Which one of the following is an examplj:2.9uh r h8hnz1s smqe of a vector quantity?

  Which of the followinw na8rb.,bk755u qs3z8hvoya g operations will not change a vector?

  Which of the following isvia4frzcg4)2nq,zm /;r y jq5 an accurate statement?

  The resultant of two vectors is the s facxmcer(0m u/ob47u t2-ti0mallest when the angle between them is

  Two displacement vectors htnfaeg i/8k.y y1tl+dmw ;23lave magnitudes of 5.0 m and 7.0 m, respectively. When these two vecto td2l3ie nyma1k+.flt;g y8/w rs are added, the magnitude of the sum

  Two vectors, of magnitudp 6ts1x*jg , x0pay(zzes 20 and 50, are added. Which one of the following is a posstzj 6 z0*xyp sx(gp1,aible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions t2ndztosuv fx58+. y7d hat a25xuy dn.s+o7 fv dt8zre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram showndbk00an:b zt (, the unknown vector is

  Ignoring air resistance, the horizontal component fxp e,-ls3xsoa qf+vih:7x97of a projectile's velocity

  A ball is thrown with a velocity of 20 m/snl 3a;lsp0 yd8 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 horit2ut8ws yu,xi7q*,y ge.f6m xzontal component of a projectile's acceleration s*uiq8t6ugx ,t,. w27em fxyy

  A soccer ball is kicked with a velocity ofcs7;f3 isj by1 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 directed anti-parallel to the velocit+:,poznhg lng k5 h5-1y ao9jky vecto:oaphl5k19y, jk+zn 5- h nggor,

  If the acceleration of an obp* te/g82zmurgwq1c.s4b 1 gbject is always directed perpendicular to its velocityg m8rg1ptg w 1q2s/u 4*b.cbez,

  At what angle should a water-gun be aimed in order for the water to la rrk 55hityr95nd with the greatest9ytk 5r5r5hir horizontal range?

  An Olympic athlete throws a javelinmk1 d;aksq x7xj4/acgk 0-b5o at four different angles above the horizontal, each with the same s/ k4xqod1 -k as jacx;kg507bmpeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. w qs97-oc;sbhui m1-h If the ball leaves your hand with twice the velocity it had on your firsuhms1c h- 7bq-s;woi9t throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spee(and-ki+y 7a ho1t9c;opd 3wrd 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 f,g r8suh+8xi7is-n imp jua98ield goal attempt reaches its maximum height, how does its speed cs g8h9pa7si8ruuj xmi8+ ,-ni ompare to its initial speed?

  A stone is thrown horizontally from the top okc1wfo 9m9lc98v 6yvkf a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level grov9kl1w 9o89m6cfc vkyund below?

  A bullet is fired horizontally, and at the same instant a second bullettlzf2dktp m20 n l*1z* is dropped from the sa 1lkzt*tp0fmzd2*n 2lme height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speea(pi1fh39pj25v4 .pxdk r s23w ywdsjd of 90.2 m/s and at an elevation of 180 m drops ak123(shj4dpi xwp vy5w329jfp s.dar package. 3.3 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 a plane, and one second la2m) 3u ngpefq)ter a second package is dropped. Neglecting air resistagp) ufeq) 23nmnce, the distance between the falling packages will

  A pilot drops a bomb from +1-lc t v.qp bn8niw.xa plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal lo1l cp+n-vn.b.t iwx8qcation of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Ev mo,.m f(er8o3lqh u7arth. If you hit a baseball on the Moon with the same effort (and at teo(qml 3,fr8 hu ov7m.he speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mk2g ogem9zqte8r51 g)b +ni5wi/h in the +x axis relative to a straight, level road and pan+w 1gtzgr5k ei982)gqboem5ss a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to crjo i t)v/8 cgwvqph0xw+;/,asoss a river that flows due south with a strong current. You start out in your motorboat on the e,/hqgoa;8 iw0c w/)s vtxp +jvast bank 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. H(xt9)9iklmjm +nd1 . ;6ck aphh:fjdhow much time will it take you to move 12: hmxam6( +th hjj9pfkknd).ld;19ic 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. Tv8)8 wpxndi9z he y component of x 8w8inp)d vz9 A is

  If a ball is thrown with4kgv4 ut9n ,gs 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 line in a directio) db1yyh3a8 bin north of east and you end up 2.0 km north and several kilometers east. How many degrees nad13 yb8bh yi)orth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity io28sjxf ko+(ks*zez (s 8.00 m/s. The angle between x*2( z(foo+ szkjek8sthe direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long sh8s6mo (sv..iag swr6um ,2fh yadow over a level ground. At what angle is the Sun.i8somu sma6vy,f rg.w6h( 2s elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3)j3eb;j 2 zpksgd*,a/p 9 (9bykjjll3d, respectively. What are the components of the sum of tslbaj*bkl,p 9 3yeg2 z;/dj9j3 d (pkjhese two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wtpo1e, m s:md8hat is magnitude of the sum of these two vectos1:d8tm , empors?

  Vector A = (1, 3). Vector B = (3, 0). Vector Cp8qgnm(y5 ;e e = A + B . What is the magnitude of C np;e5(8eyq m g?

  A car travels 20 km West, then 20 km South.sn/f wk, g63wi What is the magnitude of its displacnfwi 6k/3gs,w ement?

  Three vectors, expressed in Cartesian coordl9d5 83xat wvoinates, 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 Carazxlngwxl pm1,u5 xx )6k5m:+) yp4v atesian 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), u 1jik(/u:cuewhat is the magnitude of vector C = A - B /j cu u(i:e1uk?

  A runner runs halfwayon ; zhz0po.iiumx8 .6 around a circular path of radius 10 m. What is the displacement of the jogpx6zmzio8;ih0. n u.oger?

  Two forces are acting on an object as shown in Fig. b)uej(4 hskd a,zcad, ezr.3gp874u fgelow. What is the magnitude of the rd.cgk hg(a4d4 )j 8zas,e7u,z pu3fe resultant force?

  Two forces are acting oway8k3 b/u k2vxela5 4n an object as shown in Fig. below. What is the direction of the resultant forcev5ak3xk8a w2y4 ulbe/?

  Vector A is 4.2 cm long and points along the positive x axis. Vector benoj4, +cwj3 8 y67otsz5*vd8ckwdxB is 8.4 cm long and pointo, zte63 cvonc+j5jd*74bs 8wd 8xkwys at $+58^{\circ}$ 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 53 cm lonocm)g+02.k y0n qqxsh g and points at $30^{\circ}$ above the positive x axis. Vector B is 23 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 initial speed of 28 m/s from the ed( up+) ( ulim9azxo+teq ,7rgdge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.1 s. Wha ((xqguz po9au+t,d+mi7)erlt is the height of the cliff?

  A girl throws a rock horizontallg8xuv3wu g pu7m5,ln -y, with a velocity of 5 m/s, from a bridge. It falls 22 m to the water below. How far does the rock travel horwg x7p3uln g- uu,v58mizontally before striking the water?

  A ball thrown horizontally 8ftu7 0)1 -6cpp4c lhi6fmn4yueldky from a point 26 m above the ground, strikes the ground after traveling horizontally a distance of 17 m. W-cc yetf )64k uil6d7y8fmpn4 01 lhupith what speed was it thrown?

  A jumper in the long-jump goes 3scs34-.ray ytnmor0into the jump with a speed of 12 m/s at an angle ot-.3sc yny4ras3m0 orf $20^{\circ}$ 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 aude(mdeh xl0s. p(g u 395c(dnt an angle ofdde9dg3 5c u((phux 0l(e.s mn $33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of2w z :am0l1b xz jury+t(b; lz3wg(j+o 31.2 m/s at an angle of $14.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vs5ucj rq4o9;mb p:mi7 elocity of 44.5 m/s at an angle of $25.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an 8 +ln..kd shn6hv6oam 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 horizo( jcku4piiub- p5a75v ntally at 21.6 $m/s$ from the roof of a building 42.5 $m$ 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 /tq/ lm1w 7cbtspeed of 56.2 m/s at an an1 /tcm7 /qwbltgle of $39.6^{\circ}$ 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), v(pbkqyd*7m/d+eifivm / ro/ 7uw ;/fyou 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 a constant headwind which slows your speed by 2.0 m/s, the time it would take you to finish woulwo/ pbfm/(/qmuikr+77/ eydfi ; v* dvd be

  A plane has an air speed of 200 d7kw49* i fx y n:;ohd4u-*3llzik: yvi;hqlsm/s due North, and is in a wind of 50.0 m/s to the West. The plane *9 k-iq 3u4ldhhflxyi7s wn;:*vzkl d:io4y;'s speed relative to the ground is

  A plane is flying due South (*f shizm9 7i++inl6ll$270^{\circ}$) 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 pw5mt 98dsx:5 b3xf1q bsf l.lkm/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 cnj 8(e r4n2ruwith speed 50.0 m/s 8(n cr4ej2r nuin 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 water4mtgv/ev2:w eh03sf:l y4 lbi gbz6i 8 is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it cross 4gmzy3bg libtw6vef:4/el s2i:8h 0ves the river?

  The driver of a motorboat that can move at 16 m/s in slh+t w uyz(koetrk e, *25vj,/till water wishes to travel directl+,*hrkktj ,elutzey v 5/(wo2y across a river 1.3 km wide in which the current flows at 5.3 m/s. How long will it take to cross the river?

  The driver of a motorboatg;k+wcir oc-i*u9m9j 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 drwokgicj 9;i*9u r+- mciver head the boat?

  A swimmer heading directly across a river 200 m wide re oos x0l3dbg6+2bx vy.;s6eg c7/atgsaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wadx tol+gg.0 xbos2 6gyvbs3 7sce/;6ater?

  A swimmer heading directly across a river 200 m wide rea-f+kh4qsdy vv0 uro8pe t8,5p ches the opposite bank in 6 min 40 s. She is swept downstream ho,-+fetdky8v 5 sqpv84ur 0p480 m. What is the speed of the current?

  A boat, whose speed i o)*.b zpfkx)m,j3 izun still water is 1.45 m/s, must aim upstream at an angle ofo.ku)ip3*z m)x , bfzj $23.7^{\circ}$ (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)  $m/s$