Which one of the following is an examp7g m2ip9p/ srple of a vector quantity?

  Which of the following opera 8lfsh/c6py+t tions will not change a vector?

  Which of the following is ag 0b2ny toh9u;k,e-j5)cwj k go h0dv5n accurate statement?

  The resultant of two vectors is the smallest when the anvqm g r--2huh 7d:7iczgle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivelyc4.rg0u7m d og. When these two vectors are added, the7m4 g0co.ru dg magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the fpn8r 5eg;58go1q yh blollowing is a possible o85gn bl5ry81qh;p ge answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull og1ef)l j*kga,n an object in directions that are 1 *e)g,fagjkl $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowc42ib a6vz) ,n,fqb v(s4un5m duvc n,.df+lfn vector is

  Ignoring air resistance, o,gp)x8cg yi/the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an r7hmg8p:yt:c 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 horizobi.1-g 29ras x 6datoyp;aol( o0izn7ntal component of a projectile's accelerationbp26g i od7;o- 9s.raiaot(z 0ayxnl1

  A soccer ball is kicked with a veloci, s)gute nyo 5ja4j3yvhyk; k1f;2 1paty 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-- tzv4 nk+4wyvparallel to the velocity vectoyvw4 -+ vtzk4nr,

  If the acceleration of an object is always directed perp ,g8+kk nbgd6wendicular to its velocity 8nk+ dg,g6bwk,

  At what angle should a water-gun be aimed in order for the water to land with th9)m/ e6)yowewuuzuq4 lu6/qge greatest hori6e/ quug4y9qw6wo/l m) z ueu)zontal range?

  An Olympic athlete throws a javelin at four different angles above u p(dc3.+y 0e6cu gu(wew22njuazi8k the horizontaz (w+22(ugeiyuw.uck 03peu ca 86jd nl, 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 ball for the second time. If the ball8ezf x.+payn- leaves your hand with twice the velocity it had on your first thrxfn +8e.y apz-ow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed i cbh6r3)u:in5nu, p mof 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 9q cofa8tm )bw2;j0v rits maximum height, how does its speed c2w8 0t vqma;cjb 9fro)ompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same ind0-c7gw5+a 2iwriiz/ wv7scgjb tp 90 stant a ball is dropv-i 5779tciawpg 0i/ zw2cd0r gb+swj ped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontl sq 5u5(*miotally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times o(mut ls i5*o5qf fall of the two bullets.

  A plane flying horizontally at a speed of 65.2 m/s and at an eleva j59uo-5j qm8y,f (uzxfp+oqition of 124 m drops a package. 6.8 seconds later it drops a second package. How far apart w,-o+jpxujom8q5(9f u yq if5zill the two packages land on the ground?

  A package of supplies is otqh . pt1bt;l 24vyd5h2dpv2 dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packag 2dd.vphp;15ht 2tbl vyto2 4qes will

  A pilot drops a bomb from a planeixw /ui*qzt: +m3gvi:1ec;c c flying horizontally at a constant speed. Neglecting air req:i3c u/c;mi w*1ev cz:ix+tgsistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth x4d y9rvg.6vhof that on Earth. If you hit a baseball on the Moon with the same4v dhyg.9xr 6v effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relati;f 5grxhxtr4)wbqm)bwy/ p2l-*mwt. ve to a straight, level road and pass a car traveling w*xm/-5 wr) btr;bl.x4f)qwhyg t 2pmat 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flohs6 jc:; x+xk+i7y,la f)aanot;m 5 lows due south with a strong current. You start out in your mottx :;oayllch ajf6sn+xi o, mka +5);7orboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can moveg 60w0us. ra 3zgndxq- at 30 km/h in still water. How much time will it take you to move 12 km downstrq.u wdx0 ga6-g ns30zream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle ofoki1vq+p9 i *a zroeh d+p j96 uy;,6v.cze2pf 30 degrees below the +x axis. The y component of A iry291i+6 h oija, oqz9;vz kfcp.pvpudee6*+s

  If a ball is thrown with a jgfb)*d4gk(q velocity 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 line in a direction north of east and you l :;ovdclnfe52+.q ki end up 2.0 km north and several kilometers east. l.+nov;5 e dqkc:lfi2 How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of itsn*9a2y ivo-ay 0teit7 velocity is 8.00 m/s. The angle between the direction of its motion and the x axi 0vy inaeo2*iy7a-tt9s must be

  A 400-m tall tower casts a 600-m long shadow over avzpg(g1. 41kdsj:n kuc;( dyu level ground. At what angle is the Sun elevated above the horizu kcp4us;j1dd.y1:k(gv gnz (on?

  Two vectors A and B have componentso, /-by)2o qu o:ftylf (0, 1) and (-1, 3), respectively. What arq/2yolfu:,y)o f otb -e the components of the sum of these two vectors?

  Two vectors A and B have components (0, 1;rvwicsu bj 36 v0n9rczq; l uz:bo96v8el;z1) and (-1, 3), respectively. What is magnitude of the sulj9 z r0qznr ;s;6o3ev;8z96ucc wuilvbvb:1m of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitgs 4,zej1ig9k7rexh y/fd1 c7tmu;l* udegf zxu jg7e, c1k9;er14tdmh7*iy/ls of C ?

  A car travels 20 km West, then 20 km South. What is the magu7xmhwte:,xn 7-simomt:y9v 5v: -qxnitude of its displacemeu9xn5 m, emvys xt:h- tx i7v-qmo7w::nt?

  Three vectors, expressed in Cartesian coord9/mew w 8s2ry(yt5 xyrinates, 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 coordinxdhw3n 55-1ukjig.e qates, 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 hrslljf 2-e)5kpdcst26e5 l 4= (+3.0, -8.0), what is the magnitude of vespfcerll2e 5-dt 6kj4h)s52 l ctor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dise26xj,s 7/2p j/llt2 clts jisplacement of the joj2lsxs/2,/jce6 ptj stl 7 2ligger?

  Two forces are actinadq9vzbb2sp1tu0p 0 .g on an object as shown in Fig. below. What is the magnitudedapvbbuzs .2pq0t 019 of the resultant force?

  Two forces are acting on an object as shf0.1ghgs 9y+)ijibn;yas h-cown in Fig. below. What is the direction of the resgi-fhssa y)j.0 y n;g19 chbi+ultant force?

  Vector A is 5.3 cm long and points along the positiveie* l3m1y3m2y ffemd;uk bh/(+k; bbg x axis. Vector B is 8.1 cm longm3lf2 ybku+ hi;d*g/(b m1emb k;3yef and points at $+41^{\circ}$ 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 52 cm long auh l 36p5v 97gd2+n xevox;fhgnd points at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 27 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 spe-,qvht)d2 dmimb j522zr ehcm 6kx(p. ed of 12 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 ,6i.r5v(txp dm2c e2d)qmh-m2 k bhz j4.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a8zuc jbt0o3*d fm11sh7zyq0 u velocity of 20 m/s, from a bridge. It falls 25 m to the water below. How far does the rock travel horizo oc0d3 zyhmb7z suu*f80q11tj ntally before striking the water?

  A ball thrown horizontally rzi24lgtq9/b o fk, s7from a point 28 m above the ground, strikes the ground after traveling horizonta2o/t fb 9 qlig47sz,krlly a distance of 12 m. With what speed was it thrown?

  A jumper in the long-jump goec,+yxdh8p o:s s into the jump with a speed of 12 m/s at an angle ofcp:s8d ,hyox+ $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes icc h9b/fo;p /into the jump with a speed of 15 m/s at an angle ofob//ifc;p h9c $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launchedo2ngv,/i xeyz4 ut w.+,33o ng4 fvjtm6iob+p with an initial velocity of 38.1 m/s at an angle of $25.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 42.7 m/s at1+ e *l/; gzlgoaup4ss an angle of $31.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angrkjr 2jx2 .ywje96u/ qle 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 hn0gag+ qwku imh3-;:0cr6wja,c :udy orizontally at 26.6 $m/s$ from the roof of a building 62.4 $m$ 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 an initial speejrtlw i x: 1,*iw,)omid of 47.8 m/s at an irmtwo i,x ):i, l1jw*angle of $47.8^{\circ}$ 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 1500g fi7x8a88hvn+ jv+iq-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had q8x7+vj8+8nhgf ia vi 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 is in an0vpdx; wqo( aa80dhv5psr,q 9:3 nly wind of 50.0 m/s to the Westpwr ohqv: 3qadn a;p 0 v9y58x(nl,sd0. The plane's speed relative to the ground is

  A plane is flying duegjm d:qamr83lt e q *v-4h-)fl 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 is headedrbfu1 )lqrxn) 4s( b:z $30.0^{\circ}$ 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; ia4+w xjrkxr cr5u):ctile with speed 50.0 m/s in a forward dire5k4r j:u;c) iw+rrx axction $30.0^{\circ}$ 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 ria4qwt*6i+bib f c(ac *tc5p 7tver with a current of 6.0 m/s. What is ft6 **t(7iwqcat bc+c54baipthe speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 19 m/cv g+:kt tb qf*nk,,g.s in still water wishes to travel directly across a river 1.2 km wide in which the current flows at 8.0 m/s. How long will it take tkb: .v,tgt*c +,qgfkno cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to s:m+r b b(*eontravel directly acor*sn me+:(bb ross a narrow 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 rep7 r4ll/s* m;prlkh4,fdv5 kt aches the opposite bank in 6lkl,r 5tkrf; sm /h4p7 4vpd*l min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a5r r.jl2h c3mz river 200 m wide reaches the opposite bank in cm3jrhl5 .r 2z6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.96 m/s, must aim upst-jc psdo.;yw0s qojs1tt056cream at an angle of -5co0pts6;o.yds1q sjjtw 0c $12.0^{\circ}$ (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)  $m/s$