Which one of the following is ax0w7v 2*(vdm7ijk0m( g j nlntn example of a vector quantity?

  Which of the following operatiwk/j .lkcbm,f 5udgs 5b9 t9onu,g5, rons will not change a vector?

  Which of the following is an accurate state3/ zvj;wh1sguej,c r1ment?

  The resultant of two vectors is the smallest ww6l)(tvdm ;.r ;eh-pgr2hrrvhen the angle between them is

  Two displacement vecto a3 1w/1sf;;euxm hj )m2ujr(qdpn6rj rs have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the n qh)amwj6r(/ sf3u2pr mej1;xu;dj 1magnitude of the sum

  Two vectors, of magnit+h,7qqmm(c vaudes 20 and 50, are added. Which one of the following is a possible answer for m+hqq,a m7(vc the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull o42n(xb -i: jdrac8qjpn an object in directions thr-j42dnqpx(c:i b a 8jat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknownzf e d5p-y 3xz:l5vanw7p2ob; vector is

  Ignoring air resistance, the horizon(xpuafq.6 yyypp5a;x2f q/l 8tal component of a projectile's velocity

  A ball is thrown with a velocity of 20 1xn 0g-3yh:hk vtp,igm/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'squ;8+ jzre/sefu2qq( * yv,gk acceleration+k*u8q 2q/gz ree sjvq( ,uy;f

  A soccer ball is kick4 .8yyz3qj nfx) xx.dped with a velocity 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 of an object ie 0yfihwl18 -hs directed anti-parallel to the velocity vectorlfie0- hwy8 h1,

  If the acceleration of an object is axiltojhg6:d7+44n +ppa s kn/ lways directed perpendicular to its velocity,in6 ljx4 pson+kg+4at/7d h:p

  At what angle should a water-gun be aimed inlaj ( 29 m,xpfhyip nfg6 .vch9e-/a5b order for the water to land with the greatest horizontal,x g/9 p9f eh(-a 56nmy.fc2hvajpbi l range?

  An Olympic athlete throws a jadtis6 1c f(fvl)f4,thvelin at four different angles above the horizontal, each hf 6ltsf,i1( f4d)c vtwith 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 tk1a(7 ) m ;a3porbufdi.bgpg+vl9h9m he 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 serve) woub gupar lm 9d 79a1;)kfhp .i3vg(omb+ld be

  A ball is thrown at an or fj77d5qap az,u oftj4)gv2 6 s7xohf)iginal 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 goal attempt rea )eu6hsgm9dre.vvs pe ;6(tg4ches its maximum height, how does its speed compare to its;(reh9u 66.d4pmsegsev tg v) initial speed?

  A stone is thrown horizontally from the top of a tower at the same insr3 rerj6xd vsu*f-u ;9tant a balxjr ;u9uv6r * fdres3-l is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontalg(8z,2y hq+ew 1)elu fb)frfg irn w21ly, and at the same instant a second bullet is droppew2er(e 2,fu+lwi 1gff1qb r nzh)8y)gd from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a sgt a)y7il z ;.24ygu5p,qg vtxpeed of 46.4 m/s and at an elevation of 249 m drops a package. 3.0 seconds later it drops a s.;ayi 5pvl txq,uy t2g4z7gg) econd package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and onek1 i6hqlhd,uz+d 4 x6pe7lk m/ second later a second package is dropped.6d/h lep,mx7lqd+hk iz u61 4k Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constantsj7h) 6ln4mux speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of 4 6msjln)ux7hthe plane will

  The acceleration of gravity on the Moon is only one-sixth mlhz ie2) x6 )ea(pt9vof that on Earth. If you hit a baseball on the Moon with the same effort (and at the ximl) h6zpt2v ea)(9e speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road d jih g,-c;h ;07osreuz8 dj)gand pass a car traveling at 45 mi/h. The relative ve,0odu;;s chhd7e i)j rj-g8z glocity of your car to the other car is

  You are trying to cross a river that flows due souu* *9 e)r -l05lcfuatuqxf1nx th with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your sta l la)0u qftu1x* fncx9re-u*5rting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How ofh dm8ep ,8x7)mw mp3/rt.pc much time will it take you to movemf8ph7m r3op8e,) .wd cpm /tx 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an antt c ogqnv*jmmi8:*81gle of 30 degrees below the +x axis. The y componeni8qmt:v18ct* *ogmj n t of A is

  If a ball is thrown with a vel7v 6,n x b,/nehgj-(g4ltha6r9drcy focity 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 of east rcb /lrz h8e.. kr fw+mp7-+zuand you end up 2.0 km north and kfz r el+m8/.wr7cubph+z. -rseveral 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* bps 9o* s/mtqhfou/+ of its velocity is 8.00 m/s. The angle between the direction of its motion and thefs+ho/ /9*u pbqtmos* x axis must be

  A 400-m tall tower casts a 6050lz4p8t qdp o9qg+fz fyc.1 v0-m long shadow over a level ground. At what angle is the Sun elgv890+5zfqcpfyzp .dq4t 1 olevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), resqs+o:f )ccc mnyr y+,, r0ynw4pectively. What are trcf0sqwom + n:y,nyr)c+y ,4 che components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and u6p;eb+ybnh )(-1, 3), respectively. What is magnitude of the sum of these + bn6) b;peuhytwo vectors?

  Vector A = (1, 3). Vector B = (3, 0). V 7/9 ),drsurcdy6gd lfector C = A + B . What is the magnitude of Csld /96grc,)urdy f d7 ?

  A car travels 20 km West, then 20 km Sk7l:sap i1sx8 2(9nbe dvb 1gpouth. What is the magnitude of its displace eagvd: 27pp9k bb1s1nxi8sl(ment?

  Three vectors, expressed in Cartesian howgt3.6r,b4ux o9dmu0ry ,j*gie6scoordinates, 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 /dvb1fo k/5t:qhq2-*y y hwftCartesian 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 /.*u9bh/.l pmhu1 ;tnjapbgu B = (+3.0, -8.0), what is the magnitude of vector C galt1j9bmnh b/uu; / .p*hu.p = A - B ?

  A runner runs halfway around a circular path of r b0;16vrtg m,h2 xsdhuadius 10 m. What is the displacement of the jo;,d1hg bm s 0uv6t2hrxgger?

  Two forces are acting on an object as shown in Fig. below. What is i1y8luwf ;va+r+g6 qz the magnitude owv++8f1y6g uliz rq;af the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the direx* ry/(qhmf) dction ofx(y/rq )hfd* m the resultant force?

  Vector A is 3.4 cm long and po5x )y e8;l /hauo8o g:rol7zzcints along the positive x axis. Vector B is 5.4 cm long and poinc 7o;)zugx58lo/ oe 8rhaz:ly ts at $+34^{\circ}$ 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 58 cm lon+xzjt :vokj6b5 u9w5cg and points at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 27 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 h8npit4 c1 e*ban initial speed of 12 m/s from the edge of a cliff. A stop watch measures the stone1i84bp *nchet's trajectory time from the top of the cliff to the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velo2 oe3bii r*h;pcity of 11 m/s, from a bridge. It falls 24 m to the water below. How far does the rock travel horizontally beb3r;heoi * 2ipfore striking the water?

  A ball thrown horizontally from a point 18 m above t2np yav62o6mms4 7n:ttohl/ehe ground, strikes the ground after traveling horizontally a distance of 12 m. With what speed was it thrown tn2 6yhl2aopm:v/esmt n4o 76?

  A jumper in the long-jump goes into the jump with a speed ofvdou kr gf*e1qicm-/kbu/i6l/ d+ s:. 12 m/s at an angle ql6ke-. bgk i/ :/usdm1oicv/dfr*+uof $20^{\circ}$ 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 13 m/s at an angle nhi*do ))mlhrq5,3ng of di*),qhh53o)ln mrgn$33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wit g:20 -h5vjgktm;-;clfcrx cbh an initial velocity of 47.7 m/s at an angle of $43.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial)/ hxw+mod; rkm 0ks7psw27yr velocity of 50.1 m/s at an angle of $18.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedxid+gubc f39 od7r,w,y; po. z at 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 horizontah .p: fkia5 bht35wvdod.6 ez47vlol, lly at 20.3 $m/s$ from the roof of a building 55.1 $m$ 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 levenjqxm0i9-,.2d 7 enb eb m9teil with an initial speed of 58.4 m/s at an angleidetenm.9q2e0 79, m- ibxjbn of $47.1^{\circ}$ 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), yol*f9 t a2mnd4mu 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 headwintad4mm2 *9nfld 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 toau4 kj 9e,pf(55yrulq the West. The plane's speed rel4uu5(, qk e 95jrlpfayative to the ground is

  A plane is flying due Soei xss3o a+gpc,131yj;pa d: tuth ($270^{\circ}$) 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 spee(ap;13lzbkb.e4o g )fob*sutf i,2 to d 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 poon /wyd :(y*ev*1oearojectile with speed 50.0 m/s in a forward dirw/dov e1oyoy **e (a:nection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stilnr- d5+ f9vavcl water is 8.0 m/s, is directed across a river with a currentvr5+ v9cn-d af of 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 11 m/s in st y.prd.2-u amys, n3chill water wishes to travel directly across a river 0.8 km wide in whic- p,yy.2 r3sdm.u ncahh the current flows at 6.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in sti2zte9z rsq 4;bxn .jb;ll water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s e; 4nbz 29z.jrq;bstx. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide re t3u6 w+wrq2xfaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. Howxfq6 r2wwu3 +t fast can she swim in still water?

  A swimmer heading directly acrom7,nw -p +to/pwgqu2 oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What i ppw +-o2wq7 /u,otgnms the speed of the current?

  A boat, whose speed in still water is 1.80 m/s, must aim u:zezg0 ,tzspe 3sw8x9pstream at an angle of wg0s,:szzxez 3ep 8 t9$16.8^{\circ}$ (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)  $m/s$