ue tkj s(kb0nj0q

  A soccer ball is kicked with a velocity of 25 m/s at an a3a 1oxhgj)t1 rngle 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 ixwf ..i-m 6tvnkpd y1h1hef*0 s directed anti-parallel to the velocity vecto *.1-fmwvkidft1 phy.6n0eh xr,

  If the acceleration of an object is always directed p:ib716 fyhvev erpendicular to its velocity eyiv 1f:vbh67,

  At what angle should a water-gun be aimed in order for th1rpstda ( bdv4w xs0s2dq/4 n1e water to land with the greatest horizontal range?nsw4dq1a rx b0vt s4d12/p sd(

  An Olympic athlete throws a javelin at four different angles n sogo mf; (-f .br7:c.ptrx)am7f i,wabove the horizontal, eachp-f wora)otf7xgi..rm f m,cns;(:7b 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 time. If the ball leaves your hand withm; sy48d kmomc+be3kd6.k5 gx twice the velocity it had on your first throw, its hy 5s.md m6;kx +g8cek m3bd4koorizontal range R (compared to your first serve) would be

  A ball is thrown at an y* 1q)coa)xx bdzt, h(e:bj0wz z63 ,arqqd-poriginal speed 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 field goal attempvetitf1h- g 9e,f(oz s3vn66zke fq3 )t reaches its maximum height, how does its speed compare to its initial g v oe966-n,qskh 3fe(fzi3v)fe 1ttz speed?

  A stone is thrown horizontally from the top of a to()j ma-h6u6+)gk bnm qzm:ghdwer at the same instant a ball is dropped vertically. Which object is traveling fasterbg)j6 6mn kqagu:d hm ()+m-hz when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second,)g2 bl(*hle, igobss bullet is dropped from the same height. Ignore airbl2 e,*),ghos l(sgbi resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 50.5 m/s and at an elevation of 1paibgk) 8 8axn5)qb+ r32 m drops a package. 6.7 seconds later it drops a second package. How far apart will the two packages land on the gqp +5xbgrk8)ab nia)8round?

  A package of supplies is dropped from a plane, and one second later a second d)2 4sa cwjr,9cko xx5wht(-hpackage is dropped. Neglecting air resistance, xwj k o(w s4ht)9h,5 cdxca-2rthe distance between the falling packages will

  A pilot drops a bomb from a plane flying ho5pl)a-,v+sgvi /rs w urizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the)-s + 5sgv ulwvr/p,ai horizontal location of the plane will

  The acceleration of gravity on the Moon is only o :k6ivg4/zv)+a yrba8lfe3oo ne-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and atilvozro e /)fvg y8aa 6+b3k:4 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 straig(us*bsn,q1sh cj6)iq ht, level road and pass a car traveling at 45 mi/h. The relative velocity of your *q sb(,)jc n1hqisus6car to the other car is

  You are trying to cross a river that f89 xr 83fmqeiklows due south with a strong current. You start out in ye93xqmf8r i k8our 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 s)eyl):vq o h.dtill water. How much time will it take you to move 12ov.)edqly h): km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an a)aa hbp4f:1s os0a5o21/fjmgt jd;cfngle of 30 degrees below the +x axis. The y componejs ;fdhab: fj/0cf)mpt aog4a11o 25snt of A is

  If a ball is thrown with a velocity of 25 m/s at anav:d67ok0yactu f tc 7o00s m,3ml hl* angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight.)g ls/ : mh-tsvuvn,w line in a direction north of east and you end up 2.0 km north and several kilometers east. How many:sl v.)hun/vw,stg -m degrees north of east have you walked?

  A butterfly moves with a speed6 a(;j kps/:,pkjh/u g wp5mcb of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction ojk/hk u bwgpc/:a6 jp(5;pms, f its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angl.w usm+mmbk2xy-) zj 02rov0pe is the Sun elevat v +)s20.km-rjombuyp20w m xzed above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatv;:pyn jxml+ , nab8n; are the components of the sum of these two vectonan:;8y nl+vmjx, ;b prs?

  Two vectors A and B have components (0, 1) and (-1,of/qy fhn67 (f 3), respectively. What is magnitude of the sum qhnyff /f7o6( of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vec+ * xngfgc7l d:6zo/fstor C = A + B . What is the magnitudd 6zf7/gn+cxl*fg:soe of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of i/ gej;,sokum ) c8pg+lts displacsg+u/ok )jmpgec ,;l8ement?

  Three vectors, expressed saot +( /njt3:ov6vycin 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, expressed in Cartesian coe o7;h8u7,w 3hp8(nz j:abatn*rkms hordinates, 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)jo f-i/eo.zj6u jnx0. and vector B = (+3.0, -8.0), what is the magnitude of vector C 0ji..zj6 x fju/-oeon = A - B ?

  A runner runs halfway around a circular path of radius 10 m.nfve,nf 1-1nh What is the displacement of the joggern f- 1,nfhven1?

  Two forces are acting on an object as shown in Fiz*vi)labwu9a o,5 f)gg. below. What is the magnitude of the resultan)b) fia*azg ,lv5uw o9t force?

  Two forces are acting ft a*b6w*r0e 9 h/:wrazlql;5mll9 lk on an object as shown in Fig. below. What is the direction orw 5et0zmll:9w*9q;l/ra afblh* lk 6f the resultant force?

  Vector A is 4.4 cm long and points ad ,lr:yn2q)es :1*nzan (fuzalong the positive x axis. Vector B is 5.3 cm lo):n2srd(enf * ayn 1zlqzu,a: ng and points at $+53^{\circ}$ 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 89 cm long/x d.8 aisco bfc 07x9xf4h7hc 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 nhb hmqs ds;4fww+ e287ir4e- an initial speed of 17 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.6 s. What is the height of the cliff?; ww+e4qdsh28 7f4hre i sbmn-

  A girl throws a rock horizoq dea8(h0+h 22rvnkm entally, with a velocity of 16 m/s, from a bridge. It falls 25 m to the water below. How far does the r k0vd +ah2(e2q8 hnmerock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, strikes the gro 8: y0mmatwd*sund dtw :*ymas0m8 after traveling horizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jumu *m; o(cetg9te9 r)cmp goes into the jump with a speed of 12 m/s at an angle oft m*9)cteg9crm;o(u e $20^{\circ}$ 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,ik;2x nn 4gen jump with a speed of 9 m/s at an angle of n2g n, ixk;4en$25^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 51.3 m/s at an anglct: e*9q9:t:bdfh, ymq-ymrh e of $17.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 48.9 m/4ddqd9+ snp9jg g/ztx dzjdz- 89u+*qs at an angle of $33.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglez/7mgfeoje;: ak 5cu0 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 horizontal 2:0 7jffplpjjta/,f lly at 22.5 $m/s$ from the roof of a building 50.7 $m$ 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 froxk lq:,/ydfv4 zo)cncrs;j7 c 3a7e:ym ground level with an initial speed of 42.1 m/s at an ang kx7rsa:c7o zd;je,3: )lfcyy 4vqn/cle of $42.6^{\circ}$ 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 1506e /ztar b6c)o0-m race at a velocity of 4.0 m/s. If you ran the same race on a day tb66eor/ a)cz 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 200 m/s due North, and ib-nq36 w9*kj rk wsox,s in a wind of 50.0 m/s to the West. The plane's speed relative k jw6wobsn93 ,kxr- *qto the ground is

  A plane is flying due Southc4k4u bif yz,n;e+em( ($270^{\circ}$) 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 b:kvuqb ll.6-120 km/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 t on(xw5bogm/jz48c1n3mx j7m/s horizontally fires a projectile with speed 50.0 m/s in a forward x xmb/31 4o5wjj7 gc( nmnzot8direction $30.0^{\circ}$ 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 acros5.ak 8 fxmj fdfd48:.jbf ua3os a river with a current of 6.0 m/s. What is the speed of tj85 uj8 fdf3b fmod.aa:x. f4khe boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still w., jm z5oc;lxcbiq-.later wishes to travel directly across a river 0.9 km wide in which the current flows at 6.3 m/s. How long will it take to cross tz-j,lcc.;q5o lxm i.bhe river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to .a;ru:4rjxx8 7pez o ptravel directly across a narrow ez.apo7xu:jp8 4x; rrstrait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acrw;;fskw6y+gnw p e)ri0 7jer/oss a river 200 m wide reaches the opposite bank in 6 min 4i; p6e g;kwsnr+wrj f07/w )ye0 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite banpl: k74wg639s4at:n4 rznx bbqi nu7 t* tzdd0k in 6 min 40 s. She is swept downstream 480 m. What is the speed of the c: bw3ulanqgn*s:r d404z94k btt7n ip 67xzdturrent?

  A boat, whose speed in still water iswqec.4) rw ye1hy wk:* 2.12 m/s, must aim upstream at an angle of*4we :y)1cke .wqhrwy $22.6^{\circ}$ (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)  $m/s$