Which one of the following is an example of .szy9y pfd )xvo;3u8wa vector quantity?

  Which of the following operationfxvry5 **+ xpls will not change a vector?

  Which of the following is an a6xh+9 rkr qy,ui i*7odccurate statement?

  The resultant of two vectors is the smallest when the angle 3ggm7, p;q3 ymu b;pz0mq;gpmbetween them is

  Two displacement vectors have magnitudes k-ix 8-efl*otof 5.0 m and 7.0 m, respectively. When these two vectors are added, ti -*ftl x8k-eohe magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addedyas-*ivq m/912mx7 y9guym g/ol, uy t. Which one of the following is a possible answer formy9 *sm19gqlx- yutga2y/u 7vi,/ ymo the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on anzlv(0;p,napv 8i qtn; object in directions thav;qln0nv,ztpa (;8p it are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown ve8:ap.rcidnt0+ t:v vhctor is

  Ignoring air resistance, the horizontal c+xx g 9 p.rws* 0*ycqzm qf9; 1opxgl2rs1jqn8omponent of a projectile's velocity

  A ball is thrown with fdofg7q7 rw::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 resistas a-uzp2;q flt9d1 xl:j+m8ldnce, the horizontal component of a projectile's accelerationd: tl;ds qj9 8m+-1ul2lfpazx

  A soccer ball is kicked with a vtkl8a9g7)mr 7 jmj ,kfrgo68z elocity 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 directe ise i26:p lng8.de.kxygm8bak.s-d ;d anti-parallel to the velocity vec:amdpgx2i 8ys- 8 ;.s n de.belkg.k6itor,

  If the acceleration of an object is always directed perpe3pj1rp/mog:hx 2i t;mw,6qev ndicular to its velocity6p vq3/mo;2xrm:w,h et ij1pg,

  At what angle should a water-gun be aimed in order for the water to land with th +;cii7kw9w pae greatepi;c+7wwk9 aist horizontal range?

  An Olympic athlete throws a javelin at four different angles*kpan9tn2 qq6*,lx + rhdf/rt above the horizontal, each wi6*k/*p l9tat,h +n2fdqrx q rnth 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 forgk 5 rs8tgo 6b7g9k52mbh+i+jf g8 ygc the 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) would bey7tg sjg8 8g5ki+9c5hrbg6m k2o+fgb

  A ball is thrown at an original speed of 8.0 m/s at an angp4x6v0,8 pu 0pugbdyn le 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 ithw,im 6fa 5)-qa 8wmzms maximum height, how does its speed compare to8) m m,zawa6h f-w5iqm its initial speed?

  A stone is thrown horizontally from the top of a towe fkp r/d4p:vzli-35tlr at the same instant a ball is dropped vertically. Wp4lvz:/fik5tr l p3-d hich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and a:;wdm3p ij4x9 n 1s0zng 0 5yhyvppnyc(mm6 c4t the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bulle0pmnv:mw1ynnpz(y4 y 3 i50pcj;s96 c xh4 dgmts.

  A plane flying horizontally at a speed of 89.6 m/s o 013eb6qaxsfa;5pjs + ji;hpand at an elevation of 284 m drops a package. 6.3 seconds later it drops a second package. How far apart will the two packages land onaj3oj ;0aqphf1;p5bi+ e s6sx the ground?

  A package of supplies is dropped from a plane, zb;wu)qv9b3y1b m9u pte+i-emdk7p - and one second later a second package is dropped. Neglecting air resistance, the distance between the fee-31) uvmy+zu- tpb 9;wp 7bb9mkiq dalling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Nz/5, swx,3w .pi*vi2 jm:a yigxbrc*meglecting air resistance, when the bomj,iw.i waz b,yp*r/ ix:m3mg *c2vs5xb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is o.mrkut+ um +,vg( uevcl*1*vpnly one-sixth of that on Earth. If you hit a baseball on the Moon with the sam+lguume p+*ku(v t*m.v1,crve effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h inz nlvja15h 3p* the +x axis relative to a straight, level road and pass a car pv3 5zn j*ahl1traveling 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.+qfqyl2q r mc, l42t;f You start out in your mott2 ffl42yl cq; q,m+rqorboat 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 stil zg 8;ymk:jn*bl water. How much time will it take you ;:b gkymzn*j8to move 12 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 t 2 -qckv79apcp9v(ztwhe +x axis. The y component of A is kz99qp(cv-a2 7vc wtp

  If a ball is thrown with a velocity of 25 m/s at an angle of*ygwe/3 d58wf* oh3j yseshd5 $37^{\circ}$ 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 and9 iyjc 1m qfxoi3y9.7vi.zcc* you end up 2.0 km north and several kilometers east.fi.1 cmzio9cqvy7.c39xi jy* How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The ; 59iplqgvjua-xxt *6 x component of its velocity is 8.00 m/s. The angj;t qux*a9 g-p6 vxil5le between the direction of its motion and the x axis must be

  A 400-m tall tower cn;z y)5 og wn2tf 4clf.q942hna4ud wjasts a 600-m long shadow over a level ground. At what angle is tq4o 4g ffw)un2ah92z l54 .;ndjwytnche Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whay/* roz6 xcdja *xj/igud*vhntn 6(+;t are the coi+z u/d nnjvx xhj**g6c(6;*r/oadty mponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. W .tae7 iar wmq(7ly3 nlk8b*;qhat is magnitude ofq(i;n7y*bw3 k t.a le qra8lm7 the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, r-0)w lp(oe o0gc kdpv -k h7td-5c;jv0). Vector C = A + B . What is the magnitude50gce0 do)-l-- ; pcrwvpdkt(k vojh7 of C ?

  A car travels 20 km West, then 20 km South. Wha;4esdotn; 8 txt is the magnitude of its displaceme84xtnt;e d os;nt?

  Three vectors, expressed in Cawhe * lxpemr (v-6g/oo n1,s,artesian 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 coorj3,7wh*z28 /f tx tgaa aru*prdinates, 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.*rg)iubcl9u lr2*tu3 0, -8.0), what is the magnitude of ve9i*trg l*3u b)rlcu2uctor C = A - B ?

  A runner runs halfway a2t0tjopp w*+b7rr 9-qlneg, iround a circular path of radius 10 m. What is the displacement of theitrt*-g p wnrpoebj7+l,0 29q jogger?

  Two forces are acting on an object as sh cl0f*tc8yj: qh .s/etown in Fig. below. What is the magnitude of the resultant for yfts*c c/qtjhle.08:ce?

  Two forces are acting on an object as nz m5h a(dd,yeq 806 qdegq3p.shown in Fig. below. What is the direction of the e6 qm.dahqzg,eqpnd5d0y 8( 3resultant force?

  Vector A is 5.5 cm long and mg 0l8.xd+ iy6bw+eudpm*pq n3uxp29 points along the positive x axis. Vector B is 8.2 cm long and pow+eup3 y g2 8inxupb+qdmx6.l 0*dmp9ints at $+23^{\circ}$ 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 56 cm lon4t5(qhjx9 f ofg and points at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 29 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 initialot7 mcf+i;kot(a i,c . 5tqit: speed of 15 m/s from the edge of a cliff. A stop watch measures the stone's trajectory :iiqf tc i+a(; o5,tctk.o mt7time from the top of the cliff to the bottom to be 4.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a2*az3veo hwx., wse3s velocity of 9 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally bef 3weze2sxwohv,*.a s3 ore striking the water?

  A ball thrown horizontally from a point t/ij kx/fiin x-+g2r(22 m above the ground, strikes the ground after traveling hi nx t-ixr2k /if(gj+/orizontally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump withdhqle(:,yn0 w1 7m hpl a speed of 12 m/s at an angle of 1 ye:d7pmn h0hl(l w,q$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump gxb,uf whkkei2 7 (:,shvq*6ow wrl+m/ oes into the jump with a speed of 8 m/s at an angle of , hlub7wfv, /ek+ xw o:kw*i(hq r6s2m$23^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 37.2 m/s at a o /i 4 7u7v58p5w*hlnfi;r(hsobprrp n angle of $47.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 33.6 m/s yb7j0hw :u-b eat an angle of $49.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anzt /vi3b kc7+9 c1ahwxgle 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 horizontally bx)g0l 9fr cdgq0.lk- at 26.5 $m/s$ from the roof of a building 48.6 $m$ 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 grounx2tw y,3jhohqoay(y, s w123 bd level with an initial speed of 55.5 m/s at an angle o,y w xho33(jybs2hwy1o, ta2 qf $40.6^{\circ}$ 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), you can run a 1500-m race at a velocity hah.;n+7)oycd)g qtcj8q, l1 q*zsdmof 4.0 m/s. If you ran the same race on a day when yo* taq,+ozg )nc7m) qcslhq ;8j1hy.ddu 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 in a wind of 50.08asu d px (p oduhft/2*p+8n0x m/s to the West. The plane's speed relative to the ground isxdh*a ptu0uf8 nx o(+/spp28 d

  A plane is flying due South (z /agz30bt aya0 zr3+aer(l+vqg+ h 2q$270^{\circ}$) 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 2bp/ui+ ke: :ox l ncmj q55f:;mrxax(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 ho9m b- *pbx)zltrizontally fires a projectile with speed 50.0 m/s in a fo9 l- pb*tz)bmxrward 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 water is 8.0 m/s, isrrr) 2u v*7jxg directed across a river with a current of 6.jxu *rr7)vg2r0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motor f4bk6xsk7rg, boat that can move at 15 m/s in still water wishes to travel directly across a river 1.1 km wide in which the cu f6k,xsbkr7 4grrent flows at 4.7 m/s. How long will it take to cross the river?

  The driver of a motorboat 8xwk-gp y * qpub :v1.czdk.a*c3cqr 8that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at q.x*8z u -1.qc vcdwg3p 8rkk*:pby ca5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river)p -bs+z4qjrl(7y tqn 200 m wide reaches the opposite bank in 6 min 40 s. She is nr(b4 lpq-)jty+zqs7swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bankdr k(j/tf v, 2*pe6pel in 6 min 40 s. She is swept downstream 480 m. What is e ,6l2fdkpj* epr/v( tthe speed of the current?

  A boat, whose speed in still water i wbeh10/c 0wol 3lpgd.s 1.29 m/s, must aim upstream at an angle of bd e.wcg3hp0l o0w1l /$15.0^{\circ}$ (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)  $m/s$