Which one of the following is an example of a vei8k ;q/u. li;)yjakx rctor quantity?

  Which of the following operationsqv p5h+ h)grn. will not change a vector?

  Which of the following is an acc4zv0ow mqi94de*s,yc z xxk9: urate statement?

  The resultant of two vectors is the smalln)n,uu o px ah7yg4lo/eg,-7l est when the angle between them is

  Two displacement vectors have magni 1yq9l8yl7 vd er0 h0dcj4ado,tudes of 5.0 m and 7.0 m, respectively. When these two vectors arehj1,0vd 7eq 4ao yrl8ld dy0c9 added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the folljt8qvtq.6 3z sowing is a possible an6 sqtjqt.8z v3swer for the magnitude of the resultant?

  Three forces, each having a mqtci8 66iwc8s agnitude of 30 N, pull on an object in directions that ci8wi6c6tsq8 are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownrz+9 e5 gwj6 pfxw**dh, the unknown vector is

  Ignoring air resistance, the horu3utix x+m 3w/9g+tdfe n4-i( 8 putpfizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/2,jav:p c pdg23+syg us 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 projectile'sqx(hs)yg). gu o*1 f,gu 4fnyg accelerationhfo1yu4sgyf),g )qgx. (n gu*

  A soccer ball is kicked with a velocity of 25 m/s athrd( n,8g*ue u 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 to the velhicr*7,zedqe( pf 98bocity vectec(deh q89izr, *7fpb or,

  If the acceleration of an object is always directed per:jxh;871w y2ctsuqx) t n*tpf pendicular to its velocitp7w;hs1:2c t8*q)j ux nt yxtfy,

  At what angle should 82 * j+q g,k+,vt irjozp-kjbya water-gun be aimed in order for the water to land with the greatest h *oqbgt-kvkj+ rj,2 j+z,iyp8orizontal range?

  An Olympic athlete throws a javelin at four different angles abo) nbfy69r7thhf .z rh6.0h jbrve the horizontal, each withh7 j.ryf06 hh6 )9fn.brrhzt b 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 wi:-sw*c;pc3g z cj,i1vot kn .qth twice the velocity it had on yo: cpink13 cvcgq, ;oj.tz *-swur first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an orig *9dz -m.lnixbinal 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 reacheumwc5s 0xd ro*;r (arh )nd.f-s its maximum height, how does its speed compare to its initial speed a-dd( rwxon)hr* ru0f;s m.5c?

  A stone is thrown horizontally from the top of a tower at the same t5m* *p0+0ushbkavf j instant a ball is dropped vertically. Which object is traveling faster when it hits the level b*f0* sk uvphjtm 5a0+ground below?

  A bullet is fired horizontally, and at the same insta7d:mzj g c,x7fis d14mnt a second bullet is dropped from the same height. 77 fi mcgd mj:1x4d,zsIgnore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally a0 : /h2grms p 41pi8.p-g:zi tjxylgjda0 :xmet a speed of 58.1 m/s and at an elevation of 147 m dro:8 hg/p.sd:2g:az g0 0-tjimx1m4 piyrxe jp lps a package. 4.1 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped fromc)uxl6gb)6 sz a plane, and one second later a second package is dropped. Neglecting air resis6ublcx6sg z) )tance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speedz kd95px;q os4p/si2v. Neglecting air resi zs 4pk5iq/9dpsxv ;2ostance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only oney8:i ky (db :5ntawp1t-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you wo: y(b 5 8t1pntayw:idkuld on Earth, the ball would land

  You are traveling at w(vqjg 50wqz555 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/ww5jgqqv0 z(5 h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due souyber091mx xjqyjc 1q qz3s8d)nfj m2r8a2h6 *th with a strong current. You start xy y816nx92je jqrd8f cq*r bm)23 0hz qa1jmsout in your motorboat on 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/p*s 6wvb) qclx9rp( 6(myyld-nk- 3wuh in still water. How much time will it take you to move 12 km downstream, in a river flowing at k9wq)py-vuym6wds*n( cxplr3 l (- 6b6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. The 81 9lv,nvs zvcy comp s1lvn v9zvc,8onent of A is

  If a ball is thrown with a velocityg*y.tou( x.s /k e(xbgtp )9wt 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 directions 04 u mhss +9.ahn9l8fnizkj* north of east and you end up 2.0 km north andsl.f njz ah8n09m +s*i k9hs4u several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its veeu 8oyhpmlfsh70; - iu(fn ()clocity is 8.00 m/s. The angle between the direction 0s7h(y hnu(cu-o;fpeil m)8fof its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angla95tw lu iip60e is the Sun elevated above al9t i05puwi6the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.j1q3e: yh lp(b What are the components of the sum of these:(h l1 yqj3bep two vectors?

  Two vectors A and B have components+w5yzobf.z;l z p5k(e 2ccpxaz)le.3 (0, 1) and (-1, 3), respectively. What is mce w.z5ekxbzo.zlc 3 ly pzfpa5+(2 ;)agnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3*x v9w cs/pgbu74( dgx, 0). Vector C = A + B . What is the magnitude (94dv g g*px/sux w7bcof C ?

  A car travels 20 km West, then 2r j* pikwy)07j0 km South. What is the magnitude of its displacemenw i)j0 jypr7*kt?

  Three vectors, expressed in Cartesian coordinates, aqix54.yfv 6 4gn lc9fbre
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 Cartexsrgd /8yq9t 0sian 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 the magni8obtlyf 5u07o l ;o:pktude of vector C = A - tkpf: 5yl uo07;8loobB ?

  A runner runs halfway around a circular path of radius 1j)m1w*q+ p5t1unjhk s0 m. What is the displa1 1p hmjn)+tk*5swuqjcement of the jogger?

  Two forces are acting on an obje dqv/kt :gj:own+v 4i)so +gd)ct as shown in Fig. below. What is the magnitude og /n + 4g+jkw :)t:vvdo)dsiqof the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is m :8tg .bvd4lothe direction of the resultant t4dobg: .lv8mforce?

  Vector A is 4.4 cm long and pn,:xays4/zv5 +dokv p)d 4qdaoints along the positive x axis. Vector B is 9.1 cm long an/yv45d +ov )p ddqan,:kx4aszd points at $+36^{\circ}$ 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 76 cm long and poi4t pl5 k2,xszpnts at $30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 33 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 spece: l 10sulxbizz4ebir i05, (-fu,vqed of 10 m/s from the edge of a cliff. A stop watch miu5ez1 xq,c b 4:r ueb ilfzv,0-il(s0easures the stone's trajectory time from the top of the cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, witoko i)*zye135 )kdt4n byiju )h a velocity of 7 m/s, from a bridge. It falls 21 m to the water below. How far does the rock travel horizontally before striking the )eiin o3b4ktou1d)y* jy5 ) kzwater?

  A ball thrown horizontally from a au4uz(a5hw x8 point 25 m above the ground, strikes the ground after traveling horizontally a distance of 15 m. Wauwx5h( zau48 ith what speed was it thrown?

  A jumper in the long-judz bxsr :)e g8n-9bybuub 26w.mp goes into the jump with a speed of 12 m/s at an angle or8)wbz9dux:- uns.6b2b bgeyf $20^{\circ}$ 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 ju+w*9v x f, c4vvu(p vbkdi-7iimp with a speed of 9 m/s at an angle of 9v*k,+cdfib-vpuxiv 4v (7iw $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 25.3 m/s atqbix4 )khn2cy h(gd4ek f/r:3 an angle of $30.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity iuw kq,jg30 0brh1r35rftjs5of 43.4 m/s at an angle of $32.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at deztaw9pos lh rz;1; 8d)s2p(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 horizontall1 xy +gc0y esvd,pb*4yy at 23.9 $m/s$ from the roof of a building 69.6 $m$ 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 wil4mq.) g*bh xdth an initial speed of 44.0 m/s at an abl. 4 xh)g*mqdngle of $47.5^{\circ}$ 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 vel5 c.1btpqgej0 ocity of 4.0 m/s. If you ran the same race on a qjpt 0c1 .ge5bday when you had 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(azouq qem3a;74+ y g8xqtj3s due North, and is in a wind of 50.0 m/s to the West. The plane's szae4o u xj3ymaq837 q tq;(sg+peed relative to the ground is

  A plane is flying duiy mnaeyra).b hkqf-1c2z/1wb q7/ )+ae ss9he 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 head.icg sv6w,43u+fh ah 7bq7l3o sa;qryed $30.0^{\circ}$ 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 horizonhly31y wzz8nv)2e -untally fires a projectile with speed 50.0 m/s inn3n8uvh-1zweyy) z2 l 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 still water is 8.0 m/s, is directed a c;busfcnb,/ 4h z 4.a dasqwp,5pu1h/l9f)uicross a river with a current of 6.0 m/s/ lfw 9hs1 p quz4cfs4c ).,p5;da/bbuaiuhn,. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can movbtnf9/ ogi3c2k/m xf8e at 10 m/s in still water wishes to travel directly across a river 0.7 km wide in which the current flows at 3.9 m/s. ti/gk8m92bx noc 3/ff How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in sti9 j.:c.vkcj ryjc) qt6ll water wishes to travel directly jq ) 6yjt.r jv9cc.:ckacross 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 reaches the oppos6g; avm/qe) qkite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still/q6keg)ma;vq water?

  A swimmer heading directly across a river 200 m wide reaches the opposit wk8btk3m* el,e bank in 6 min 40 s. She is swept downstream 480 m. What8* tkb3emk,l w is the speed of the current?

  A boat, whose speed in still water is 1.05 m/s, must aim upstream at ,(j9qu7 hs.r -3usnzv mazxs. an angle ofu.sr s-u.nz,qsj v (ah739zxm $31.9^{\circ}$ (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)  $m/s$