Which one of the foll6opv357h e kluowing is an example of a vector quantity?

  Which of the following operations will - ; pn:8gw6br: mlks7me m2ntznot change a vector?

  Which of the following is ak t* za9imkq69p s4vadm;9k (yn accurate statement?

  The resultant of two vectors is the smallest when the angle between then8l +3xjo9-)vqh sui fm is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivsw/n gu5277j v1lc9jxzd cjdjw;u: a*ely. When these two vectors are added, the magnitude of the ul;x c7zv52usjw1 / j 7*d:a9gjwdcnjsum

  Two vectors, of magnitudes 20 and 50, are added. Which one g2548 rh2rm8lh jzsbt of the following is a possible answer for the magnitude of the resultantz2b l2r8r4jmh sthg58?

  Three forces, each having a magnitu 0bw feql**.0sht)lrw de of 30 N, pull on an object in directions that arbte wqllr0sw* )f0*.h e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowrfe4x8+ upgaz(7k cg7n vector is

  Ignoring air resistance, the horizontal kfhm.he6kic *p76n/t component of a projectile's velocity

  A ball is thrown with a w )3csdwx-h(zao2z czd:0o1o 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 horizonk vih,abf-) n:tal component of a projectile's acceleration:afvbih-n ,k)

  A soccer ball is kickh0d+ ta 1+jzs4yev 6wued with 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-p/;opllb0/)dwmhl t kkqft(oz4k,p + -arallel to the velocity vectokko ldt;h+ lm(zp0wq4kb-f o)tl,/p /r,

  If the acceleration of an object is a5-;.0:zitdzzru kv c always directed perpendicular to its velocityk. zvzu 5dit:r-z0ac;,

  At what angle should a water-gun be aimed in order for t(k4 zi5yt tc*zhe water to land with the greatest hork c*tt5zyz( 4iizontal range?

  An Olympic athlete throws a javelin s; uq1ri m8j ol4cyv.6at four different angles above the horizontal, each with tu4.jrly vscio8q 1;6 mhe 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. q .ri9jn qti.m0hmj6-/ugfo 1( acmb) If the ball leaves your hand with twice the velocity ijtiaobg u (i1cnjrmq.m0h fq-6.9/m) t had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at ah3nsxznfj47-a ap-+ k1pmb) c n original 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 attempt reaches its maxi6mgcl o 58t:almum height, how does its speed omca86 5:gl ltcompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a da *u puxy70:lball is dropped vertically. Which object is u*70dapl yu:xtraveling faster when it hits the level ground below?

  A bullet is fired hou4bg*3.jw lvbfek9 p( rizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Comparebgkblj3 9 u*p.vwf(4e the times of fall of the two bullets.

  A plane flying horizontally at a speed of 55.2 m/s and at an elev a*coyf2. bvo6ation of 209 m drops a package. 5.4 seconds later it drops a second package. How far apart will the two packages land on thy6c. *2fbaoo ve ground?

  A package of supplies is dropped from a plane, and one second later a se9r;t0+r :heuqmc i/ (qkh;a aw7 tv2amcond package is dropped. Neglecting air resistance, the distance between thewq+eakur(h :7tcam t;m vari9/ 0q2;h falling packages will

  A pilot drops a bomb from a plane flying horizontally at algd8r8 x1 dqxz(h. )tn constant speed. Neglecting air resistance, 8)d.tln(zg81xh xqrdwhen the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on thev/hk+mqx3e.csg 6tq 3 x;ll2d 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) that you would on Earth, the ball would land6gq.2 vmkl3 sxldth/ce + ;3qx

  You are traveling at 55 mi/h in the +x axis relative to a straight, level, z6usajho +u;(rhy:xuj(l3q k9m: 5p nib5nv road and pass a car traveling at 45 mi/h. The relative velocis:jq;uz9i+l ju,h(nu a 5y6:(onbvp3r m5hkxty of your car to the other car is

  You are trying to cross aln;4/ tg9- dqa5rd .ug j) mwkew)hn2o river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to rearn q/;mdjn)k u2ldt945e) ow .- ahwggch 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 gggm sifp.j0m91m3 -gtake you to move 12 kjgg1ig fg90m3s- .pmmm downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 u16u v (rckd2jmubi0 3degrees below the +x axis. The y cj3 2mui0v6 kc(u budr1omponent of A is

  If a ball is thrown with a velocity of 25 m/s hg 4y6qklraz )lggio.ka/ 4l*z/e;0mat 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 d:4oc cs)lc2cdirection north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have yoco) 4c:lcs2dc u walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of itgg(jhw *wk -:ws velocity is 8.00 m/s. The angle between the direction of its motion and the x axi:j-hw*wgk( w gs must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. .o)fpipfv gc9r a5/h, vv5s jube 9k19 At what angle is the Sun elevated above tpe5pfck/9h s vobav,)j vui.9f51g r9he horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. dd m:a6d(tl,b What are the components of thlt(,:addd m b6e sum of these two vectors?

  Two vectors A and B have components (0, 1)wlw*md6 icqv 9-rk(m 7;zb,yk and (-1, 3), respectively. What is magnitude of the sum of these qy*-dmc9;6b km7rw,wzli k (v two vectors?

  Vector A = (1, 3). Vector B = (3, 0).z*c) yhlvp6 / :wbzko* Vector C = A + B . What is the magnitude of C:c )* z6/o*bwhvzy kpl ?

  A car travels 20 km West,/mze3hkeg5)2il 4ok45pqa nd then 20 km South. What is the magnitude of its displacement?2)qpngde54hk5 z e/olm4i k a3

  Three vectors, expressed in Cartesi( ,kix 6,cmykwan 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 coordinatestzeh b,v :vpmocb.+h:j:ec (,, 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 magnitudetfgtmdx t;509 of vector C = Attdx50f; g9t m - B ?

  A runner runs halfway around a circular pat9 u1..a;tiiz4mro-gzvtt4cy q)g yv6 h of radius 10 m. What is the displaz y6vtu)yig vtct1r.-o9m.;z 4aqig4 cement of the jogger?

  Two forces are acting on an object as shown in Fig. below. What ilh. ocz f1.5i kp4nb27 9unfvas the magnitude k .hia pcu .7vnlo ffb4n9521zof the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the joy-l ,+k))ruf ku+x ndirection of the resultant forcn rfl,u)y)xkko+j +u- e?

  Vector A is 3.3 cm long and points alofm4mq jla (3)qng the positive x axis. Vector B is 7.2 cm long and points atqm(jml )q4af3 $+57^{\circ}$ 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 63 cm long and po (7 vi8*xttn6;trolnjvj x-s;ints at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 21 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 ixkt 4m9rr8nd p0j3vb/nitial speed of 18 m/s from the edge of a cliff. A stop watch 8 vk 9tdjrbm/04p3xrn measures the stone's trajectory time from the top of the cliff to the bottom to be 3.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity+v)ln 0 hmeecw3f.- ( a9l3 :k y(swkbq*dsjvd of 15 m/s, from a bridge. It falls 29 m to the water below. How far does the rock travel horizontally befo9-dd .v0)+ b3(eslmv3fynswaj:*h kwkl (ceqre striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes t7u n 6p3tujc52yougp *he ground after traveling horizontally *ny jo326 uct5g 7puupa distance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12jtkq*.e52sxtx kfq whsh( st ea/.7+) m/s at an angle kkxjset e h x/s7 qt2*.s+qf5wtah().of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intol(1kxjahh;obc;a -w.l - a)j *h qswc) the jump with a speed of 15 m/s at an angle ofqlo*h()1 wc.jhxcjkb-wsa;)- ah l;a $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched witixp;vhqa78hfr aih a)p+ yd68a*; x6bh an initial velocity of 35.2 m/s at an angle of $39.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched e*(+ ixcidw9u with an initial velocity of 32.8 m/s at an angle of $24.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglejx yfg7sfr66+ 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 horimd5y-vg)3v +z n 4toab )x9lbqzontally at 19.5 $m/s$ from the roof of a building 34.0 $m$ 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 withf th7knd+f, k+ an initial speed of 62.2 m/s at an +n7 fdk+k fh,tangle of $38.7^{\circ}$ 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 cazwyptj vp56mfs ;/yq / lr7b9*n run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when yos t pl*ry;95/bjzqy/w6mf 7pvu 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 Nort9mh6;ik )ygiv+ 5 pbmuh, and is in a wind of 50.0 m/s to the West. The plane's speed relative 6yv5h+i ubi k)9mp;mg to the ground is

  A plane is flying due Soucqo4hd4:thn 9 th ($270^{\circ}$) 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 headedq3d8+cja(mf.bhhn 4l $30.0^{\circ}$ 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 horib72fil 9os3b g zloveg+ /)0jyzontally fires a projectile with speed 50.0 m/s in a forward dirf7l9y0+ svgbejgzol ib)2o/3ection $30.0^{\circ}$ 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 8.0jim0u no.4ntni0o9-s m/s, is directed across a river with a curre0un9 n 04o.jtsn-imiont of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can movy+)lak -,e 9rp jr+ddce at 18 m/s in still water wishes to travel directly across a river 0.7 km wide in which t,d rkr9jd+pay+-l ce) he current flows at 7.2 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 wishp, 2egt.8fhtv qt o6qlplv-bs7c+0a3es to travel directly across a narrow strait in which q3h2p tb. c0vve s8q+lg7a6pof ltt,-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 mqlbl bk+0 4bm7vx d(ow7pw3k1 wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in st7 b0x 1kblok(7v+b4 dwlpw3mqill water?

  A swimmer heading directly across a river 200 ma-;ri th j8x5x wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the spxi-xtjh8ar ;5eed of the current?

  A boat, whose speed in still water is 1.92 m/s, must aimn cfy;): ,8t faitttz( upstream at an angle of8(t:nfctti f,tzay ); $13.0^{\circ}$ (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)  $m/s$