Which one of the following is an example tiw vm 9+u)iislr7u2 -of a vector quantity?

  Which of the following operations will not change a vechfp)*w2fxks2m fh1t(bu k+e3tor?

  Which of the following is an accurate stateu**q lojl)t-a;gnd p3 ment?

  The resultant of two vectors is the smallest when the angle betwevlrb91o9 3cwv r9i.jcbt d+j:en them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectiv0xhz *1qfyb 8cjqa8v /ely. When these two vectors are added, the magnitude of thc1/*f xhqb0ajvzy88 qe sum

  Two vectors, of magnitudes 20 a 5ixbec9/h7z p- pj cd2r8( i-;ywnhfhnd 50, are added. Which one of the following is a possible answer for the magnitude of te/8pjn ih(ihcw bx;rpfc z7-2d59- yhhe resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in d*wh:oaz;dq. tp/ y5 2hts3 lcdirections that are/5z:y scldoah td*.phq2 3;tw $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the 9rv g)))wd(v vbuzr 0punknown vector is

  Ignoring air resistas58k:8ey cn zdnce, the horizontal component of a projectile's velocity

  A ball is thrown with a veloci:o8e 4nnpi:(nr+d xjcty 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 horizontal component of a project.svo: se1mkuj* 8 /fjrile's acceleration*f.8v mju/sker o sj:1

  A soccer ball is kicked with a velocity of ;vf hr j5id8ym,sk4f* 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-parallel er-jko-07jard 47wx6 ipci a0to the velocity ck4j0rd7owei xaj - rp6a-0 7ivector,

  If the acceleration of an object is always directed perpendicular w; x(td o5,f+14gbbko,ksrg57njpxw to its velocity,5o(ks1 k wj5;n gr7, 4o,+ftpbxwgbdx

  At what angle should a wajqd16zz 3mla 4m(e4 va q6*cydter-gun be aimed in order for the water to land with the greatest dela dj4(zcmqq61mz*3y a4 6vhorizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizontg n, z0gqtp.vxd 2(w-kshf-uar57 t.gal, each with the same spetd 5gh-. r- zugpnw,ats7.k q0gvxf( 2ed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for t f.hm1acp r 2h/nw1op6xx.bu; he second time. If the ball leaves your hand with twice p c.uo1;. wfx1h/2xpbr nh6mathe velocity it had 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 an ano-u kt 1d)qksr- pjq: ratm022gle 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 ma4eqhg p65n2lo ximum height, how does its speedo2e5 gh4q6nlp compare to its initial speed?

  A stone is thrown horizontally from the top of a tupd*x psl- 6opko*1 r+ower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground beloup+d*k *lxr s6oo-p1 pw?

  A bullet is fired horizontally, and at the same instant a seconysm36 v:ni.x t7ryeu79lkkbv -l ty/2d bullet is dropped from the same height. Ignore air resistance. Cov t 7- k37blsi:euk.xly2r /vyny6t9mmpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 48.6 m/s and at an elevation of 123 mhq: osh 5 ydw957in5ht drops a package. 6.6 seconds later it drops a second wi:s7 tqn y9o55h d5hhpackage. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a pu4nt *2ptzhqq* 73q gvlane, and one second later a second package is dropped. Neglecting air resistancen7u v t*z*4qhpgq3qt2, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizo ru;or gcw2 5)sn)0tfdu ni+0yntally at a constant speed. Neglecting air resistance, when the bomb h0 u05ns yc+fg o 2;)nruwtird)its the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that ot)9hoa7grt .(7lxtp eyfqc2 5n Earth. If you hit a baseball on the Moon wfa7(. tpxeto92y t)gr7lcq h 5ith 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 * +y adoa2nz k-*,ml kfk+y*myaxis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative vekkmf ymad *k,lo*- a n*2+yzy+locity of your car to the other car is

  You are trying to cross a river that flows due south with a strong curi+s4d*pj/d(3- dg5 h amq kmbarent. You start out in your motorboat + - gkha5 ddj 3(*4apdmbsm/iqon 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 still wlx uk5hm5ljg 8uc7 +jzemp w949xb43zater. How much time will it take you to move 12 km downstream, in a pu93z45lgx wchulj 8jekmbm5+x7 z94 river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 db2fkt+vn ;i9legrees below the +x axis. The y component of 2lnk;iv 9tbf+ A is

  If a ball is thrown with a velocity of 25 m/s at al+j:+6 hh6el* zvrzs5i xzp.a*r zze9n 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 eas7 h tbk2pdrjtoz3jn-53 crh1 5v,mbh+t and you end uvtpm- cnh drbrbtzj73k+25, j 531ohhp 2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of.md l/.v;w/meztxg4)o0 c b wb 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its moez 4wvml;tmbwox/ b)/. gc.d 0tion and the x axis must be

  A 400-m tall tower casts a 600-dejm 5u-hdu .xdz-x - a;t+ o,q.bekq2uh/u5hm long shadow over a level ground. At what angle is thq udtx.bxh -.e/ udmza j-h2o-e5;dq5h kuu+,e Sun elevated above the horizon?

  Two vectors A and B have components48 sz,251zsajk+jyhd4eb usp (0, 1) and (-1, 3), respectively. What are the components of the sum of these ,y2kzd s j 44b85ae u1shjz+sptwo vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatvg4 9ckt +y+sgh: q4ct is magnitudvty hgtc+4:q4s9 c+gke of the sum of these two vectors?

  Vector A = (1, 3). Vector vj 2u 25d6z )gq+gsjlbB = (3, 0). Vector C = A + B . What is the magnitude of vs+ud)bg6jg2 l jz52qC ?

  A car travels 20 km West, then 20 km South. What is the magnitude ox,1 gl,p fif0w2lo*fi f its displaceme,21 xwilf 0i,g f*lpfont?

  Three vectors, expressed in Cdnatvh3k+,xox v,)t)cs p4 7 martesian 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, expressedz 2v8lu8b0-7i wez bmj in Cartesian 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, 2 zu*bdan2n;(d q9rs p-4.0) and vector B = (+3.0, -8.0), what is the magnitude of vecqzn(p 2udr9;abs*d 2ntor C = A - B ?

  A runner runs halfway around a circular path of radius 1shjm i;j6dw*7q;xb(p 0 m. What is the displacement of the jo*ij;xm j;bd(sqp7w 6hgger?

  Two forces are acting on an object as sh/ a0iu1ih fexwyz.2d;own in Fig. below. What is the magnitude of txyh aid12zw.u;/e fi0he resultant force?

  Two forces are acting on an object as shown in Fig. below. What iti:0*b qz0ihd s the direction ofb ti 00*hd:izq the resultant force?

  Vector A is 5.4 cm long and points along the positive x 6) ltzx;zhg1 3q ccno1zn8/qiaxis. Vector B is 9.9 cm long and pozgnz3/inc xh6181 ql cqtoz);ints at $+58^{\circ}$ 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 78 cm lonm h7 dd/mwq8f5 lup6zg1ld6 9ig and points at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 24 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 of 20 m/s from the e6s4r* -e;tok- zlhdyo dge of a cliff. A stop watcys-kelot *;rzh 4o -6dh measures the stone's trajectory time from the top of the cliff to the bottom to be 2.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, from a bridge. Ia1 /( aqrs +x8yvnk-ugt falls 16 m to the water below. How far does the rock travel horizontally before striking the wkvx- r 1/(ays8auqn +gater?

  A ball thrown horizontally from a point 19 m above the ground, strikeuj7o2w arg l93s the ground after traveling horizontally a distance of 19 m. With what gorajl wu 7923speed was it thrown?

  A jumper in the long-jump goes int 4.p*nmu 4h )4kdbdwiso the jump with a speed of 12 m/s at an angle of ud n4*khd)4mwi.4bsp $20^{\circ}$ 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 qae1: 5+7r cfx zfwz3lm/s at an angle ofl7xzf+c:q efa1 w 3rz5 $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an init 5,ew;3l4 mrmcic)kbm s:;wilial velocity of 46.8 m/s at an angle of $49.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with y7z*i3h gudoj f*ps1,t fxa4-an initial velocity of 42.9 m/s at an angle of $27.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofms v6s-/kxv :paor/z pq;1; fe $30^{\circ}$ 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 16. fg m: o4pc,kvuv lslz.(u8,l+9 $m/s$ from the roof of a building 50.1 $m$ 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 init mm n7;0pjht5mz7hs.rial speed of 39.9 m/s at an at7s h m7 prz.mjh0m;5nngle of $45.6^{\circ}$ 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 run0mq) l 2 ncefhd8, f*/qrxxl-r 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 constn,d2)lxhq r0 /rqm-*8cfle fxant 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/s8u evzs f3c1wd9fq6a9 due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to sq6c3w99vzdf 8uaf1 e the ground is

  A plane is flying due ua-avcu x3 7x-xo 0;rl.l3 jxcSouth ($270^{\circ}$) 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 sojpv+u+ 3e/;xvg)on kpeed 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 205q5 ccnomvgqmwi i: ;w; ,/8mz0 m/s horizontally fires a projectile with speed 50.0 m/s in a forward dw q8z 5:winm,o 5mgv;cimc q;/irection $30.0^{\circ}$ 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.cvn*it3:0c l 6tzgduj*r)v;u v ub3;g0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the b uv j0 cniu3*z:g6c ru)*d;vb t;vg3tloat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in s 7e7ni:ad a;6ukezn8 htill water wishes to travel directly across a river 0.9 km wide in which the current flows at 4.1 m/s. ni6 haze8a: kdneu7;7 How long will it take to cross the river?

  The driver of a motorboat thoz c(d5tk0k4 glb3 ua7at can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the cl(0b 3ck5dzg 4 ta7uokurrent 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 reaches the opposite bank idi 6(t7+xuiekd br-/jn 6 min 40 s. She is swept downstream 480 m. How fab/7+t iud dkexr6j- i(st can she swim in still water?

  A swimmer heading directly across aqa):9w/wj nlbkix - wak5*h t. river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the -*ina.l:kj/ 5 tk 9q)wwwab xhspeed of the current?

  A boat, whose speed in still wate8qhn9yq0 .m,e ;cyqymw*4 oml r is 1.79 m/s, must aim upstream at an angle of n0om4;q. yyq wqclm*meh 89,y $22.6^{\circ}$ (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)  $m/s$