Which one of the following is an example of a vector quant+ p,h8vbwqui1ity?

  Which of the following operations will not chzvc9 /f8u1 hgous1 vg4ange a vector?

  Which of the following is an accurc6hq/1e.+xsndt-,.j .lk jioplj(ain 0 vpu +ate statement?

  The resultant of two vectors is the smallest when the angle betweenu;8:evs sj*vk,ye; z d them is

  Two displacement vectors have magnitudes of 5.0 m hvq38pf*d 46v 7z e;ma si1yivand 7.0 m, respectively. When these two vect4 z6*qhm v1afe iiv;sp87yd3vors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are adbl n1apd 0)xq-ne5wo+ejp)u*ded. Which one of the following is a possible answer for the magnitqj+)p ad*n e 05bn-x)l1e wuopude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direxc i5duvw5y 20ctions t2 viyd 5x5uw0chat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, yh shc1la;.8 f hg;6qithe unknown vector is

  Ignoring air resistance, the hori t 7wcfxexy 6r*f+9+wbzontal component of a projectile's velocity

  A ball is thrown with a velocity of 2j x bqsmcz ;z7w3,cm*- wkp7ka) jkz8;0 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 resistang3z)i zysu 0j7e,9na k 4n2ath2 r7xkqce, the horizontal component of a projectile's acceleration2yn3sq7,9urt2n zek4)0 hjikxaaz g 7

  A soccer ball is kicked with a velocity of 25 m/s at an anwcq0f2fdgl;p,7rgj j. ly*n*h )tec5pa i*y (gle 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 veloj6q eu+yp;0 qdnmf, (f2jei2i city vecto,f;0dnu (f 62ijq+ ie mqypj2er,

  If the acceleration of an object isdc,mm+olak- : always directed perpendicular to its velocity -mdmk,c+a: ol,

  At what angle should a water-gun be aimed in order for the water to land wi +7iwy*33d.8fxf3ctt m)cx:s1w.evsrztrr z th the greatest horizontalt+s.tw*r cm8y 31w7sr. z vefxdxzrfti:c)33 range?

  An Olympic athlete throws a javeliwmx4e3zm t;8: nqtssb f+x/q7n at four different angles above the horizontal, each with ;qm /f+ z 8xbtet s4s7q:nwxm3the 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 lbwjmtrxktg6 oq;5p4 4.nv w,da7v)3your hand with twice the ve3tpv 7w )qmlr4oktjdw6;4 a n.5bgv,xlocity 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 anglelvz) o.:xa ge :ab-z*mmkrn78 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 attemne;qb /z zws lzq9l-4-pt reaches its maximum height, how does its speed cnz9q-/wzb zl4 e-q ls;ompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant ag ;lqzj5 7u5ap ball isg 57 qup;zlaj5 dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instantyg ic0k7 :i93h7ibkywoxl(3qg a9ks2 a second bullet is droppedi i0kgs73:(9ix k 7cyyh293wq aokglb from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 93c42nh:(8t bzgxc hkjc0;6m lfwok3+f.1 m/s and at an elevation of 154 m drops a package. 7.1 seconds later it drops a second package. How far apart will the two packages land on the grk 3f+ ; c 4nb682o:xt (cfk0hlcwhgzjmound?

  A package of supplies is dropped from a plane, and f *ii,a7ej 59sdz 1cdvone second later a second package is dropped. Neglecting air resistance, the distance between thfjdd7i 5se *a i,zcv91e falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant s- w orsc3 vkle82ge+0pbw(tk,peed. Neglecting air resistance, when the bomb hits the ground the horizonc,kwwet +2bk 8lp 0ser( 3-gvotal location of the plane will

  The acceleration of gravity onjsm 4zf/8lzp 6r 2g,qp the Moon is only one-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 would on Earth, the ball would4qspf p8/z m2,r6zljg land

  You are traveling at 55 mi/h in the +x axis relative to a straight, lev 9b1qwbmf69uvpa0 q hs.pba61el road and pass a car travel6m 9.fa0ab9u h wb6sv11 pqpbqing at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flowsu)kbjwe+9 2tx / i-a+qbru g1s due south with a strong current. You start out in your motorboat on the east bank desiring to reach the wes29kbq + +/uu-g)trex a1 jwsbit bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How iiek7 (k 3;sfhyzg)9qmuch time will it take you to move 12 km downstream, iegsy)f ik9q;hkz 3i(7n a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m aeai-/+7ggmy2uklg7b0jynev b5: iq6t an angle of 30 degrees below the +x axis. The y component onvie5gablmb:e 27k+/u 0gyg 7-iyj6 qf A is

  If a ball is thrown with a velocity yr6x,2)rc 7tvlepw i sh.-mbb+cim0 . 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 direcl rji mgbz).+hrw.b8:tion north of east and you end up 2.0 km north and several kilometers east. 8.jbb) rm rih g.:+lzwHow many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocirwh6p:q 3 os)hty is 8.00 w)h 3qhr:6 posm/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m longe*au4 poc;v/p*e2 q:qv a,mb h shadow over a level ground. At what anglema2q*e,/up v ap be: ;qo4c*vh is the Sun elevated above the horizon?

  Two vectors A and B havvvkj v4;5 xt9xe components (0, 1) and (-1, 3), respectively. What are the components vx 4jx;5vv k9tof the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whdua 7dt:o:f- qms qjs .:kx80 j/uog+qat is magnitude of the s q: o:7dxqsugaoqj: 0tk. -+f/8sjmudum of these two vectors?

  Vector A = (1, 3). Vecvgfqne1m f)v xm:3f:) tor B = (3, 0). Vector C = A + B . What is the magnitude of ) fm1 e:)vfx qmgn3:fvC ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disew3/pt mnd,y mn)3.xwplac/3) wntdpe nx3 ,ywm.mement?

  Three vectors, expressed in Cartesian coorj(xz*e lo: z5udinates, 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 Cartesia7:hlbf8fw m y6n 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 m-aezg p;dv+:), what is the magnitude of vda+p -zv; mg:eector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. v4h j ut/x9y.*y xf7pe What is the displacement oj pfe* xtx9 v4yu7.y/hf the jogger?

  Two forces are actingsp hz6vdkw kj(32c1.x3u5+/ tavskj l on an object as shown in Fig. below. What is the magnitude of tlx 5t16u3j(wz3jv/p kvck+a2s dkh. she resultant force?

  Two forces are acting on an object as shown in Fig. below. What is thcohxc:bw7yf-al -.b;bk -2 rb a4 vji(e direction of the res74xr -bbf -2c.-kbyj ca;biaol( v:whultant force?

  Vector A is 6.0 cm long and points along the positive x axis. Vec a- l cxk6l4e776ogiritor B is 5.5 cmli7rxa-eik46 o6 7g cl long and points at $+51^{\circ}$ 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 83 cm lowh9 g(wn(y 1ibng and points at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 25 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 10 m/s from the gw*im kqf fvnj1 p/dc2,a,56qedge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.5 s. Whada6w1 qkpc, fn5fj,/g2mi *qvt is the height of the cliff?

  A girl throws a rock horizontally, with a velocity :* pwx3lsmzv do*p:2aof 7 m/s, from a bridge. It falls 10 m to the water below. How far does the rock travel horizontally beforxovs* ml: pzw 3a*2p:de striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes tlne7 bu - e pa4s1jifvg71o5h;he ground after traveling horizontally a distance of 12 m.levhnepibj7 1;- ao4g 5f7u1s With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angyf;*c 4cjk,c:u: wexyle of ;,xe*fc :juc:4c wyyk$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump)cojja5 8;dfd;)ea4 o.cdsi 1gkyf(lsz,iu 0 goes into the jump with a speed of 9 m/s at an angle of 8 1 yeajad0lc4).(u5siooc;kdi,;z)gsj dff $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloc8j0 i5d(5.zgy0mmzz. bain saity of 32.3 m/s at an angle of $12.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 47.7 m+ qg* 2yk7mepz/s at an angle of $24.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angld9/j.he zr)7qu uhjr/e 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 horizvwt(xko , e3z0ontally at 21.8 $m/s$ from the roof of a building 67.4 $m$ 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 lk tnk6vl j)+15ph9 syground level with an initial speed of 66.8 m/s at an angl1 kplhvn 6j95+y) kslte of $44.2^{\circ}$ 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),, n qiteq-8y(y you can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had ay8ni,qt -q ey( 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 due North, and is8 zb7z))oqxxig:,snvw5 qrzk4x83z h in a wind of 50.0 m/s to the West. The plane's speed relative to t5, w))vsozx4q 8xbi:x 3rg7 zhzkzn8qhe ground is

  A plane is flying due d ,-izb5pcz g.d0.pj ix65 undSouth ($270^{\circ}$) 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 s+3+ns-w h(bee twv 0hem4se) apeed 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 spmcj:h 9h*fb*qb e 9in-eed 50.0 m/s in-hfb9ei*mb*qnh: cj9 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, w+; :w2 toova8s celeu9f5+xtis directed across a river with a current of 6.0 m/s. W9 s8+;:+ wfv ceteotouw5ax l2hat is the speed of the boat as it crosses the river?

  The driver of a motorboat that can movfirjjp 9/vljyn)f2f +n(5yv3 e at 17 m/s in still water wishes to travel directly across a river 1.7 km wide in which the current fl v f3/jn25pnyvy+jr(jflf i)9 ows at 5.1 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 tocasa5 p14w(e d travel directly across a narrow strait in which the current flows at 5.0 dw14sc 5 eapa(m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a r n*tll+sl ysj1 yq:vi*j9ohey .o:i4; iver 200 m wide reaches the opposite bank in 6 min 40 s. She i* e vs9i+sl*q4lnh ;o:o1t y:yjylj.is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches pn-ho-a;hb7 ya :vk2h4 q bdk4the opposite bank in 6 min 40 s. She is swept downstreahb;k -4h oa7d:v bkyh2p- naq4m 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.06 m/s, must aim upstreq) v.h8ywshe0k sf5(k am at an angle of e.v 8ssyhq)k h5 wf(0k$30.0^{\circ}$ (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)  $m/s$