Which one of the following is an exampleen+ +yv mlt5e. of a vector quantity?

  Which of the following operations will not chasyz3zbk te6*.nge a vector?

  Which of the following is an accura9 ujo.mvlr7m s l*whf b98m2 8hmc*oe;te statement?

  The resultant of two vectors is the smallest when the angle between them i8akl1 ik 5s-lyj q4u6as

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respec9jc sdzp*tu , doghyhst ;+)73tively. When thes+z,th ; js hpc )uddgy9o*7st3e two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50 *x.ir4nocz e/n7mqvt0 tfxf7jd d*90, are added. Which one of the following is a possible answer for the magnitu *e 7dv4fz9j*xn7 c n/do0t0rfi txqm.de of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an o - 1qrs5iyr;gubject in directions that y- 1 srurgqi;5are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector/x4 r3f j.vuwohdv 65il8 p+gn is

  Ignoring air resistance, the horizontal component of afu4frnj1 dh9v 1n zf97 projectile's velocity

  A ball is thrown with a velocity of 20 mqgmjd1 f1xwk7s6/tzz)3 1s sz/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 resistaf) ikgeac c0;-nce, the horizontal component of a projectile's accelerationgc -;)ie0 cakf

  A soccer ball is kicked with a velocpbtm*ep(k qt03ei mv;i .v;p *ity 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 anti7g ati 5;b1,8 )nqm*l+y 8xzz6mqagdlo1 fpbs-parallel to the velocity vect)yz b8sq8 lx,z;laimt15dg6+ 7qafogb1n m* por,

  If the acceleration of an object is always directed perpe/ (m;ljfqpo 4kndicular to its velocity,o;fl(4mk/ j qp

  At what angle should az+s;z 0 dr-fz dno(mn5 water-gun be aimed in order for the water to land with the greatest horizontal 0-nm+nodz;z(5df szr range?

  An Olympic athlete throws a javelin at fo-x eqvny:78lc )grfx0sc/ da6ur different angles above the horizontal, each with the x g)e6d0 yqc/ v8xlrcn-a :fs7same 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 fodfd, r-kbg + wt;o/ms, x)zf*lr the second time. If the ball leaves your hand with twice the velocity it had on your first throw,td,d/gls*; zo m ) frw,bxfk-+ its horizontal range R (compared to your first serve) would be

  A ball is thrown at anxxap8 x(1ps +jr81y nz 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 maximum h/ jj, w9qifpol.mx n7*eight, how does its speed compare to its o.ifjlwm 7n9p *jxq/,initial speed?

  A stone is thrown horizontally fr2 : sdq/pnvf8uom the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground d pqsvu 2:fn/8below?

  A bullet is fired horizontally, and at the same instant a second bub fa2o +y)dk+allet is dropped from the same heiof+ky)ba2 + adght. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 78.4 m/s and at an elevat+ro 1bhyb0k 3tion of 203 m drops a p1r0b 3 y+hkotbackage. 4.5 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and 00a s,-t6k;dukr bpez one second later a second package is dropped. Neglecting buda0 - tek p,ks06rz;air resistance, the distance between the falling packages will

  A pilot drops a bomb from avpgymezzn*2 6lwu 54vas.* f4 plane flying horizontally at a constant speed. Neglecting air resistance, when2fy. 6v5menul vz**a 4sg4wz p the bomb hits the ground the horizontal location of the plane will

  The acceleration of grav xoq1p 5tt(r1d1 mgl g dz;oo/t+9:trhity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the ;tl9qo511/g:tpr dmtgoz(hod+trx 1 Moon with the same 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 relative to a straight, level b w+:7 jcmnt9si-( bfy bn;jzni6)9gbroad and pass a car traveling at 45 mi/h. The relative vel nmb( nbi9+t:cybj) s9 zg67b;inj-wf ocity of your car to the other car is

  You are trying to cross a river that flowo) ikr+h* q-cvs due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting po+r)qi ck*- vhoint. You should head your motorboat

  Your motorboat can move atr)0 kf8 4dkury 30 km/h in still water. How much time will it take yr)0ruyk 4f8dkou to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an anglex4j6p qh(wl bwq / *tymj97f 7z:y2)hubejr.o of 30 degrees below the +x axis. The y component of A iqh:z mbf7h(/u7e.6p w9t)2r4y *q jywxljjo bs

  If a ball is thrown witg: (r,j9 hjomeh a 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 lineo0/wi+u t y;r1t*dxvh8 evfo( in a direction north of east and you end up 2.0 km north and several kilometers itrvo*du / xfv8ty( 0owh1;e+east. How many degrees north of east have you walked?

  A butterfly moves with a speed oll ljpl. 6vy5,y1bza:f 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of it6ly , z1j v.y:5lbplals motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At wha99r vj* ;dz 15s lfump(7ocqsxt angle is the Sun elevated a7s(pvs1x ;5o*9 u dcqz9 jflmrbove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respecti9jeto5o w e:e7;jl 9gkvely. What are the components of the sum of these two veco5wtee ol9:kje 7g 9;jtors?

  Two vectors A and B have compon*m*:)mnwd;6 gmz+bytj 8 n4x3 glupn pents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vn84*y 6dux+mnw* )bgt ;ml:gn3jpmzp ectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + 3c9aro(s-7e 8 pthurz)lm r .wB . What is the magnitude owm- rtlhc.87r9o) zru3ap e (sf C ?

  A car travels 20 km West, then 20 km South. What is the magnrnjkuk (:culi9o urg594-sa-itude of its displacemer5n:luj 9g - ai(9uckk -o4usrnt?

  Three vectors, expressed in Cartesian coordinat)yx+ ;l sb+dnj vsj-i:es, 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 y;b, pq0n9wu trq:z1 aCartesian 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 h:a 7pn-;xwyj7d ctw9the magnitude of vector C = A - B ?jx yw7 a-:; 7cndptwh9

  A runner runs halfway around a circular path of radius 10 m. What is the displb qondl 3ma5 qo33f)*ov6)pdmace6)3o)ddn3 *oml v5 fboqma3pqment of the jogger?

  Two forces are acting on an object as shown inxx(vcvc 0b3 )w Fig. below. What is the magnitude c xv0vxc(b)w3 of the resultant force?

  Two forces are acting on an object as shown in Fig. bwefh sn:e (i0b6(wlw3elow. What is the directiob3lnwf( e6(i0we:shw n of the resultant force?

  Vector A is 3.8 cm long and points along the positive x axis. Vector B i:axk vjt. l ).hf2l.qcs 5.2 cm long and pointsljvc.khf2altqx :) .. at $+43^{\circ}$ 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 and point43cu0ds8vyxlkj2o5tv ) awe /s at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 37 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 ofu;,c:oilr/ bjo-rg- :f ifqx2 25 m/s from the edge of ;ji :lbf- gi- ,rrxou2o:f /qca cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 77 39 axshtyix6.p2gt a m/s, from a bridge. It falls 12 m to the water hx sxy6i927t apt3g.a below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the gra/2v/d cdeds -wm i53jound, strikes the ground after traveling horizontally a distance of 17 m. Wvjsm5 -cwded/a3 di/2ith what speed was it thrown?

  A jumper in the long-jump goes into the jump withlztcrhpy2(ruye (l)+ve28k c0 )- eb f a speed of 12 m/s at an angle o ly(ztvb) u208rkp(-e2 le +reyhfc )cf $20^{\circ}$ 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 a speed of 12 m/s at cccixd bd kx+8ca4(**an angle of a4 idx d* cc(cx*b+ck8$36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched5bvku nfdo2i60(jk;p1w ub.j with an initial velocity of 39.4 m/s at an angle of $48.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is laun-qgo; 8i;mxvn ched with an initial velocity of 24.2 m/s at an angle of $33.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anw 5+g84jbcklubdf 4.mgle 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 horizoiigzk4do- ( :ny ( ymlo92clcl a4r,0ontally at 27.0 $m/s$ from the roof of a building 58.9 $m$ 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 ay b ,2h .-t/lq0rqkahfn initial speed of 67.9 m/s at an ang.,2 taqfh-lqrk y/ 0bhle of $41.4^{\circ}$ 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 velocihln +wjv4hpv54p0q5q et:, rmty of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slo wlp4 45j:tmv, er hnh50+qpqvws your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed ofj 81fbglrz7 s6 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relag sz6 17lf8rjbtive to the ground is

  A plane is flying due South gwk)ml)liz ct: c9v9+ fvkxve:4 1mr;($270^{\circ}$) 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 3p1if4e8 r :fcrgm m,jbt8e (hof 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 m/s hor.mp vuw63egfxc) r 39uizontally fires a projectile with speed 50.0 m/s in a forwaru)er 9um6cw px3f v3.gd direction $30.0^{\circ}$ 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 directes q/gg(s i h(qs96a.dd sogn4.d across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the rgo.s sg9(q.sh(n4qid/ sg6a d iver?

  The driver of a motorboat that can move at 16 m/s qcfz pc* 3nh3+in still water wishes to travel directly across a river 1.4 km wide in which the current flows at 3.8 m/s. How long will it take tof3nh+cp3 qz c* cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wip*-h1s;gien5m2le5u8o a 9vvyjz0ywshes to travel directly acrov5hzg9 j5s 1 e*wp-02ynumvy; oaie8lss 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 reachz2wzj2xkl0 1pes the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swx1kwp0 jl2z2z im in still water?

  A swimmer heading directly r7m+2 (js:p6cilp:avyx)c )dgcy5z3k h+be y across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of th b)y:(scvxcky i 3pgdpz)+e l65+7mj2 rahyc: e current?

  A boat, whose speed in still wateroinjd6eorr .a .b/ h-lj08h;b is 1.92 m/s, must aim upstream at an angle of .i or;aodbeh jln/-r8h .b0 j6$17.8^{\circ}$ (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)  $m/s$