Which one of the following is an examplz7a 5nzz6t+nttq5 p5 6hxdt/ ie of a vector quantity?

  Which of the following operatn*w 5kzc bh unb/pi2y::/9 tmtions will not change a vector?

  Which of the following is an a ((h opiu5vujug,(xt, ccurate statement?

  The resultant of two vajl) (* 3 bvwy7;sz5ht a2trruectors is the smallest when the angle between them is

  Two displacement vectors have mag ;:msy2tnss8,r p:y8pby /bu obn9js6nitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnito9p;68rbu /js y,yybbpt nm ss:n:s 28ude of the sum

  Two vectors, of magnitudes 25;7l44t: * vpuem)hue/1 mzrh flz epf0 and 50, are added. Which one of the following is a possible answer for the magnilhh eu7v4: p* 1;rl4)/et5 mumfzz peftude of the resultant?

  Three forces, each having agwy5dv jif6 l ptq840: magnitude of 30 N, pull on an object in directions that are 0lq 4gp:8v5w6dtfjiy$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectje m+lsgf5 qex*8 v:)gor is

  Ignoring air resistance, the hoa h,cs3n1 fa,lgb *ug;rizontal component of a projectile's velocity

  A ball is thrown with a velocq ./txd0qnuqgw c;idw.0 lv 1j7fv8*m ity 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 horizontal component of a projectile's accel5pnw fx- tje6;otl-6a eration; xjw6 a onpe-l-65tft

  A soccer ball is kicked with a velocity of 25 m/s at gk8s 2h2nl0r dieb;a,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 antizoe1(tde 1u6 b-parallel to the velocity vo (et1z1eu6 dbector,

  If the acceleration of an object is avmh/h8:pw q u) 4)gkqelways directed perpendicular to its velocitye)gw8 4)vhq:h kpm /qu,

  At what angle should a water-gun bel4yyyisf. mhjv3g094 aimed in order for the water to land with the greatest horizontal ran 4l f.vjy 0i39m4syghyge?

  An Olympic athlete throws a javelin at fo hxqsj) ,ldh;:ur different angles above the horizontal, each w xd,j;h hqs)l:ith 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 sec dt27(d5vd guqpnh/.le )ryp- ond time. If the ball leaves your hand with twice the velocity it had on your first throw, itsy q()hr-5u7pg nlde/ vd2.p td horizontal range R (compared to your first serve) would be

  A ball is thrown at an cl(vkn t;gsh tu) ,l:1original 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 go.h+8) hq6g ctycxlxt1 al attempt reaches its maximum height, how does its speed compare to its inyx lt6h1 8)qc.tgchx+ itial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a* ,z 0sqm mom;x;skaa/ ball is dropped vertically. Which objec/, mo;axmzm*kss;q a0t is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the sasfeg.e* ei;+hbi+ 90 rl cbdj9me instant a second bullet is dropped from the same height. Ignore air re h9ci* je;s 0blf d+r9egi.+besistance. Compare the times of fall of the two bullets.

  A plane flying horizon jjup(iqcwan.28/ h0stally at a speed of 68.6 m/s and at an elevation of 220 m drops a package. 4.7 seconds later it drops a second package. How far apart will the two pacniqh p02 8.sc(/jj uawkages land on the ground?

  A package of supplies is dropped from a plac c:tu )/ay-vone, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling p/y-ou)ac:c vtackages will

  A pilot drops a bomb from a plane flyi+ec 60zw t60nyc dm w1q+o;bxsng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizont oqe10;m s nc+b6t0+wzyd6xcwal location of the plane will

  The acceleration of gravity on the Moon is only one-54fk5)8isat-er pzj asixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) th)j4kpa s8a 5rz5-e tifat you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a stra a1d4 3w;.zqn8laqhln qu:1cczny /l00jc:dsight, level road and pass a car traveling at 45 mi/h. The relative 1n w3n:.zl l:lchdcduq4q8010 ncqa z/a;sjy velocity of your car to the other car is

  You are trying to cross a river that flows due south3ejvr3 a c1f hw:+6tsu with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your staruew3vsj 1 6r3cha :tf+ting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time w2drgu5 lnbut)1 e- rx6ill it take you to move 12 km downstream, in a river flowing at 6.0 km/h?b )genu-1u2l56xr drt

  Vector A has magnitude 8.(f7 rubuz :q4*0:abj bm2 yylh0 m at an angle of 30 degrees below the +x axis. The y component of A u *:zr04l:jqyb mbay2 hbu(7f is

  If a ball is thrown with a vg+z 0wkwrlbqjo4i 9:- elocity 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 direction north o(w4- c4hnm xxgig ,0-xy*eh 5 gbmg2zsf east and you end up 2.0 kz- 4-ggxyh,csgiwg 0 4 (xme2x*h5bnmm north and 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 ia)xa+ ttuwq,985u dwtfgyf2op 0d 9q4ts velocity is 8.00 m/s. The angle between the diretu+wwga)qf t9a ,98y 50f2u4ddqt pxoction of its motion and the x axis must be

  A 400-m tall tower casts a 600z6otgn-t(ydnkhma)h 3fw **9 -m long shadow over a level ground. At what angle is the Sun elevmw*t9 (yt)nza6 g- * fdnh3khoated above the horizon?

  Two vectors A and B have components (0, 1) and (o5k0t 97-5hmt jxsjkj-1, 3), respectively. What are thej7 0jhkxt-595 mkts jo components of the sum of these two vectors?

  Two vectors A and B have components (0,rv3a f0o qmww87b,lwgh,(;l(hrk vj2 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectorhlhj wqw 3 g,korv(80 ;l,avb7mw(2rfs?

  Vector A = (1, 3). Vector B = (3, 0). Vector C =kls i c2cyt:. m(djqht7 v m0))5y3zlr A + B . What is the magnitude of:.m2lyml)kc)( qdij03 cr 5yvts h7zt C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of itsv4 uw5,tcgh z35.q yjs displacemen vgyc . 5,sw35jz4hqutt?

  Three vectors, expressed in Cartesian coordinates-0bcp1 ig1xmb , 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 co5 *ln.j/lidkcordinates, 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) 3qv+m3uif/b wzo:u(wand vector B = (+3.0, -8.0), what is the magnitude ofi(+u3 mzvwqfwu :/ob3 vector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. Whatm4 qr1 sr*i/oftat/zvp:: qk /v)b2ww is the displacement of the/atqsp:wvowbtkm v4r :* q1 fi2//)rz jogger?

  Two forces are acting on an object as shown in Fig. it e03 ojfz4;vbelow. What is the magnitude of the resultant 0eo;izv t3j4f force?

  Two forces are acting on an object as shown in Fig. below. What is thelw1b54b9 g:bz e+,imq yo*w9 mtxz(bh direction of the resu 9b: bme1w ,o945iht*(mq +ybzg wlzxbltant force?

  Vector A is 5.3 cm long and points along the xv /pc l-v0tle,)06dg 7a- evenu,6x zuaocz8positive x axis. Vector B is 8.9 cm long and pointsu)odue/7 v0 ,,xg6 n vxat6elclcz8pa-v0ez- 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 89 cm long a3n xft;36 m(g8nen;(pkosbz dnd 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 34 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 in/c,eh: qthw bqu*k9 ez)) gwj +wdr-)yitial speed of 21 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the clitwy)b, w +)cjguh :ez/q e*q-w9hdk)r ff to the bottom to be 5.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a veloc50e p-*:dd/bkb jlb kiity of 11 m/s, from a bridge. It 0k:*lkjbbei pdd-/5 bfalls 24 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a psoy-x/ r r5vvjz3m7z 7oint 24 m above the ground, strikes the ground as-vo5ymj v7rr7/3zzx fter 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 o8 sw07opq bta4:g*dye f 12 m/s at an angle :w aes 4pq gt7odb*y08of $20^{\circ}$ 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 15 m/s acwpeyovo)s ah;/1ja4.* k ( ldt an angle oow ka/pcvd ;.a()4*o shy1eljf $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 22.5 m/s at an anglec. 9x)jsqlbobqb;0u; of $13.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 37.5 m/s at an angm4kl(/wn 53(bvwmik. vg 8q xsle of $24.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at n3l3cev :x vnqmgfc9cx 3)w5cisj;: -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 horizongks7.;c 3myo dtally at 17.6 $m/s$ from the roof of a building 48.4 $m$ 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 ground level with an initial speed of 50.0 m/s at v v;8n03kdr,zc*a pl ban anglvkd*nl;p zca30rbv 8,e of $46.0^{\circ}$ 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/s. Icav 7r+g4lrtrqx 9;8fk x7y 6if you ran the same race on a day when you had 8xtg7 vrif4alxk 6cr+; ry9q7a 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 is in a wind of 50.0 m/s t topdx/( ms6ek h/+gfy04hh:mo the Wpmh4hy6+d/:kt x hfes mg(0o /est. The plane's speed relative to the ground is

  A plane is flying due Southo4- z4j 8wemhj ($270^{\circ}$) 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 120w.fnjh fs +1zs35r6g4d x 0rzz 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 horizontallk/legcv6;l( pr wpsee 06sn-o7b1e4d y fires a projectile with speed 50.0 m/s in gs(l 1s 6 p;veobc0de-6prele/kw 4 n7a 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, is3r 4 bo.i jlk:sfta02f directed across a river with a current of 6 j:0for 3sabl4fitk2..0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/s in still l3 89 3jc/2uu2xk-c ok)yi1h mbpmc okwater wishes to travel directly across a river 0.9 km wide in which tho-3x2j3lyp9i1ck) k/uohc 2bck m 8m ue current flows 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 strc2k: 6s3s vozill water wishes to travel directly acrossc s3kr2z6os:v 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 wi --nd11.t : jf3zoxc xd8ykiggde reaches the opposite bank in 6 min 40 so-xz:.nt318 gdx fycg 1kd j-i. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rxc 00nhg 6: kr/n0kblgiver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the curren0kgxb:/rkn 0cgl0 6hnt?

  A boat, whose speed in still water is 1.09 m/s, must aim upsn 0d kjdlaybr3rtym1m/8/fs+;f88 a ftream at an angle of dfl rkf jd/;famsmy8a13 y8t+ n0r /b8$21.9^{\circ}$ (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)  $m/s$