Which one of the following is an examploc)wb**buye00oy 0r 8zk c+qxe of a vector quantity?

  Which of the following bb on)rx027-)fygh+f+bfpe kk , ) )qnv; flcqoperations will not change a vector?

  Which of the following is an accurate stii3 mq)m*pb(m :;lk ejatement?

  The resultant of two vaj*/v8fe8hpysf3. x4a mx7ntectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m avn(+ye us f(s59jv3msx3l7 ,en 4szkrnd 7.0 m, respectively. When these two vecvenrx+sk j3zsl 5n 3s f7mveu,( (s94ytors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following evd40 yse4f6;zh2, /ln,rhlbghx6p1o3iad i is a possible answer for the magnitude of the resulg;d fhhn idp el3 hx,li0rb2 4,so6/az 16ye4vtant?

  Three forces, each having a magnitude of 30 N, pull on an objeq )lw4/1 6x5uqzet uaict in directions that are zax15quqt)eil4 w /u6$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vwlvhixop*aqu314bmm7vd, x 7-c6 +fo 8+pneyector is

  Ignoring air resistance, the horizontal component ob t:; /k)2znrdwq n,whf a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an anglegbudv )h7 ).ecz xd1bs5h,h;n 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's yov/z l)5y1suy00y moacceleration)yl1zy0 vy0os 5yom/ u

  A soccer ball is kicked with a veloc,l:5uy z* e;tz ;w: mvddeg/qtity 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 o;l qj ahj2y.t6f an object is directed anti-parallel to the velocity vectohj6l a2jty ;.qr,

  If the acceleration of an object is always directed perix4 (xopeb-n /ym** kkpendicular to its velocityex(im no*x/ *p4kykb -,

  At what angle should a waterua,yhbax8gp * s*hkpn--a*q/ -gun be aimed in order for the water to land with the greatest hoky* a*a/*8nh bug-sqa hp ,xp-rizontal range?

  An Olympic athlete throws a javelin at four differe, (c lc54o3pr+bhcqts nt angles above the horizontal, each with4c5+3 rol ctc(, shpqb 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 ballhgtb dl zr 6gflcqkn88l54 63) for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first sedf8rtc ll6gl6) g4kzq3h5n b8rve) would be

  A ball is thrown at an original )6eak9fdt 8 ruspeed 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, how cmgy 8d0h8vg0fw3 +xbdoes its speed compare to itsc8xwbg8dfym 03g 0+hv initial speed?

  A stone is thrown horizontally from the top of a tower at the samzzah2 s vvfd 83x1.h+ve instant a ball is dropped vertically. Which object is traveling faster w83h2hx zv a 1dsv+zf.vhen it hits the level ground below?

  A bullet is fired horizontally, and at the same insh4 -dv1jts1 pa69yyantant a second bullet is dropped from the same pdyjn6h a-19 4 s1vaytheight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed e*:obfk14ep ox1b-ou of 66.0 m/s and at an elevation of 254 m drops a package. 4.7 sec1xfuoebb-*pok e:1 o 4onds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is *2,vw guv1on u 7xe ov 2zgz0r5ehyz10dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between tez*zzegrv5hg1 0 uwo12x0yo ,v v7nu2 he falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant g;yk hr a)d4s(speed. Neglecting air resistance, wh(4hgks;) yd aren the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravit f8qcj5ji-cxyv.b5*6ow7zft k oh7 6s y on 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 angl58*6w5fo7jz-c . ikf bhy oqvcj67sx te) that you would on Earth, the ball would land

  You are traveling at 55 mi/h inrzoq;b*+ ;v7ccm 7thp4fyzzt -jk1 /l the +x axis relative to a straight, level road and pass a 14 rp/cz tv b qm;*7z;lokzhyf+j7 t-ccar traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong c79 -qxhoxbe wkd(3r*murrent. You start out in your motorboat on the east ban - o(md7ek39qxh *xwrbk desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take jzu(v/ /*ugxehbjj9;you to move 12 km downstream, in a river flowing at 6.0 km/h?/xe(u v *buj; z9jhg/j

  Vector A has magnitude 8.0 m at:pk cj ;*id*ci an angle of 30 degrees below the +x axis. The y co k ic*;p:jcd*imponent of A is

  If a ball is thrown witv5b f:k35gnwjw4c(q lifg/e.h a velocity 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 h lwvpq2(nophs6d /6 av nxa+:y 19*j uf5okb1line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east havbvaw5h1 af (*pjousk96q/ 1 odn :nhypx+26lve you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its ve7bykhp a53 y0 tn:2di/n 7vbrr8h6xezlocity is 8.00 m/s. The angle between the direction of nbe7 xkyr : 8rdz yv 5/hip7n2h63abt0its motion and the x axis must be

  A 400-m tall tower casts a 60 us2(eypma7 s(j/gdkhia50 x00-m long shadow over a level ground. At what angle is theaj h(/mdka2yx0s7egu 0p5s(i Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. c60 a+: r gnfmzgih1/nWhat are the components of the sum of theic azhn1fg/n6r:g + 0mse two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What v kqtqovye.i2*9 12csr( c psi5i6eb.is magnitude of the sum obs..y5e6 iip1c*evc2q2irk 9qv( ots f these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vec7x4jq;z xi+og tor C = A + B . What is the magnitude g4jx xo z;7qi+of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of4l va/()aan kl its displacemenav4 a(nkll /a)t?

  Three vectors, expressed in up(y-lk 1oby i96 j)gtCartesian 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 Cartesian coordinates, ar,h u+wk:hj4;tae;)w f ceort /e
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 magnirabew,;cm ;om v4of0 4tude of vector r ab4;o wf;c vm40oem,C = A - B ?

  A runner runs halfway around a circular path of ,n gx gp5y9j1chnd:0gradius 10 m. What is the displacement9njg0g c gn5dy :1phx, of the jogger?

  Two forces are acting on an object a,egy cd;4) aes6hl(ibs shown in Fig. below. What is the magnitude of the resultant force?4ahe )g ; bc,yldsie6(

  Two forces are acting on an object as shown in Fig. below. What is the k;ixyrd(d 35 zdirection of tzxk5;(d3r di yhe resultant force?

  Vector A is 4.6 cm long and points along the positive x axis. ez x.i5be778ufk j(+aqh.i b h Vector B is 6.2 cm long 7u .kx.zef ibeih q7+bh(j58aand points at $+45^{\circ}$ 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 64 cm long and points 077yo g4mt;)cxmw vwpat $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 46 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 ini: f5rslpl4 ex/ eb1)fttial speed of 24 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom tpft:5/rx) 4efsll e1bo be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 14 m/s, fri1gu+smmd o 1z5td)gzrzxd(p+gg :s4:r f; /eom a bridge. It falls 11 m to the water below. Howz df mtggm1s g5+d/ i+xuz)o(edzs: 1 ;4pg:rr far does the rock travel horizontally before striking the water?

  A ball thrown horizog:sgo).oxo f8ntally from a point 19 m above the ground, strikes the ground 8of.s)go g x:oafter traveling horizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 * rtnl72g av1z, .rhzgp08ikom/s at an angle ovhar7t 2. pl g0izo,k8r1zg*nf $20^{\circ}$ 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 10 m/s42fife6y0 k4hucvpo3 at an angle of 43foh2ipeu 4k vy06 cf$26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 37.6 m/s at an angli- e xsaj2, 5(pogg6d(ms1(i jgt g-aye of $47.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of,)huqr8k9gqgb2p+f9om b-gbv7u7 xi 29.2 m/s at an angle of $16.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired amh(lhff+m:;e)v acj+t 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 horizontally1 oo2; -e yt:wlih;cuk at 18.2 $m/s$ from the roof of a building 48.3 $m$ 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 with anlp+o,+z8 g ov ec4+yd 5yqjni5 initial speed of 63.6 m/s at an ajid5g +nov5c,8+yz4qep+ yo l ngle of $47.4^{\circ}$ 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 4.0 m/s5 w x6 t4e-vinrgml;-h. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.4in-;lx6 tvg mrwe5- h0 m/s, the time it would take you to finish would be

  A plane has an air speed of 2r60)ftkqiphbw *lq/8kzrz -j1e20nb 00 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed rela*i ke0btzl8 )q6 qw/j frbp nh02-zkr1tive to the ground is

  A plane is flying due So ,t/9anzbjrellm2 qk* -r rc67 xy-o.suth ($270^{\circ}$) 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+ a x;nlc-va;xbrc sc4q7 r(4t 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 20073*t 0axwrx ,d mxz2nji02nll m/s horizontally fires a projectile with speed 50.0 m/s in a forward directi2n7wzjm0r2n ,axxid tl*l0 x3on $30.0^{\circ}$ 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/ mf4 r4eqp*qxa*xp+ 8fs, is directed across a river with a current of 6.0 m/s. What is the speed of thex4p+mr4ex aq8q ** fpf boat as it crosses the river?

  The driver of a motorboatscz) m8j t(x7 ppv0;dg*:oe5pn8j vce that can move at 10 m/s in still water wishes to travel directly across a river 1.4 km wide in which the current flows at 4.e8 *jg7:5 d;c8 eo0pcs(zptvjnxv m)p1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can moe2 f39yvs d:, dqh/vrw e/uk1cve at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver hdyf9 ,u2/dv3qrw : kseh1/ evcead the boat?

  A swimmer heading directly across a river 200 m wide reac dpb;dy3*smm;hes the opposite bank in 6 *; bymd3pdm;s min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly acroc7+wpf( l8mnsss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is thewm(lp+s fc n78 speed of the current?

  A boat, whose speed in still water is 1.41 m/s, k68kirg *uu09qua /fya9m ea+must aim upstream at an angle of ka9agm 0yuukrui*9+ef6 8 qa/$25.4^{\circ}$ (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)  $m/s$