Which one of the followhs3 ,fl+/;r ljc0dl nzing is an example of a vector quantity?

  Which of the following o:zev t)oeazd/s3 r) 4-kq ntj+vf2 ue9perations will not change a vector?

  Which of the following is an accuratw7)a,rfg2b+h1kxq c z e statement?

  The resultant of two vectors is the smalldc qlmyl13.aph b34-kest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m8yejj2balpc 5ca)l2om7p y 06 and 7.0 m, respectively. When these two vectors are added, the magnitude of 0jmb6 ac22lcp8)57y oep ajylthe sum

  Two vectors, of magnitudes 20 and 50, are added. Which onl3 entco7c2 l1e of the following is a possibl2tnelc 1lo37c e answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object mn /l1pw1ygew648fv1s,c q d ain directions that a6s f eg 1a1l,vqw8n/4pyw m1cdre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknq* nc,wy3cg v.own vector is

  Ignoring air resista oyh- vh7st+e+nce, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/gjb-smef v04 t(dy k+/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 e o7zc /o9jgu0component of a projectile's acceleration09 7/jzoc egou

  A soccer ball is kicked wiiq4xw3 +gm;tith 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 o2 bpr2i0;6 b,0/nnwr8yxe 0acfp vg qcf an object is directed anti-parallel to the velocitybvyq2a n,;f 2e0x 8rpgpb0wc/0r6icn vector,

  If the acceleration of an object is always directed perpendicular to oe ,1yw8x*gb hits velocity * h,1e8obwgxy,

  At what angle should a water-gun be aimed in order for1e, 2qbb5 z-zp 4n;h c3hbgbwi the water to land with the gpezn3 b1 4;b5biqg 2,zwhbc-hreatest horizontal range?

  An Olympic athlete throws a javelin at four different ao*n6g c 89brexngles above the horizontal, each with the sagx6r89oc*b enme 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 mox 2 +*i 9cul6 imkmmflut*+;)y lw.lball leaves your hand with twice the velocity it had on your first throw, its hoylu*++li )i2c*f; 9ml xlmuwmmtk.6orizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m9s*jt:/fl cz y1j r-wsdzz1 spv/:+ zp/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 reaches its maximum height, how doef6i-c 9;abv3 wy(lnvb s its speed compare to it yvbbv i;9lwn-( ca6f3s initial speed?

  A stone is thrown horizontally from the top of a tower at the same instayeml/ oxvhqd hzitl8-- l+9: (nt a ball is dropped vertically. Which object is traveling faster when it hiti zxlo +-lhm/ 8deq-tvh9y:l(s the level ground below?

  A bullet is fired horizontally, and at6(1z1ay; qiwrk-e. ifale:z9 hm b5rr the same instant a second bullet is dropped from the same height. l 95rraza reyzf.:-1bm1( w;qik6 heiIgnore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally wxr-)o q7x( 65tzc xo 9ifo1bbat a speed of 94.8 m/s and at an elevation of 235 m drops a pack-cx9wotb x)5 x71zof r(6oibqage. 5.2 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 later a second g+m z zvwxbokgq/k*,(j 8/ac(package is dropped. Neglecti cgv a8q(+mwz(gx /,*/ok jzkbng air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying wh.c m10p1n gkhorizontally at a constant speed. Neglecting air resistance, when the bomb hits the groundn k11cgh wp.m0 the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-gjilaik30on317o7g s/zo m f /sixth of that on Earth. If you hit a baseball on the Moon with the same effogo73snomo0z aifg7 / 1ji /lk3rt (and at the 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 straigv0gfu fmkwi4i2 v; 2l.ht, level road and pass avig4;w2uvf0fml2.k i 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 south with a strong current. Y1kek.3)roe yx5ar y, oou start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting pointkx)oay 3 5.rek1,e yro. You should head your motorboat

  Your motorboat can move at 30 km/h in still water..ru5q o70j llz5cejl9h -qvhn-kt , wk6rcz: 1 How much time will it take you to move 12 km downstream, in a river flowi7q- hezzrrlch 6ncj50-l5jk1 . :,wvqtuk9 l ong at 6.0 km/h?

  Vector A has magnitude 8.0 m at an anij .ldn uc8,q hm;h6n8gle of 30 degrees below the +x axis. The y componeu;n , qdhmc86h8i.jl nnt of A is

  If a ball is thrown withv a(uzr u/:xy (el+6ax 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 directia+yt e j u6ly3l2z0mh7on north of east and you end up 2.0 km north and several l l2 eh6j+auyt0ym3z7 kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The.s-mvk gqb t92 x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must btq 9gkm2vbs.- e

  A 400-m tall tower casts a 600-m long shadow over a leors(y krfp,bs .gp(y: (k.1uk vel ground. At what angleurof .((bpsyyk:.ps1k r (,kg is the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3 zdlh1 nd-;t1f), respectively. What are the components o1ndz1d- fh; ltf the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What i7,ipxk3m seu;z.7ydrer) / n us magnitude of the sum of these two vec7n/k r yp. 37;rexu)ismeu,zdtors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B .b z;j hpw83imdz k36i4 What is the magnitude of C ?384d; wk i p6mbzzh3ij

  A car travels 20 km West, then 20 km South. What is the magnitude ow5 g9j-3rqfs y5 arnjawl9jj8m0 d6l2wv+ w: tf its displacem80j w- va5ml:rjtw ywrj+agd w qn9529sfj6l3 ent?

  Three vectors, express n jm *wyns544yb 6 opi+co.8ucmhla6,ed in Cartesian 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 coordinates, eox y8:;xtywx v/4/af7el; zb 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), what is the me 2h;,a;./4fzo v lvhpidcj *bagnitude of vector C = A - B c2jl* ap4feh/zv.; ho;,vid b?

  A runner runs halfway around a circular path of radius 10 m. What is the dik(w-fh-2 lrnd askqzb::,my)splacement yk-,:(mzkd b alr-wh)nq2: sf of the jogger?

  Two forces are acting on an object as shown in3bjfij0rfm1 8xav.vwl9s6xk e;xe6 9 Fig. below. What is the magnitude of the.63kbiwvmfsj9 ;v9exx8x jf 0a1 r6el resultant force?

  Two forces are acting on av*(0zgmsx -m fn object as shown in Fig. below. What is the direction-gs*(xv 0mfmz of the resultant force?

  Vector A is 4.7 cm long and points along the/hs ;xbp4 uzmu/t 73v,+ yoekp positive x axis. Vector B is 9.3 cm long ae4sm u,pu/kytv +/73x;o zhbpnd points 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 66 cm long and19+fsr uopxm; points at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 43 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 initialbr krd*(9upg/cd/.b0mur cl8 speed of 18 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 3.9 s. What is the height o* 0.guprck/(d89 bcul/r mbrdf the cliff?

  A girl throws a rock horizontally, with a velocittx oxvo1e8yl.;h zlk)o6ux / 6y of 16 m/s, from a bridge. It falls 10 m to the water below. How far does the rock travel horizontally bt o.oulohxyx z8;k6xe )6/v1lefore striking the water?

  A ball thrown horizontally from a pointoq* ).*thww:;vvfyq s 18 m above the ground, strikes the ground aftww)qtyo v;q:s. f*hv* er traveling horizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump e 0bqdtr uu,;:goes into the jump with a speed of 12 m/s at an angle o br0d;u :ut,qef $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump94don k5-s mjp q;a oy vs6fw-wt5zopid)(3 s2 goes into the jump with a speed of 12 m/s at an angle of m j of3ydo-kpn6d9t2p5w ov5-w)isq4sz (;a s$19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitjzj3d csoi2k op/j1,9y of 32.4 m/s at an angle of $47.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 52.1 m/s at aaq*73m b+x2 srutx(d an angle of $19.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired st:6 w*xnrb0e 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 horizontaz)4ucwo +o;srlly at 18.1 $m/s$ from the roof of a building 68.3 $m$ 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 gromr3/f cfo qzpst*6,r0und level with an initial speed of 65.2 m/s at an angle o3zc sqrf m0ro/*tf,6p f $47.2^{\circ}$ 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 1500-m race at a velocity of 4ks7 -mt-fc /*3p y)ic2piq qgv.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, tpkq-c*fyqc svi-i/ 3)m2p 7gthe 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 dqq(x : dh,hbpk k:*c450.0 m/s to the W4,(b*xhphk d: q d:kcqest. The plane's speed relative to the ground is

  A plane is flying due Soz7mg2oza z0+),zsqiqc k)1n duth ($270^{\circ}$) 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 ; p23dhfhbz 1ygzi7z4 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+luiqj6w+ ,tr d:. ffn with speed 50.0 m/s in a forward dir6l j ti:f+,.nfurdw+q ection $30.0^{\circ}$ 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 dir8mysn /6qgq 2me0.ae 1hgwu4oected across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses. ngs6 8ygo0ehmu/ 4w1q2maqe the river?

  The driver of a motorboat that ca7ii3cn 4borko6(gc v 7n move at 16 m/s in still water wishes to travel directly r6b (cng7i4o7ov 3cik across a river 0.9 km wide in which the current flows at 6.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to i:fw-cqzf +.m travel directly across a narrow strait in which the current flows at 5.0 m/.wqzcif-: + fms. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 2004rrei axp;-ozbb/a)+3p yup(o :p4hq m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she sp +ep3(qz/riry;pbuxhapb4oo:-4a ) wim in still water?

  A swimmer heading directly across a rin:p ve:ap4io-raa- 3y 6/l2o4lhandyver 200 m wide reaches the opposite bank in 6 min 40 s. She is sweoal6n-rn34av d/ php 2iya -:leo4y:a pt downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.26 m/s, must aim upuo2+qr1*urgz rns 92 r2smvm.stream at an angle of q.u 9+12s2vm2o rrrsng mrz*u$29.9^{\circ}$ (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)  $m/s$