Which one of the following is an example of a vector q0d*i n,r4+ ;b7olvz:jyxc pe;ol 3sqauantity?

  Which of the following operations wilaj0nj4uk -9cbl not change a vector?

  Which of the following is an b35+rj sdl: tkaccurate statement?

  The resultant of two vector)+ dfc k - rgnxl-/+wydlkph41s is the smallest when the angle between them is

  Two displacement vectors have g7dxak/zy v:(magnitudes of 5.0 m and 7.0 m, respectively. When these tw:av(zy7g dx k/o vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one * fydw)tx 5ba)of the following is a possible answer for the magnb)w x 5dt*yf)aitude of the resultant?

  Three forces, each having a magnitut,q xyr2q(z way4x :oe*k +p9qdl m21mde of 30 N, pull on an object in directions that arq(myzyw2aptklx 9d,o1 x :4q mr2*+qee $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the*nv8 l1uweo (o unknown vector is

  Ignoring air resistance, the er,++3p amg1uf-p wkchorizontal component of a projectile's velocity

  A ball is thrown with a velok djv.ml hs72sth,4 o,city 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 myy rv46d 5ffp /qy(:ahorizontal component of a projectile's accelerationyqv:(5 fdyrfa/4 ymp6

  A soccer ball is kicked with a velocityo-w 2g o9hp9du of 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 d(aw4/ 5v9gtqcqv y-e kirected anti-parallel to the velocity vcqg k9qvv/a-4ty5 e(wector,

  If the acceleration of an object is(7 e2/ zhl:uziid :hhe z7cyt*j3vo;k always directed perpendicular to its velocity, htjkh73:i/(oz ele yv:h7ziz2uc;d *

  At what angle should a water-gun be aimed inxgvef6:in3 b5 order for the water to land with the greatest hoe6fg3 :bnv5xirizontal range?

  An Olympic athlete throws a javelin at four different angles abov-4f skgnx w*0me the horizontal, each wi4s km*gn f0w-xth 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 haygqiw4tzl,ym 6z)x *2nd with twice the velocity it had on your first throw, its horizontal range R (c* ,ztizg6my)xyw2 4lq ompared to your first serve) would be

  A ball is thrown at an original speed98v se6pgf.ic bp9s/q +fbye8 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 maximum height, hmg3n)q.u nh:u-dh;lw uo:lt1ow does its speed compare to it u:dlh -g:hun.twmol ;q nu)13s initial speed?

  A stone is thrown horizofs6g ;naz(8rkn* k x 8:jiry0hntally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster whek: rrkfz0s6ij*nxg8;( 8h nayn it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a xa*0:bz1odkn)9o gv u p/9y7t0n3u 6a ygwmxasecond bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of pu00xog/ 9mu gxnn7wy)az by913ok : atva d*6the two bullets.

  A plane flying horizontally at a speed of 80.3 m/ bpm3;,g6 :10ykm gbwm) nbezq/0jno ts and at an elevation of 298 m drops a package. 4.0 seconds later i jt,b:n;qkg w/n3ymeo01) gpb 6z m0mbt drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plamc 1lgfz)n*w (ne, and one second later a second package is dropped. Neglecl*nw( 1fczm)g ting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neglpfvt8ygw+6o -1n u)b:o naz(t 3w3xlpecting air resistance, w6)+pzatlnu:bo(y1p3g 3 n xvwt ofw8-hen the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth ofpoplor g/(0hb keptt-55s7w * that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that bpoptt/ 7 kr-5(opl05e sgw*h you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x ax-,km /lju8ri/i m/ du:s w1tbvd um28jis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity jubkv/d du/l -:msrmu88j/ m2,itw1i of your car to the other car is

  You are trying to cross a river that flows due south with a stron g xcv:4ngljw nf 5c4ct0e(h5)g current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your monfg5l4)xgec4nt0 hj 5cwvc:(torboat

  Your motorboat can m)x, 1 95z0qppxtwvwkk :lwm*u ove at 30 km/h in still water. How much time will it take you to m wvm)x159*0kxqtzwl kp pu w,:ove 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. ,1op13z5(x lkahh j rpThe y componenx ah,hp53r(o1l1zkp jt of A is

  If a ball is thrown with a velocity of 25 m/s at an angle ;1pa )cdok cehc)vev 9s7h1py/. 4cpr 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 east and you enddeh31.rb n -m9j9lpub up 2.0 km north and several kilometers east. How many degrees north of east hhen lu-pb dr9mjb391.ave you walked?

  A butterfly moves with a speed of 12.0 m/s. The x o(/ ,l(ngcnq - 6mnsorcomponent of its velocity is 8.00 m/s. Toc(6 mqo/nlsn (r ,gn-he 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 gr f,wmzzi9-ca:ws3;ry ound. At what angle is the Sun elevated abc,9s a fz;:zwm3-rwyiove the horizon?

  Two vectors A and y -s49vlk nhe6B have components (0, 1) and (-1, 3), respectively. What are the com9yk 6-seln vh4ponents of the sum of these two vectors?

  Two vectors A and B have component-zba hd8k,u+k s (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectorskdkz -8bhu+,a ?

  Vector A = (1, 3). Vector B = (3,ew9k)e.yx -.3 f kn*,iaeobyp 0). Vector C = A + B . What is the magnitude of9 eewn,.i. opyyf-ka)kx* 3be C ?

  A car travels 20 km ,/ z;,nsouej+; -ickrzs jd romv(5o,z z4 /wsWest, then 20 km South. What is the magnitude of its displacementz;or 4ze /oivzjjs w,dsnm( r s-/;+,cok5,zu?

  Three vectors, expressed in Cartesian coordinates, aivn: 3mjn f*7ekpd7c5re
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 Cartesian coordinatedk n75q o1;rnbs, 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 thehtys;flo qlx834. :-1ru ge+ xvqd iqqc08ri: magnitude of vector C = 8r t q u:r4;0qdx1cyqho.i-qfv: 3sx+ge ll8iA - B ?

  A runner runs halfway dgfs3 agcf- dv+w:b: 2around a circular path of radius 10 m. What is the displacement of the jo2dcv+gfs- w g fb::3adgger?

  Two forces are acting on an object as shown in Fig. below. Wh , yuymf a+ehjc-bjyg0 l+9j57at is the magnitude of the resulta5ly 9h,0cmfy7ujaby++j -gj e nt force?

  Two forces are acting on an object as shown in Fig. below. What is the ddg))r1o wab:i irection of t1ira:wb o)g d)he resultant force?

  Vector A is 4.3 cm long and poir-na a.:(jyb 4xye5h lguuy70 nts along the positive x axis. Vector B is 9.5 cm long 5-y0 h7 l : uybnaeruax.g4(jyand points at $+60^{\circ}$ 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 51 cm long and points at v:lrxxnugs1 wp/4- ; q0t pcx2$30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 22 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 the e44vgt)g xfo 6sdge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3ts6vg )fgx44o .9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velovmr ) l(5t b3g 4)bfx9m1lwztny3s2tecity of 8 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before strmt (zn3b)2 1te)vgtxb3yrslf mw549l iking the water?

  A ball thrown horizontally from a pointz3y:q2 6qvtq( -hch,+ dromg d 28 m above the ground, strikes the ground after travel y qr+qmthgd(o6 qv,zc-:d23hing horizontally a distance of 13 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump wik;o :y 5vlci(6, 1 7cqcrdetyxth a speed of 12 m/s at an angle :c dxq5o1 (,yc i6v;tr7yelkc of $20^{\circ}$ 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 11 m/s at an angl*.5xgsurzpgkr510 a g*k yu .c f8j:yme ofxr 8* pujyrgm5 0sfkkg.uy . zc1a*5:g $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity 9 eng)) -buctobhg;. .ax pavt3m),ndof 44.3 m/s at an angle of $41.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veuqg ywog -n0*w :sc8x .1fk.jvs7qxq,locity of 23.0 m/s at an angle of $45.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofen*gq2n.j n6 byrq-*+o4qdlp $30^{\circ}$ 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 26.3r(jv;1szkdwm8ymi 21px t * 9d $m/s$ from the roof of a building 40.0 $m$ 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 initial sp ngfdi c41w;z1eed of 41.7 m/s at an angle of i ;wn 14dgfcz1$38.4^{\circ}$ 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 velocity of x p)z jb7,iq;zw -zh8x4.0 m/s. If you ran the same race on a day when you had a constant headwind whicz 7 qxi-)z,j b;xhwzp8h 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 due North, and is in a windz*xyv7l-*wp8et n (dm of 50.0 m/s to the West. The plane'sed lx* -*wtmpny8v7(z speed relative to the ground is

  A plane is flying duegm8rhme1h 6l 5 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 1f82)-u5d.nth,-ek un b ls uwz20 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 movi,twk ijg8 bf9h6 hg.j5ng 200 m/s horizontally fires a projectile with speed 50.0 m/s it5ggkjj b.f8w,69ihh n 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 directedk:zb)w qv7ta0jtf2bm1 h* 3la across a river with a current of 6.0 m/s. What is the speed of the bbkwva07tqlhm:a*z 2t jb f)31oat as it crosses the river?

  The driver of a motorboat that can move attz 3 2la4 *ki2updl1offeo9t : 17 m/s in still water wishes to travel directly across a river 1.2 k9f*2 uak:d1lt4i3 to oe2p lzfm wide in which the current flows at 6.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can movelh*au*8xy g5i at 10 m/s in still water wishes to travel directly across a narrow strait in which the c h8*g*xa5iul yurrent 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)fzz.c(o 5x xz in 6 min 40 s. She is swept downstrea.x x5zo)(c zzfm 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppos.h3+zilydy u8 :s pl+0oex*d fite bank in 6 min 40 s. She is swept downstream 480 m. What is the syfxli8+hs 0. : pl3oedu+zd*ypeed of the current?

  A boat, whose speed in still water is 1.36 m/s, must tog fw47;jt0w /8ctgx o*aib2aim upstream at an angle of4/txf2; jtb0g8* oowt cwa7i g $31.0^{\circ}$ (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)  $m/s$