Which one of the following is an example of a ve5:wdqornd e0lsw *tvbbp6k)6sd9n8 ,ctor quantity?

  Which of the following operations will not change a ve6 b e+j2.tv/x+. u- supw.dpnl3nqn zqctor?

  Which of the following is an avajg2d)oeo9-9d8 q6u g0qs e fccurate statement?

  The resultant of two vectors is the scz0e.b+ op- dsmallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m a9fpkk(/c eh*q)v+v0xj8a hyl nd 7.0 m, respectively. When these twoje +hc/v)a9y0kpxhf * kq8lv( vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 1q +rwtalqdn;(4 9*ixsh 9w3lt n*ilv50, are added. Which one of the following is a possible answer for the magnitude osh*4(9lw 93t1;lnqn *t ix+lqrvd ia wf the resultant?

  Three forces, each ha kshrb z;6vs1yh2 :t.wving a magnitude of 30 N, pull on an object in directions that ares6.s wrzv hhy2 1:tbk; $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the kvbpx*;7 hfh7sa 4yj,unknown vector is

  Ignoring air resistance, the horizontal com 1ay( ca ;oj4i:ijyr ukrxiq/30:j8wjponent of a projectile's velocity

  A ball is thrown with a velocity of 2zwmk.* w1 ndw) i-7fre0 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 horizontal component of a projectileom,0v 8ddz 3qd's accelerationdoqdzv3 0md8,

  A soccer ball is kicked with x h qriblkj6u-dl4s* v18roe3f(8.i n 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 vecto0o+o7lizboz8wz6 t )r r of an object is directed anti-parallel to the velocity+rz 0 )oib7zzl8o6wt o vector,

  If the acceleration of an object is always direcmf, z.91mr in 0upi5dxyvue;( ted perpendicular to its velocity,u9; nixp y,mdu1v0.i r f5m(ze

  At what angle should a water-gun be aimed in order for the water to la j+/nk5ifc 5vvv1 v6;eiked3wnd with the greatest horizontal rekvvn 6d3f+c /5w5j vki;i1evange?

  An Olympic athlete t k/8rzu)(ezzglp9h+f6z cpd0v hw,5l hrows a javelin at four different angles above the horizontal, each with the samezphukrf 6zvz8 ze 0 gh(c+)pl/9,dlw5 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. d6x(s:f 9dfquc :4(z8 dshkawIf the ball leaves your hand with twice the velocity itska6w:cdhf(xzu8 4f :(sq9dd had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8. r(j t m+ywhk9yi5r :ge(0htu30 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 reaches its maximum height, howm vw9-vb8ja v4n+x pkzmg:w, tx :a9f+ does its speed w4p 99 tz: f +:maa n,kjw8bgxm-v+vxvcompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the:*nm: (f+ zt9f iyntar same instant a ball is dropped vertically. Which object is tra*tfm nt f:n a(+9z:riyveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at3p escq6/i:me/kx yh0hl3qu3 the same instant a second bullet is droppcq p633yx0sl:e/ki/uq em 3hhed from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 102.3 m/s and at an 69zasdfw8vl ,elevation of 225 m drops a package. 2.9 sel86,9 d zvwfsaconds 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 secog/fny 0bo zx:wc:+/ wind later a second package is dropped. Neglecting air resistance, the distance between the falling package0 obnx gi+z/::fcwwy/ s will

  A pilot drops a bomb from a plane flying horizontally at a constant speed-s;d 76hwg -djs 8hc.dh 3ukfq. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plans6-d ud j d7hfqw83gc.h ksh-;e will

  The acceleration of gravity on the Moon is only one-sixth of that on Ear.oni xdzs+an-j5r0:l.)r j fith. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the brd.nsfi. lxaz j+n) o 5j:-0riall would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level rhc ma3u*9 qy7tl f;uu2)tjy 3eqo9h9eoad and pass a caeh9lu q9o u2qm tf;t*y7jue h )39c3ayr 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 yb.7z*i *ne 9gdooij.due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shouldzy jb7o**9iginoe ..d head your motorboat

  Your motorboat can move at 30 xg1 f. xz9( j2btjnxioiqr;-2 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowii1to9r.z-( n;g j2xjix2 bxfqng at 6.0 km/h?

  Vector A has magnitud h 09l nj-)f(ewrch)n)bqi0ude 8.0 m at an angle of 30 degrees below the +x axis. The y componenej0-) 0(lhnun9f drhw)cq )ibt of A is

  If a ball is thrown with a velocity oyb ixce p)lp nw(m/q99by4 f9x j0s*c)wt :jj1f 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 you ennr1hvhm/mf xp; w ;h,*p79huyd up 2.0 km north and several kilometers east. Hpvmm r,h;9 yp1*wun h/;hh7 fxow many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compd4. 5oxhk.j 5ho m8mkhonent of its velocity is 8.00 m/s. The angle between the direction of its motion and the x aojhh.85mhm k xk 5do4.xis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground8oa fmvzgglu0j*9 9grh: .3d j. At what angle is the Sun elevated above the890:h*.zfd a3rgvjlujm go9 g horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively.z 5 pztoj(n p-(d:u2xyt2cz4u What are the componp2( (nt2uoyjp 5u4z- z:dzx ctents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whabz8/e grth/ mn (0sj0jt is magnitude of the sum of these two vecg/jrbmh t0n sj/ 0ez8(tors?

  Vector A = (1, 3). Vector Bo8r:vnh d4rl 6 = (3, 0). Vector C = A + B . What is the magnitude of C lvr846 ord n:h?

  A car travels 20 km West, then 20 km South. What is the mhowz -:ymqmw-g ,;op/agnitude of its displacq-ohpomw;m, :zw- y/gement?

  Three vectors, expressed i1+w dd5savg 919v9 jpkur:vten 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 Cartesil2svlsza6r1rq0cns) z -c+t0/omz :b an 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 8bm, gh6ot.jdm 5lmx1= (+3.0, -8.0), what is the magnitude ofdbmg to.x j6l18hm,5 m vector C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. Whaixe1cxpl- uq+)k/uz g3p7 v oz7 ;qf:gt is the displacement of thv x koezuc ql uqp/z1+3gg-;fx7:)p7ie jogger?

  Two forces are acting on an object as sh2yqtkcfpzafti).2 16 own in Fig. below. What is the magnitude of the re2zca1 qfkty6 .2tfip) sultant force?

  Two forces are acting on an object as shown in Fig. below. What is the d31 a tu2 ouxzw5:b.is am3-xomirection of the result .xbts32wmua3iz a- 1uo5o xm:ant force?

  Vector A is 4.7 cm long au /w )hp-tswok 2yl4r3nd points along the positive x axis. Vector B is 5.6 cm long and points 3w2tp4r)s hw kulo/-yat $+28^{\circ}$ 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 86 cm long and p3otx7./nn* ox5xfjk:b f zijs( -1uyshz c))moints at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 24 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 1ev34*tg lgsr )hwn.io:s1)t r y;xk3.ojh 4eu1 m/s from the edge of a cliff. *3htu toxvry:.4k e;wrlh4 n )s31)eogs j.giA stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, o phifj)a:8(5z j-apb u,2esewith a velocity of 20 m/s, from a bridge. It falls 29 m to the water below. How fa 5ai:pb8heoa -,je(uz f2jp)sr does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 mzdnzw 2-03eb*afcl e: above the ground, strikes the ground after traveling horizontally a distance of 17 m. With what speed nzezl2 cew db0:-3fa* was it thrown?

  A jumper in the long-jump goes into the jump wit( s+s)d6 ajqx x +4nwx5wr76mv,llvush a speed of 12 m/s at an angle ofr vj)mw7 xux4w6 s+vqlsnx+,as (56dl $20^{\circ}$ 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 lo cz (uq9/hy3jump with a speed of 13 m/s at an angle y lz3/u9(coqh of $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an i+v s+kn:g a4npnitial velocity of 39.8 m/s at an angle of $13.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 27.3 m/s at an anglu1t-7 np ipl:q.qnr p5e of $22.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of4d3c+jw: q9nus el 0x qm:tw48wxp5qc $30^{\circ}$ 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 at ;eiy esz,89wf(rbk q- 25.9 $m/s$ from the roof of a building 51.0 $m$ 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 speed o8my dn,4 1cyoa.ne(emf 57.3 m/s at an angle d,c( 8aoym1ennm4y.eof $37.4^{\circ}$ 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 /yawv w6f/ ,s.+tnuqt 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 in/.a6fy t/wwvsu,qt+ t would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind 151f:h0fq9ta a oiy- ah* bgcsof 50.0 m/s to the West. The plane's speed 15q os0t-9 hahfacf*:gi 1 bayrelative to the ground is

  A plane is flying due Southx xako(o+s8y( ($270^{\circ}$) 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 ishl32 2ag-c ywc 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 hortiibh9 tpd; g vk5-p*2izontally fires a projectile with speed 50.0 m/sgvpdttb i;9hk 5i -2p* in 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 water is 8.0 m/s, is directed across a river w6/o5zhwlwvz(z5+ k1+ lre ropu64kmj i/7x jxith a current of 6.u 6m/o jz/ le r57lk+1x5ri +w zpw4(jzko6xhv0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move a(ue 9gc2 yvqrsx 3uzr*,g33hpt 15 m/s in still water wishes to travel directly across a river 0.6 km wide in which the current flows at 6.8 m/s. How long will it take to cross tuh3z pxg, rg 23u(esq9yv*r3c he river?

  The driver of a motorboat that can mj1x/b (l v :)zrztajw9ove at 10 m/s in still water wishes to travel directly across a narrow sr jt/9a wxl(j:) bvzz1trait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wil +n; zake3 u* *ei)p0rcdic-xde reaches the opposite bank in 6 min 40 s. She is swept downstream 480 mr zuapk +-l*c)x eecin;0d*i3. How fast can she swim in still water?

  A swimmer heading directlt6ukkd:o: pu1 y across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept down 16ktd:upkou: stream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.96 dbrqxs90 m8.i o g9mi,m/s, must aim upstream at an angle ofs,9d9i.mmi8 rqgbx0o $29.5^{\circ}$ (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)  $m/s$