Which one of the following is an eqj,a2ydggg-dp;ha(/; s h pa-gl v.4yxample of a vector quantity?

  Which of the following operatw8zrxb6(v u a-5kvtobo( 5ct 0ions will not change a vector?

  Which of the following is an accura,kqdkg 1 a-gu1b,z+ asjvn7l9te statement?

  The resultant of two vk+ bwmk/s4q nziuv(7+ ectors is the smallest when the angle between them is

  Two displacement vectors have m9lno n:u9r 52osun1x8x6h c fqagnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are addlroq86c9nn fs2h9 xn 5xu1 :uoed, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, tqgpg /vwym*7j1+*.on liu3 h are added. Which one of the following is a possibp7m qj*l.tiy hv+o31/gwgnu*le answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direction7b9z+7 i8 xstzxh+ikes that are x+sbx+ kz 7h78iez9i t$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unxju u9zk42 5m,vbea+0ft+ iq xknown vector is

  Ignoring air resistance, the horizontal component of a projed,4r0fb0)5o uy2jk zeji oa .qctile's velocity

  A ball is thrown withnb v .e8zi3p7mol9 /gm a velocity 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 proj 51v/mbm 1kfq:tt2 otxectile's acceleration 1t1/ totmmv x5k:bf2q

  A soccer ball is kicked with a velocity of 25 m/s dnkc ,vzgmo1vx(k(9p/6h:k:sev t k2 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 anhxp0gt; 7gy ;f 1-ed ;fozij)c object is directed anti-parallel to the velocity vect;ih0-c t;d7)f pgz1jx ofyge;or,

  If the acceleration of an object is always directed perpendicular to its vw-c.r s vz-w kzu/( tht1md/w.elocity-kw /sw/hmd1wt- .t(r .v zuzc,

  At what angle should a water-gun be aimed in order for the water to lj j78)jxjstq :o4v2nd,mn: s qand with the greatest horizoxdjq: 2j:mn4,sjsj8q 7v)tonntal range?

  An Olympic athlete t1. 4sz qtw2ypuhrows a javelin at four different angles above the horizontal s1 wzqpy4t.u2, each 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 time. If the ball leave / 1s5bizb(ztrk0ylh 0s your hand with twice the vzsi0zl 05r/ybk b (h1telocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original so 5)ohii rg43ipeed 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 reachiz pfcj)(3 bxnu0s *vja60psn7sbh .,es its maximum height, how does its speed compare to its s( i7hab.0)xc s,*0svnp np3f6 jz jbuinitial speed?

  A stone is thrown horizonk u;pn 06cbelad izbxo/69g+ hiho +43tally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hih9xodcg;+3n6b6u l+ia hopi4ezbk 0/ ts the level ground below?

  A bullet is fired horizontally, and at ther8- 0 2ndfi(mf rn;cbm same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two cfdbn mm;(2i rn8-rf0bullets.

  A plane flying horizontally at a speed of 65.3 m/s and at an elevat8eywz buf: ()pion of 139 m drops a p):e fuwpyb z8(ackage. 5.6 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from an-oiqdqs pp8fm4 a) -. p1o(xk2pzzr) plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falozk a) xp)48p zfdiq-2rm -sq no1p(p.ling packages will

  A pilot drops a bomb from a plane flying h jxmph:lz69p)md n7t3 tpwq0h x..j4 sq8vj z/orizontally at a constant speed. Neglecting air resistancx9q thp3l vz.hm0 xqj86d4/w7ptj.j n p)zs:me, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-si1 1srwba5 jdc*xth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed andr*d5b1 1csj aw angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relativ0-5tket,y gp *d yk(ope to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car (tp5yko*yk pe tg0, -dis

  You are trying to cross a river that flows due southq k81vfjbyh69 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 poiny16j hkb8v9qft. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much t0jglo 9g62p8j1x pkfbime will it take you to move 12 km downstream, in a river fbj6 l918kp pg0x2 gjfolowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an antx3n 0sc reiqf5v0 )4zgle of 30 degrees below the +x axis. The y component 5 v4) 0ct0ixzq3nersfof A is

  If a ball is thrown with a velocity of 25 m/s at an anbnrv u9*n 2 hrsbl:o)5n71hih gle 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 nortpwz,m ,xqh2y i:j +i,dqxs; 3th of east and you end up 2.0 km north and several kilometers east. How many degr:;zsi2w,xx ,ip qh j,m+td3yqees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/sezfa0 x5/g9k1kx idb 3. The x component of its velocity is 8.00 m/s. The angle betw01e 5zxd3f 9a/i xkgbkeen the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a4k4m kf:n f4btj3h7f)+d 0cr ps,jlpd level ground. At what angle is the Sun elevated above the horiz l)0pnbf:d +scjkf4p4r 37 t,4fkdhjmon?

  Two vectors A and B hj,wakh wh;/ kbz;1s5z ave components (0, 1) and (-1, 3), respectively. What are the coh kjkw,zw hs1za;b/5;mponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivg+ d1lcu 5mce8ely. What is magnitude of the c8cd1+5 mlgeu sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is (8e 7ocplga8othe magnitude loa8pc8oe7(g of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude7(2q:highzk co 48xci of its displa(qiki c o c284hxzh7g:cement?

  Three vectors, expressed in Car *bz 2bp(tq6rytesian 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 Carteshsb3.d7te k/hox b 9c2ei5uh8ian 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 vect8pvbof 0binr l;2i/qp)e( )a wor B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?qr)8b(i ole a;vp nwp/ i20fb)

  A runner runs halfway around a circular path of radius 10 m. kzj*zm 0j24h /q(uoy jWhat is the displacement of the jogj z(j /zqjymo02*4ukhger?

  Two forces are acting on :dw s6vbib3 g(an object as shown in Fig. below. What is the magnitude of the resultantbg v: w63bi(sd force?

  Two forces are acting on an object as shown in Fig. below. What is the directi7xnxo+* +)5q*s l kgz/vqo ebfon of thexz7qle5+bno)qos gxfk*+ * /v resultant force?

  Vector A is 4.4 cm long and points along the positive x axis. Vector B is 5i -j; gm ms1iph.-*zef.6 cm long and points at mze;*f-.ijihsm- p1 g$+23^{\circ}$ 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 and points l37wy zuj1ge7 at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 21 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 22 m/s from(g;7 ltlo* igo the edge of a cliff. A stop watch measures the stone's trajectory time from tloi*; 7(gg olthe top of the cliff to the bottom to be 2.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 11 m/s, from anbew8u y +o:y2i-z eyr9,bor+ bridge. It falls 13 m to the water below. How far does the rock travel horizontally before striking the water?+r-un,wzy bo ob8i r:9y2e+ey

  A ball thrown horizontally from a point 19 m 3 bx 3cd 8v:mw,4bmyvdabove the ground, strikes the ground after traveling horizontally a distance of 15 mm8: 334y,bdvd xvwcmb. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a sped;(.x2 qpt xcded of 12 m/s at an angle of ;.qdc2pxt(xd $20^{\circ}$ 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 mm96h7iolxq g,n hi7-15 m/s at an angle ,ihi 7m7h9gnqm-xl o 6of $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitycs9s 1 7q qsq*b1jk0g hv:u.ok of 33.9 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launch8iafuw, l 9:eclc/iz +ed with an initial velocity of 23.8 m/s at an angle of $44.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofs06ji h4 v.sfs,5hp3 wl(uj yn $30^{\circ}$ 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 horizont/u( 09gx*xx *upjrdzgally at 23.3 $m/s$ from the roof of a building 32.2 $m$ 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 initialrj 24(edy8 4.qvqku aq speed of 64.0 m/s at an angle2e8vqkqyj.uqr(a4 4 d of $39.2^{\circ}$ 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 150nioo9y:4;j j 6lba4da0-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take you to94abj a;ijod : n6yl4o finish would be

  A plane has an air speed,. 8f2l z9f p,mzfortw of 200 m/s due North, and is in a wind of 50.0 m/s to thff2z o, t8f9,wrml. zpe West. The plane's speed relative to the ground is

  A plane is flying dun40y4c1 -x( ,ti8sbdvmquezs mo3b o)e 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 120 km/h is k;tps3s8n h hgy+97 nn4k2pwxdvnr9 , 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 pr xynjy 3 q 9hc lbbdep+)z(45xvvo+j:/ojectile with speed 50.0 m/s in a forward directij)4plez dy+yc(vx5bq3+ :xh/jon9vb on $30.0^{\circ}$ 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 directed acrowu:bn i7pfm3re 9:r a/ss a river with a current o 3:muri9wp7bf a/:en rf 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s i:w p+b4fla;0pkmt0um u:-(ms9gor fm n still water wishes to travel directly across a river 0.6 km widestmr fpkma(+:lum0owf0;:4p m u9g-b in which the current flows at 3.7 m/s. How long will it take to cross the river?

  The driver of a motorboat7 m;8s0 :ugx/ hunw.p)knol od that can move 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 driveru kdghspol0x8 7.) /ouwnm:n; head the boat?

  A swimmer heading directly across a river 200 m wide rsvayy 6 wk85mc,j b,y4eaches the opposite bank in 6 min 40 s. She is swept downstream 480yayw4j cbsv8 ,5y6 km, m. How fast can she swim in still water?

  A swimmer heading directly acrrrli9p-w/)u g oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed ofplw/r 9u ig)-r the current?

  A boat, whose speed in still water is 0.91 m/s, must aim upstream at an angleyu+ ew/h 6fn81 ols)st of oe8)uh sy+1snlw/ tf6$18.2^{\circ}$ (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)  $m/s$