Which one of the following is an example of a vector quantixo avh,o 6n4y6lzx ,+qzo2/bdal+2 eb ty?

  Which of the following operations will not ua15d vg3u1 zmchange a vector?

  Which of the following is an accurate statementwc l1+f,il7pel 8 tm/n: tvyzbq ;e4d(exet2+?

  The resultant of two vectors is the smallsamim y.g q;85est when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Whenijaalkcs; ;j7l;y11bop 0ug6 thy6uolk1acji l agp;s70;1 ; jbese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followi7h5 - uw y/-7sl9wy,n ozf03nnzmp vlhng is a possv5w0/hz 9n yhf 7w7lyuslpn nm-3z,-oible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of,6igxh6xalw4r r)k-k 30 N, pull on an object in directions thaxh gk-, wkr6x 4)alir6t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vesu3 h( m;.ktfwctor is

  Ignoring air resistance, the horizontal component of a projectile's velocit4j)eprk.0 fk4 jbqq s;y

  A ball is thrown with a velocity of 20 mj0 a*i, bufe(e/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 projectil:yjeoc,7o r6ne's accelerationn7 oc,:or6 jey

  A soccer ball is kicked with a velocity of xcie qta l0,p1m/ do4325 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 ant of+kko3t 8tz;i-parallel to the velocity v ktkzf to+o3;8ector,

  If the acceleration of an object is alway ifd*qz8 ai5i l)jj*n4s directed perpendicular to its velocitq*n8i4i*f)j ij lz5a dy,

  At what angle should a water-gun be aimed in order for the water to lahia.yp m -/d93junbz5nd with the greatest horizontay 39adbujm./h5z n- ipl range?

  An Olympic athlete th5cs7 h skeiok7/ 2jni-8k:3ckuovj8r rows a javelin at four different angles above the horizontal, e 5k3isho:r87 -8/o2 jnu js iekvc7kckach 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 tim8 gwfod:( ly hef(.vc:e. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) wouldyc8he dog: f(.:l(fvw be

  A ball is thrown at an ort itu-- lin1(s+l.uzrgy . n3ciginal 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 maxi/nm: zgu leru*w3w i28mum height, how does its 8nmweulzu2 gw:3 ri/*speed compare to its initial speed?

  A stone is thrown horizontally from jc) ui .c7tyesxwe0c;a 6,7x nthe top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster w;e.,cw )n7 ecsj6u xxt0ciay7hen it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a seconw8 )f4qyjvy e x dyz;/26dpn,jd bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of theeq;2x dv/j p)ny84yf,yzjd6 w two bullets.

  A plane flying horizontally at a speed of 119.6 m tjo4j2+0busi/s and at an elevation of 220 m drops a package. 5.0 seconds later it drops a 0j 4u2otsj+bi second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, andb wk0 g+;6s.1llcysdz one second later a second package is dropped. Neglecting az+k.0 ;ld1blw csgsy6ir resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. ueotkdlr-mf+b*v*yp z e3 +;*Neglecting air resistance, when the bomb hits the ground tp+m d3ot bzu yr**+*-ef evkl;he horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on El oc/ -hfd/w,aarth. If you hit a baseball on the Moon with the same effort (and at the speed anoh c -f,d/lw/ad angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relativh +le uv1ouc,/e to a straight, level road anl+1v/ouuc ,h ed pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a rib.9r gej cn/( s*flyeb;h)*kiver 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 your starting pointneecihjy9)k b*b fr; *lg( .s/. You should head your motorboat

  Your motorboat can move at 30 km/hkh(r3w1s: cq e in still water. How much time will it take you to move 12 km downstream, in a river flows(3 whqk:c1er ing at 6.0 km/h?

  Vector A has magnitude 8.0 m mx,f4k(n2 npv+pw buvu)5* nyat an angle of 30 degrees below the +x axis. The y2 4 wunbmfy*v )p(+p5v xku,nn component of A is

  If a ball is thrown with a velocity of 25 m/s at an ang43h 7sl26b7.sn q gebv gk07fj grakb6le 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 92hhaa0 f0w fq 41axeqof east and you end up 2.0 km north f92h1awfhq40 0exaa qand several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of -aap +nd7x+ iy12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must-x n7+a+i pyad be

  A 400-m tall tower casts a 600-m long shadow over a level ijdeo 50 muol2o yaaz,a9.2k0ground. At what angle is the Sun elevated above th2,.ao9y0k2j 5emou0ilza da o e horizon?

  Two vectors A and B have components (0, 1) anm)1u pj;w5ua, 3 gxiawd (-1, 3), respectively. What are the u ji1)axg,m;a w 3p5wucomponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), re((s tsx r9tf/d; skqc4spectively. What is magnitude of/( 9 dqkftsr(c; s4xts the sum of these two vectors?

  Vector A = (1, 3). Vectordk0xq qhy2+c-pctq4y f szx;,d (z(t- B = (3, 0). Vector C = A + B . What is the magnitude of(p y;c0hkxx2,dqq-y s4tz(tzdf-qc + C ?

  A car travels 20 km West, then 20 km South. What is ypjatp e , 7qj8ohe su8hy8hq7.3(vy/the magnitude of its displa jeo7.(pvy/8y8j y8 3psheut q hqa7h,cement?

  Three vectors, expressed in Cartesian coord/rt v62.6anan,t balrt6 sg q.inates, 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 nu1c-(yd x: bwps zy75in 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, -4.0) and vector B = (+3.0, -8.0), what is the magnitudeyw -(8wc ak;.ih1snjt of vector C = A-tc(swi1 yha. nj;kw8 - B ?

  A runner runs halfway ar1k- xmx-v, cvhound a circular path of radius 10 m. What is the displacemc- ,xxmvh vk-1ent of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is yc4 n:kypv7xq223 rn* t: mplethe magnitude of the resultant fptqkx:2: 2y3 p cemvn7 nrl*4yorce?

  Two forces are acting on an object as shown in Fig. below. What is trskpbq./u ;/l 5 i,cxktt;wi.he direction of the resultant ,l uq5xk;kc/p/tbir t..wis; force?

  Vector A is 3.0 cm long a, qafrk695* 6rvc xfu7+s myjqnd points along the positive x axis. Vector B is 5.4 cma5fkv xyrqq,7m+j6s *uf6rc 9 long and points at $+38^{\circ}$ 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 71 cm long an ,x1pvw2iv1gdzh5(3g jf au- yd points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 23 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 14 m/s from thekbg8.lrt4 w (m fau05w edge of a cliff. A stop watch measures the stone's trajectory time from the top of the8w l b.(g0m uktfw4a5r cliff to the bottom to be 4.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 14 m/s,j; m6 - pn-soq2;a)wa nbxuw7 qv6zp-y from a bridge. It falls 19 m to the water below. How far does thez uosnqn2q;j) - apby;amw-px76 -6wv rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 25a krj t 1y/bn9p:yi8x4 m above the ground, strikes the ground after traveling horizontally a distance of 24 m. With what speed ryt 9i 5b kynp1j:/x8awas it thrown?

  A jumper in the long-jump goes2 8i6ol tj; 6vm5rhjgl into the jump with a speed of 12 m/s at an angle of r;o6 6g hjj82livtlm5$20^{\circ}$ 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 14 m/s at an angle /s7mzgkz/m p1 of mp1mk7/gzs z/$26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 34.9 m/s at an angl.;pbkkm; cm,te of $34.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 28.8 m/s at an angle a. hkr, nkvg(1of $49.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an35c*fzo6pczo w+y s, igle 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 hv,y eq00q, wkiorizontally at 22.1 $m/s$ from the roof of a building 51.0 $m$ 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 initiall /c +1vych5bze5vj ,v*fic:t speed of 48.4 m/s at an angle ofc+ y1z5fjvb/*ch5c,vit v le: $44.2^{\circ}$ 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 5at4 d;f-r eozt hmz7/at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which stf /h om-a5;4dzzt7relows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed occ.-spk j80aqf 200 m/s due North, and is in a wind of 50.0 m/s to the West. j pc.8aq s-0kc The plane's speed relative to the ground is

  A plane is flying due South7xt ugry7)7:7s7jqdb jrq;u 0n o ue7f ($270^{\circ}$) 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 headeduqu ;-w59ms3jraqsxc(t4n9s $30.0^{\circ}$ 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 projectilemcoo))ece2yn h7ki7mj,7 t f; with speed 50.0 m/sne7i; k) jhtfyc7,om 7) o2mce in 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 dire7y rqt-l)gq 4hcted across a river with a current of 6.0 m/s. gh7q4ry)- lt qWhat is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 15 m/s in still water wishes to t3/b /;tiv7wyuf wew d-ravel directly across a river 0.8 km wide in which the cybu t/w;7wfwveid-/ 3 urrent flows at 6.1 m/s. How long will it take to cross the river?

  The driver of a motorboat t; 9d)cn4c ahjhfq;. zthat can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the curr4thq jc af;9h )cd.;znent 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 bankbv 6vjweo e.*: 9sc5znp0k h7c in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stiw65pce.* jc0evvbh o97sn zk:ll water?

  A swimmer heading directly across a river 200 m wide qd0 hxzi5k (u/p(w 1rareaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of thdpu(0z1ikx(a5 r hq/ we current?

  A boat, whose speed in still waterd1 d6 z*ei5r , knn( mx6s3gn50lzcngh is 0.91 m/s, must aim upstream at an angle of6hzm*dl 5x 6zn3 g 0kisrn5g(nd1en,c $21.9^{\circ}$ (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)  $m/s$