Which one of the following is an example of a vector qb3v1j82kb 1bocmh*eu+4j 0xfmhrk 0n uantity?

  Which of the following operations will not change a vecto80 k0-uz )e;w)wcdtsl+za jo19mzqg gq+w 8ndr?

  Which of the following is an accuratep.+y3q a oe sg3g.1rpa0im/h l statement?

  The resultant of two vectors is the smallest when the angle betxzz1 x:7 2 sw(gd8nnhbween them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively.f :v/ i1bd a1847cqcvnf py1 c3nefqe2 When these two vectors are added, 21/v4d b3ae8qfvyif eqc1 fnpc1 c7n:the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whxn( .b( r3t1 2vhguvk)wm+ b co+sf6wv1oxfv-ich one of the following is a possible answer for the magnitude of the resultantcf2 tbn.or s)wmx(fug(1v3kwx+vhv 1o+-6 bv?

  Three forces, each hay); k(72nij)eff)s jhah u d-gving a magnitude of 30 N, pull on an object in directions that a de(-jfg)k)n hf)uaih;y2sj7 re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the udhaq1/z m, jf.. zk4gunknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velodb7+t 8v 0goczcity

  A ball is thrown with avwebn066 7blo 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 horizon1y4w8 zrd tpclm d13)ztal component of a projectile's acceleration yddmpzwt48z1c r)31l

  A soccer ball is kicked w do t2kg.ovl1*ith 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 is directed anti-parallel to the v-r pzuw naf)w-6i10fyelocity vecz prnw-u0yf w i1-6fa)tor,

  If the acceleration of an object isp .fs g25keqqs;f8qx6)ft d; w always directed perpendicular to its velocit2qesx ;) tkwsqff 6 gdfp.8;5qy,

  At what angle should a water-gun be aimed in order for the watixp 8k.fmddunkj7 1 );er to land with thejf.8d1u7)kpkmd xn; i greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles abovey)i,b 9)5u p 3 fvsdr6lg6ebze the horizontal, each with the sa efr,)) yz9 s6gdv6bb35lue pime 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 secon r-eohm y:a1h/d 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 1o/-hyae hrm: serve) would be

  A ball is thrown at an original speed of 8.0 m/s k0 m)rk8mnc bjf/m0u-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 maxi0r- qoon/hs+ zmum height, how does its speed compare to itr+0nhoz - q/sos initial speed?

  A stone is thrown horizontally from the top of a tower at the samea+ v, mf8vn3wd instant a ball is dropped vertwf8 mvv3 dn,+aically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a secon *f oiswqre2.5nt8ji mix4*,hd bullet is dropped from the same heig.qw o e,*fj45*rihsm2 ti i8xnht. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 91.4 m/k.pp v(2uqtg) s and at an elevation of 176 m drops a package. 7.6 seconds later it drops a second package. How far apappv g qu()kt2.rt will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a sqtg f9 .hlu9 l.)9sgm 1el(awdecond package is dropped. Neglecting air resistance, the distance between theg9llf a9s el).(d h19.q mwtgu falling packages will

  A pilot drops a bomb from a plane flying horizontally at a comg3xcyaza q.g1dt k-t8 7xlf4g/ d 9t,nstant speed. Neglecting air resistance, when the bomb hitkzxq 7d.9 -/4lgf gt3ya 8tcg1mdxat ,s the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixiik izg q u)+a3)l)ro/th of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Eartu)i)lro3 i)iz/aqk + gh, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a sibft1y6a7l:yecw1.+ cgnn 6u traight, level road and pass y t i wug1f.7c1cn6ye: lba+n6a car 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 southd02+mi1ra 2rbfn: .udl 1bf* zhj/t jg with a strong current. You s+0hrn dz m22dg1rfl. ujt*f/abbj1:itart out in your motorboat on the east 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. How much time;v/tdvok7,bt/im66 ,h qpq mr:tv :pd will it take you to move dvtdtqt :6 mv 7pp/ kr,b:,qmhv;/i6o 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an6 8wjyv;k* 3oekw 1 u1ls(bvrkms+jj8 angle of 30 degrees below the +x axis. The ywjj j kvm ly1(oe6*sw;138 bk+8kvu rs component of A is

  If a ball is thrown with a vef p0o mbv/34)vleqd o:locity 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 and f2r3cef/+zofr9 u/kf you end up 2.0 km north and several efoz3c f/9 ur+f/fr2kkilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/foszm 8)/-4w ly n:b bsvclny3- 2uf;hs. The x component of its velocity is 8.00 m/s. The angle between the direction of -l;b/osshby)3 c un: vyw- z82mf4lnfits motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground- cn1ev-9pk xe. At what angle is tpnv ce-e-1 kx9he Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What rtsxr9t6med re4uz348:g y1 a are the comp4d a8utx41s3:zry 6 egr9emtronents of the sum of these two vectors?

  Two vectors A and B have7r4ql+pa hslw i5w az(p1z8p-tl0 e0e components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vee eil5-lpsl t70rppwz(8 h+z4wa1 qa0ctors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnit a kj00g(1s 96pcxiysthez3 r.ude of C 1c6e.gsai( 00tp 3yj 9zxrs hk?

  A car travels 20 km West, theni m2w6hnbox0kr :)o;09hs qyo 20 km South. What is the magnitude of its displacesqr2xh n6y o0ko0)mi ;b wo9:hment?

  Three vectors, expressed in Cart5 ovaqq4d-9o gesian 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 1eyieir t4: td(vxe:7iu6ug dzj+o;.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):s or ru5k+bj)*m rvg) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - j )rusbv+5):ok r*rg mB ?

  A runner runs halfway around a circular path of radiop;kw/b mzf bi,4+ ,ekus 10 m. What is the displacement of the jog,z ip /m+ofkb4w kb,;eger?

  Two forces are acting on an object as shown in Fig. bezd,1r2:sj q k0h7c:4dhon mz9f) h iillow. What is the magnitude of the resu0jdfd)ihq9,k hm4c1hni os7:lz:2rzltant force?

  Two forces are acting on an object as shown in Fig. gpdwy8m/ o;* y6is7hfbelow. What is the direction of the resultant fowo /6 g7y *ipy8dmhfs;rce?

  Vector A is 4.9 cm long and points along the positive x axis. Vector db.hf afmp)m6e6lnx r+5: so8B is 9.0 cm long and point pnb).f ah6s65 mfoe+d:r8lxms at $+28^{\circ}$ 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 ayidbp h*e .q5.la xnp4)ts -)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 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 an initia3k z m2o0q4txyl speed of 14 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 to be 2.4 s. What is the43 kmq2yx0ot z height of the cliff?

  A girl throws a rock horizonta mb5pdw,y9/cp h*;iq di m*3aib1zvc(lly, with a velocity of 14 m/s, from a bridge. It falls 23 m to the water below. How far does the rock travel horizontalla9cimc *qpip * h(vwm1/ib3bdz,;y5dy before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes tqxk-,kc6 4no md 9)9tesdt*kahe ground after traveling horizontally a distance of 2 ak,4 9ctkmonxse)-td9q*d6k 1 m. With what speed was it thrown?

  A jumper in the long-jump 0- wresk5r)ed(,n7h r 77bacmdy+qy tgoes into the jump with a speed of 12 m/s at an angle ofd +s(7,yrmenrh d ct-y 7er5kwb0q7a) $20^{\circ}$ 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 wii 4vr;1+yp xtzth a speed of 10 m/s at an angle o i+pzy; trv1x4f $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initia3qwn 9vj)w z.el velocity of 43.5 m/s at an angle of $21.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 40.4 m/s at an angl mgo5,6i,6 b(wppcqmy8sy/ou e of $31.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired lt*-xl wp2q eot,qe4 a5e58eu 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 shotapo;.o+hrp oy+oy*c c 5d40lj horizontally at 17.6 $m/s$ from the roof of a building 57.5 $m$ 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 grouqsn* n+7wt82bs bmd, hnd level with an initial speed of 62.0 m/s at an absn7,q8 m nwhb2t*d +sngle of $45.7^{\circ}$ 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 cc*u/8isoqwoy i(r (q 7an run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a oc8q /(y( qiu wsi7or*day when you had a 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 y 3u x*yk+r5zzp;f(j bin a wind of 50.0 m/s to the West. The plane's speed relative to the ground izbyjxfy(*;5k z+ ur3ps

  A plane is flying due Sou lwkzb-p9y ,f)th ($270^{\circ}$) 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/h4o o4.3dovu ht 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 g.);hwbobys z94 (g ;s6iks cug/2oahwith speed 50.0 m/s in a forward ss/2bw; gg g9)b6ksza .ohhu4oy( ;c idirection $30.0^{\circ}$ 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 3l yzs3j;dfbj: n3t6 jdem)7d ;mtx ;edirected across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses 3 :3f;l3ztbmtm) j;j 7 ynxdjs6; deedthe river?

  The driver of a motorboat that can move at;+po- oqs 7rdt6zlj*c 15 m/s in still water wishes to travel directly across a riverdqo7sl;z 6 +p-tj oc*r 1.1 km wide in which the current flows at 4.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s r8suj lhd5(;mm q2e kam1s(t. in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstr(kma r( m1;28tushs .md5jqleeam should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches t zpku 8x2ki1h;4s4yffhe opposite bank in 6 i8 ysk;f 14zp24hkfuxmin 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oot( qh3)r*5um hywb1v pposite bank in 6 min 40 s. She is)*o hb 5mt wrq(yh1vu3 swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.u 0*y9t toimf828 m/s, must aim upstream at an angle of 0*t98mfy tu io$24.7^{\circ}$ (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)  $m/s$