Which one of the following is an example of a vector quan;fr.x nh-t v-eyze(.2;jh m aftity?

  Which of the following operations will a3to t7e.jo+ 9 f l(lab9)jfptnot change a vector?

  Which of the following21g2m1q5 y8doddrg um is an accurate statement?

  The resultant of two vectors is the sm-6 a yxnnj)ktgg47d n*allest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.dxz,v -l v-xpk9t8 hdr2dt1 3y0 m, respectively. When these two vectors are added, th9k-vvhdzyx r18 ,dldtxp 3t 2-e magnitude of the sum

  Two vectors, of magnorv27njog7x/w * k+gritudes 20 and 50, are added. Which one of the following is a possiblevjxn7w*/7g g2rro+ o k answer for the magnitude of the resultant?

  Three forces, each having a magnitude ofad*lcvg.tz -ve di f72o;4lo* n7nics5v* -it 30 N, pull on an object in directions that aav*7i. 74of z oecvil n5;lgid v 2*s-*nd-tctre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector iseefxhd s,.a, ki+d62*bs4 w3r q,mq(:d zmk la

  Ignoring air resistance, the horirxd8l 3a+bzo( zontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle drvn w o,p+x:5of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistanclk bdpz rxi1( e:(g.r,e, the horizontal component of a projectile's acceleration biz 1r.e:(d ,xg(pklr

  A soccer ball is kicked with a velocity of 25 m/s at an a0xb6/0qabnm.0wlp jkngle 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-parallel togp:intv t*0(do6y(zrn )6e:q ;wzas u the velocity vzuwg6 6ra*ozen p0t()v :;(ntyisd :qector,

  If the acceleration of an object is always directed perpendicular to its velo 5p p *, f*4aoqaokcs2ge0y2ei0burp/ cits q*ac e,y*bau2po 4/ ger5 0ppi2of0ky,

  At what angle should a water-gun be aimed in /h gk q ps1c8/zyprc x *kw0zacdf6)90order for the water to land with the greatest horizokczh*61r 9y pczd0 qsc0p8/aw/g)kxfntal range?

  An Olympic athlete throws a javelin at four )50og ax0:aiot8ki5a9 vv f blj8jfk;different angles above the horizontal, each with the same speeda08)loibavk0fv j9jokg5: 8; ixf5ta: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 z :q.5nio k4dkhand with twice the velocity it hn.okq4 zi d:5kad on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at mn;xff.jpg)8n*dzgtmw3 o:j+et *i( 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 ream+k enx md*701n wg7ibches its maximum height, how does its speed compmb+0k en m1gn77xdiw*are to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a b/) cg7fmnhn ;tall is dropped vertically. Which object is traveling faster when i; )g n/hcf7mntt hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second .8 xaifv( nea.bullet is dropped from t.fx8 vneaia.( he same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed l9vlj9h4y8s9pt lhcv0tot6 x yf-1t .ir( g t:of 86.9 m/s and at an elevation of 174 m drops a package. 5.7 seconds later it drops a second package. How far apart will the two packages landh4lhrv.1v:l t69t to9x 8-(tfyc0s9tgilyjp on the ground?

  A package of supplies is dropped from a plane, and oi-6fxcwa-te ptl .27: zm-ttmne second later a second package is droxwi ztm-ecpa - 72 m.tl6-:fttpped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flyli 6.,j fqy/ 1jb2x io3rh xd7/gfrsx;ing horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane willojjf1ri db/ih3;x6.r ,xgs2x fq l7/y

  The acceleration of gravityuv*w l 5eyyz 08gjko+xq30uhv5z-vu . on the Moon is only one-sixth of that on Earth. If you hit a baseball on the e8*h5 zky u yv xu300.wzo5-uqj+vgv lMoon 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 bhu j3 :bs4h 48 c h)gd/s-qyjyhin.k.the +x axis relative to a straight, level road and pass a car traveling at )yych. s/bi .84 dhk4sjghu n j3:qhb-45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong currejp0f am. nj4y.jjbzjr/l3+ u)nt. You start out in your motorboat on the east bank desiring to reach the west bank directly west from yf + prj)maz0/y .j43jjulbjn. our starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much rmayzq1;we1 2sy(j mkx,r749fsub0c time will it take you to move 12 km downstream,u4e9,yx72ymkqs(w1crmf0 a1s r jb z; in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an zn ab*vrp.61langle of 30 degrees below the +x axis. The ybzvp* r6. aln1 component of A is

  If a ball is thrown with a ve 2j dy52b; jwujubloc d)1-q9alocity 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 azo2q 4+d u3dddirection north of east and you end up 2.0 km north and several kilometers east. How many degrees d+3u4z daoqd2north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s.gq1pf4 yy+qd+xb x.m2 The x component of its velocity is 8.0+ .pq1yxf bm+gx d2qy40 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At7eq k (o6lkultz(1+,gy0e0f-cog l of what angle is the Sun eogku oey 0l +0gf- 7lo(1fec,lkt6( qzlevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiveg+ /x8cur* vlnaz8a*m*a5 qmvly. What are the components of the sum of thesxnmcavr 8/q8u+zl*g*maav5 * e two vectors?

  Two vectors A and B havesperm-k* l40 zocjl5: components (0, 1) and (-1, 3), respectively. What is magnitude :j*ml4 k0-zep5 solrcof the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + Ba; jdg 4(vcs/g . What is the magnitudeg 4vdc/a; (jgs of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its displatb sn,l ;)+r7*mv pgke2mc3 kfcement)7e,f*kk;c2m r3st g+bv lnm p?

  Three vectors, expressed in Cartesian *5egb lc 40dbjcoordinates, 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 5pm;zkix o-.cnqb ca 1b:4i *wCartesian 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, -8.0u b9(zt 9i+ (f4bqpxrn), what is the magnitude of vector C = A9ui(pq( bx4tr+9nbzf - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the e-ixvu wt5- 2y.sh -l.9ptkj udisplacement of the jogger2-v5i--ytk .tp9x ewjsh.u ul?

  Two forces are acting on an object as shown in Fig. below. What is thp/) lqsu/(u843qn c ja 5 .dv2pzpdypxe magnitude of the resultant force52pnd( a.p/qv8y)c 3 jpusudx 4qzpl/?

  Two forces are acting on an object as shown in Fig. below. What is the directiolz2 i1c9* ldjdn of tjdd2z ic* 19llhe resultant force?

  Vector A is 5.5 cm long and points along the positive x axis. d:-1q.kl q sv7 vrx/h/j 4nwnr Vector B is 6.8 cm long7ns: w 4/vd./xk1rq hrljq v-n and points at $+59^{\circ}$ 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 50 cm long ambgu7 b k/:g d,;jpfjiud+v59 nd points at $30^{\circ}$ above the positive x axis. Vector B is 23 cm long
and points along the negative x axis. Vector C is 28 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 horizorbi 3x ;b;9f8d.cfqnnud7j o7ntally with an initial speed of 25 m/s from the edge of a cliff. A stop watch measures t7;x qduf873ndi o bb f9.;rnjche stone's trajectory time from the top of the cliff to the bottom to be 2.7 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 11 m/s, from a bridge 7xf wyfyjs9k838k5zpx -6qlj . It falls 14 m to the water x5xls3fjpwyq876 f-ykkz 8j 9below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m abovey3d1kl. 8b s 2yan*6qhvw75 oreoy d6q the ground, strikes the ground after traveling horizontally a distance of 22 m. With what speed was i h2o8ysek1d.qa3* 5y y7vwbro6 nl6dqt thrown?

  A jumper in the long-jump goes ik7lmfsz 6e0;qtz-qc1+f dr5 g nto the jump with a speed of 12 m/s at an angle of kgffc;1zd+65l 0 -mt e7qsq zr$20^{\circ}$ 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 at6uln q8c*d1s q an angle of nlu qq 1*86cds$20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initialj 3x +4cr q66vtf:yise velocity of 45.4 m/s at an angle of $42.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 20.6 m/s at an angle of zz*-j-hyjv:13 thoi e$13.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired al; xbl7 ujxg,u1: f 0+bsfp(+zngqf)et an angle 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 25.9 .. dzir3wqq3w$m/s$ from the roof of a building 36.8 $m$ 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 speed of 59.9 m/s qumr; r; j.hzd5zu 27uat an angle of r;u5u mz 2q7u dj.zr;h$40.8^{\circ}$ 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), you8dxtgp8(zb o - can run a 1500-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 wodgp-8 8 xzb(thich slows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air s8p 3 d9cjlk5glpeed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed re p9ldj 8ckg35llative to the ground is

  A plane is flying due Sa79ateb6 qu4q y eww1yurp+5w6 :g6 yjouth ($270^{\circ}$) 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 spn.u.1 wp 1 3orxxqh-ueeed of 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 horizontal6 dcibr7gkxk +l 8l -4.zw4(iei od(ooly fires a projectile with speed 50.0 m/s ik (l4c+rii- 8xd6b7w (4zeo i.doglkon a forward 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 s(1q) vy-,hk v3mzreu1yvwi,htill water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of th-vv ukzhq3iwye ,yv,1r)(mh1 e boat as it crosses the river?

  The driver of a motorboat that can movg/4yshho e t*/+hp u1ve at 14 m/s in still water wishes to travel directly across a river 0.6 km wideushe vhy+/tg*p4 o/h1 in which the current flows at 4.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/si0,*zf;cn rgd.joy2cf +rff 3 in still water wishes to travel directly acrosc+ofgrr.0zci; j d fny*f f,23s 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 reapa *ko2n(n yl. (5x),osuvxo ;,sz m1e1kiqv aches the opposite bank in 6 min 40 s. Shezn(y(ss2unpim o )lo,qakekxo.1x; 15 ,v*av 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 oppo1oax b6nrs)d( site bank in 6 min 40 s. She is swept downstream 480 m. What is the s x1rn(boas) 6dpeed of the current?

  A boat, whose speed 51ma( mr*zlrne7/suz z-4 swhin still water is 1.09 m/s, must aim upstream at an angle of n/1er*s z7zm(a -mzl54wrsuh $27.1^{\circ}$ (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)  $m/s$