Which one of the following is an example of a vector quan ng0ro ,vk vuz4-afl//tity?

  Which of the following opet9/d m,ea:lh9k jwz vvzd+i(9 rations will not change a vector?

  Which of the following is an accuraw 08p 6lrqzhf-te statement?

  The resultant of two vectors is the smallest when the angle between themw qn ro)a9qm,ylby;n0c2, 3oj is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respj18z-gi :sq(h du b0ocectively. When these two vectors are added, the mquib(h-j8 1zgcd0:so agnitude of the sum

  Two vectors, of magnitudes 20 and 50, ar+jixzrxp7*s6+q2 ta 8 hllgp6e added. Which one of the following is a possible answer for the magnitude of the resul+pj6 tplax +*l2g8 7xiqh sz6rtant?

  Three forces, each having a magnitude of 30 N, pull on an lh afit-1ax+ xik;wra( 3m(-jobject in directions tha3+ jta(x -hm -x(fail1iw kar;t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecsx n0x:l,d+kctor is

  Ignoring air resistance, the horizontal component of a prelyl.v03y4jxzdp6 : k ojectile's velocity

  A ball is thrown with a velhs w cnjz.t)q2, n0i/55soj72unwr 1: msra pgocity 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 compone9qpxkde:y)(cu; wb ec- a* j.wnt of a projectile's accelerationwpx ebq e.(cuw*cja)-yk9 d;:

  A soccer ball is kicked with a velocity of 25 m/s ktm 7mwjsmh1 pi15 f+avp,8;uat 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 direcymy4 i ,l+q d*zpmk*0cg oh;,qted anti-parallel to the velocity veykd,impy4go*qqc m , hl0;*z+ctor,

  If the acceleration of an object is always directed perpen o-a*pmgsz+t 222wz lhdicular to its velocity,2+ga*ohp2mswz2t z- l

  At what angle should a water-gun be aimed in order :us7 w7wp*tb -2hel0f4jxzr6en1 ug l for the water to land with the ge0e*jwngfz 4 6huptx:-7 1 ls2 7urblwreatest horizontal range?

  An Olympic athlete throws a javelin at four different ang*kaun ezh -cv/2xp)-a les above the horizonta2e*a un )kvc/-azxp- hl, 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 ball leaves your hand with r,n.zuoqhn y.eskwf:9w/m+* twice the velocity it had on your first throw,z:nmwknhf. 9 *yu,o/rwse .q+ its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed 7 a/ga*rwpj,g 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 fw:y6pg6b)fx94l s (f0) i6pjjl tcnyu ield goal attempt reaches its maximum height, how does its speed compare to its initial splfls9)p: 0ijt(xb g4 6wj66yf puny )ceed?

  A stone is thrown horizontally from the top o , dsuz,qdc lx,1oc+)vf a tower at the same instant a ball i lsou,,+q)c d1z,x cdvs dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired hori,a 8*m4ucldt--i qwaizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bulletstiaciwm* 4q-u-d 8a, l.

  A plane flying horizontally at a speed of 82.7 m/s and at an elevation of 181 bb,izk c(tdi 0fp*5w4m drops a package. 3.6 seconds later it drops a second package. How far apart will the two0tcw4f(b5i kidb p*z, packages land on the ground?

  A package of supplies is droppeezzulp4 +rf 4vl)-v7xd from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between tvfuz- 47+e pl xlrvz4)he falling packages will

  A pilot drops a bomb from a plane fly4t 2o 5*5s kow /dbcl8ze7mliring horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane db5re/ tl7 kom8loc sw5*4z2iwill

  The acceleration of gravity on the Moon is only oncsvc8 ,hf ;c7ko4jdcfqj zfp1*1 d18le-sixth of that on Earth. If you hit a baseba1jlc dhcf pcf7 osv1;8z,4jq 1kfc*d 8ll on the 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 2of413ja nqwn mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car isj4wfo 1q3an2 n

  You are trying to cro+ dqgjk 5g1os1ss a river that flows 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 gjd+q gs5o k11your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h ib4z4sob-rvu.h::o g vn still water. How much time will it take you to move 12 km downstrea4 ho4 zo:b. bsv:vgru-m, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belowky b/e-avs)ir02n n. a the +x axis. The y component of A i-n ivk2be a0ay.nsr)/s

  If a ball is thrown with a velocity of 25 m/;*y qch, bgq +9ckktepm()b;f 81cbqrs 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 east4rygb.a 2 .cxf and you end up 2.0 km north and several kilometers east. How many degrees no4cagr .. 2xfybrth of east have you walked?

  A butterfly moves with a speed of 12.0t2r)u2)on xpv 48sfz e m/s. The x component of its velocity is 8.00 m/s. The angle between the diexv8zf ) 2)not4 u2sprrection of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long sh kjp7s, n.nh;y;va;n0 fj.h gladow over a level ground. At what angle is the Sun elevated aboveh p n,gh 7knavjn l;0y;j..;fs the horizon?

  Two vectors A and B have components (0, 1) atx fbc m:)p*7h7ibf.x0 p8ueind (-1, 3), respectively. What are the components of the sum of teumcb*t7 87:0ppxib xh f.i)fhese two vectors?

  Two vectors A and B have comph*g j6wkdd i:.rh)db1 onents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these twojd dwgr: k.ih61hd)b* vectors?

  Vector A = (1, 3). obv8j8yj3; tc0ort6sVector B = (3, 0). Vector C = A + B . What is the magnitudct 0oob8j8 j ty3r;6vse of C ?

  A car travels 20 km West, then 20 km South. What is the magnita/ ,0r rtyzpk/ude of its displac, 0 r/tarpykz/ement?

  Three vectors, expressed in Caesiy3:asoy1)0(hpikza4qb a6p2 h* mrtesian 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 Cark*hu t9dvv7tnw,(t b 6tesian 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, -46zq6:ipxbnz: .0) and vector B = (+3.0, -8.0), what is the magnitude of vectozzn :6pibq6x:r C = A - B ?

  A runner runs halfway around a circular path of radius 10 ) .my dq ya.1fk2shn7ypj)l.tm. What is the displacement of the joggeyhty1al. f q 27kps..)y)mndjr?

  Two forces are acting on t zq+8 zbmx:cr,upt+( an object as shown in Fig. below. What is the magnitude of pub+c, q(z:ztmt+x8rthe resultant force?

  Two forces are acting on an object as shown b r1 9/b)1zitg3hkfrkin Fig. below. What is the direction of the z3 )h bbrkkrf9t/1gi1 resultant force?

  Vector A is 5.0 cm long and points al5unx(;/daa zmpb-z q*k07 afh ong the positive x axis. Vector B is 8.9 cm long and poud-5azhfxq n7/pkz0* a(ba m ;ints at $+25^{\circ}$ 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 61 cm long 0w *b tvjaof( c8,38vr)zgv.hf) spyuek)f / sand points at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 34 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 29 m/0 l9tbjuu:q b2s from the edge of a cliff. A stop watch measures the stone's trajectory timetlu2j :90qb ub from the top of the cliff to the bottom to be 4.5 s. What is the height of the cliff?

  A girl throws a rock hor. hs2mq;y 5vr/rfq a)nizontally, with a velocity of 13 m/s, from a bridge. It falls 14 m to the water below. How far does the rock travel horizontallrr.5/ yf);vmqsaqn2 h y before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes the grounqb +d 0p/ wpn2bi/7e/nwb7 awqd after traveling horizontally a distance of 22 m. With what speed was it t2bb i pwab 70w/p/7q/qd wne+nhrown?

  A jumper in the long-jump goes into the jump with a a/o c-du /h6ktgr)dm.speed of 12 m/s at an angle oc/da mogr uk.)6-h /tdf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump 2roda( g(5ko/x 6af:lhmmu9a goes into the jump with a speed of 14 m/s at an angle of5k9 ad/ l g f6a(hmo2:oamx(ru $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an i ja)k h)nlkjuf0 gb7/hb* x 8*3idix/onitial velocity of 57.8 m/s at an angle of $30.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vel )8b9qlfdo 3icr.w,c0y 2;)m p jh;lkobvt sb4ocity of 55.0 m/s at an angle of $30.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglefre6l kh7kv,bm v9u* 6 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 b:u4q)4lp-f ee de+5q yjd5 auhorizontally at 27.7 $m/s$ from the roof of a building 54.3 $m$ 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 -m2g. vha bd+wwith an initial speed of 52.0 m/s at an anglevg+ adwm.b2- h of $42.7^{\circ}$ 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 can run a-amd. gwz0.pn hj3oq her6,n +vbn5a/ 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 which slows your speed by 2.0 m/s, the time it would take you to finish woul 3-h ad 60o ./rmane ,hzpgbn5nv.w+qjd be

  A plane has an air speed of 200 m/s due North,x 4r7sq ptf;;,g vl9we and is in a wind of 50.0 m/s to the West. The plane's speed re 9sfw, ;lep4vqg7rt;xlative to the ground is

  A plane is flying due Soutbx t,vkifs i3mgr-rhs)4v ylja 35/(, h ($270^{\circ}$) 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 speedp dg,*kj;.aj x 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 horizontally fires a projectile with speed 50.0 hjh ld6hs/1pbt -n) 9:hxga)am/s in a forward x)ht1a/g)b j n-hd6lhsa9 p:hdirection $30.0^{\circ}$ 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, a1gju * kx47udd.w,b6rroev -is directed across a river with a current of 6.0 *dx 7 jur ga1ku-ov4.bd,6er wm/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 9 m/s in still water wihy 6)h vuj,8uzshes to travel directly across a river 1.7 km wide in which thezh8 uy)u,6j vh current flows at 3.7 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 wishes to h(1 mx7l13lzcp1qhz x/ ot,7gatru8o travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream sho/zt 1o 7u1lx(7 xtqz clhp,oar ghm138uld the driver head the boat?

  A swimmer heading direz pnnowqpl3(mb+ e:d*2z wt/2ctly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fasww2 znbtmdo2 l*z p:q+pn/(e 3t can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the otc(m u36 9qtgedr; hi,pposite bank in 6 min 40 s. She is swept downstream 480 qrg d e6tm hu,it;(c39m. What is the speed of the current?

  A boat, whose speed in still water is 0.89 mcqet8 z 6;lrsq v5;we s75+eso/s, must aim upstream at an angle ofo75vet5rwe+ ;;8esqzs6scl q $25.5^{\circ}$ (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)  $m/s$