Which one of the followib4o :v 9jrzfo3b(ak*0g d/i *nqco4oing is an example of a vector quantity?

  Which of the following operations will not fw1(q,qi5xqt.iw7ssi n* pz p )0vrs)change a vector?

  Which of the following is a872sc,x 1 kpfzpj-6nne igbo 5n accurate statement?

  The resultant of two jyz4e/ivb- 0h vectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m sk *cy l.yz,sx,10h( w9f(bu m7rsjnland 7.0 m, respectively. When these two vectors are added, scm0.,bfy zxuh7*r1 ,(k jyw 9snls( lthe magnitude of the sum

  Two vectors, of magnituxm xzpx f.7bvlu d(d u/09d+9pdes 20 and 50, are added. Which one of the following is a possible answer for /xp bxl.9z79vdm +(p u 0dfduxthe magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directiongpw,/de4xe b 4s t 4gee,x wdp4b/hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the ekdg 41g9euc7unknown vector is

  Ignoring air resistance, the horizontal component of a vcx5xzl- xq mbb+t5w3()cxnp1k+i. pprojectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle fo)tvuf2q:z:vgy37ge u i-b7 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 co: 0q4 jkhqjzy4v+cw q1mponent of a projectile's acceleration0q wvzq4qy1 cjh: jk4+

  A soccer ball is kicked with a velocity of 25 m/s at an arpa59 zmp sr x7o+0ko0s/g w5gngle 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 ant0 ofpd n ealuv;qb97:9i-parallel to the velocity vecto90ofd:nveb lq7 a 9up;r,

  If the acceleration of an object is alway0y9b8 drll*2ujq 8igls directed perpendicular to its velocityl2guj*0b l8qi9rd8 yl,

  At what angle should a watel* sk7h5cm,u ab;e/yp r-gun be aimed in order for the water to land with the gpum5,*k 7 e;abysl ch/reatest horizontal range?

  An Olympic athlete throws a jvof/ (u xo6t,(p :*xhq*i4x znqctv,lavelin at four different angles above the horizontal, each with the samehctq* x/*t l zv (xv:qi( 4o,xo,6pufn 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 ball leaves your handypcl 4-x+m x112hrlbh with twice the velocity it had on your first throw, its horizontal range R (compared to your first servebrlmc 2h14 hxxylp-1+) would be

  A ball is thrown at an or avuu(u1v/ol06yqak1 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 atte :4tle5jfqzb. mpt reaches its maximum height, how does its spee45:jfbz.lq ted compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at *xmo epw2n9:z4wdy k. the same instant a ball is droppewxmne*2:w. ypz d9o 4kd vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizots i;gy1 i7t3pntally, and at the same instant a second bullet is dropped from the same height. Ignore air resist1i3 7t;ipsg ytance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a spedhd.r.. :ij vced of 75.2 m/s and at an elevation of 268 m drops a package. 2.6 seconds later it.d hcd:..ijv r 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 abrw 8 ei h;gnse 7 g-28lb9w;enzr90 s-vyhe)second package is dropped. Neglecting air resistance, the distancesl 87e eg9gnh-zhwbi; n)y0er2w9-; ab vsr8e between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a fgjlb:ixt9 0q7*)aga constant speed. Neglecting air r)j7q :la9gitb0 gxa*fesistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. 3xrt+yd72v xg6 g j5g ikbl*4wIf you hit a baseball on the Mo3iwj x2y g 4dl*vbgg+x56tkr7 on with the same effort (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 ) -vpy;btndeb e1ey- 2axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to-tby-n ;ve 2b1e pd)ye the other car is

  You are trying to cross a river that flows .s dwppej5(() d,hqicfmqiu 7:ip) m5due 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 st7( f( :jiuw.icsqe5md)mdp 5) pipq,harting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still wmc3 d,nvpa:bdy8,ke /ater. How much time will it take you to move 12 km downstream, in a ricna dydb/pk,3m,e :8vver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 l* s3e4(dp8bxdt g0j rdegrees below the +x axis. The y component of A 38 p4bxetsrg d0j*(d lis

  If a ball is thrown wit6b(7 ga*fu9: wdxkg bzh 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 direction north of east and you cg.3. 4j2 acpt5.dk r)cgwtftend up 2.0 km north and several kilometers east. How many degrees north of eastgd r4cta 23kg.5jc..p ftct )w have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vel ;q bc)l.qg4i/zbx,-mx ebd fj:b9b e0ocity is 8.00 m/s. The angle between the direction of its motion and the x axis mustxzb:. 0; bmfqb -4d,9 lejecq/ibxbg) be

  A 400-m tall tower casts a 600-m loh406p g1( aa gxe:whxxfraaa6i*)1cung shadow over a level ground. At what angle is the Sun elevated above the horizoa)r:1ux1 xpia6a xh f60aa*(4gg w hecn?

  Two vectors A and B have components (0, 1) and (-1, 3), rn6)rh:0 f pav4g7iy orespectively. What are the components of the sum of these two veof: )aypr 0h4g7n6virctors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatix2;bo*poc b t qk5xn v5+to++ is magnitude of the sum of these two vectors?xno5 +;vb x+kc5t*t 2+booqip

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . 1c9kc(v(4sxfs f:7mdk/msy ttpt56k What is the magnitude of C ?f9mf v 514tsct/ks pkxktd7s6 :mc(( y

  A car travels 20 km West, then 20 n0/rz*p uo4-gwmdq,jkm South. What is the magnitude of its displacg mq -ru4*pznjod/0w,ement?

  Three vectors, expressed in Cartesian coordin (wluz1(x zslu3wc6 0mates, 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, expressuqo; ;f7p ns gcjfalyk,+0v27ed in Cartesian 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 = (+3.0, -8.0), what is the magsj:5f -ochz 5znitude of vectorhs :fz55cjz-o C = A - B ?

  A runner runs halfway around a circwpfe d *64sfb6 )49k: ac:8vbahdmffq-pu,s fular path of radius 10 m. What is the displacement of the jogger4wqf: h:ffv8bf ,s mfdebac4 u )pk96*a-dps 6?

  Two forces are acting on an object as se6 e0nhf3 bkj mzx;0b8hown in Fig. below. What is the magnitude of th;bxzk 0fh8enj0em36 b e resultant force?

  Two forces are acting on an object as d4jy;ito qf0e ,naeo(9(ezn+ k a(3xfshown in Fig. below. What is the direction of the resn(j4yz e3exko iqf(;d0,a+ ea9ont f( ultant force?

  Vector A is 5.3 cm lonxa5 qjj 8fg0+tg and points along the positive x axis. Vector B is 7.6 cm g aj5jfx+0q8tlong and points at $+51^{\circ}$ 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 62 cm longhy k e:mcm/e.++muq 3z and points at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 48 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 wi cnxzyq6w* 5/lth an initial speed of 15 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 2.2 s. What is the hei5cn q/yx6*w lzght of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bridge. ik-- fy9j(nh,zg4ah7r qp4l bIt falls 25 m t lkhb4ai7f-pn,zhj( -94gyqro the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m abo6pnn6iygj z766* k.fydko aoa,u2:rnve the ground, strikes the ground after traveling horizontally a distance of 13 m. With what sp* 6ygpdfzkn .j7r6y ,6:uknaoa n2 i6oeed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angw:fc rff3 eh3ds.ca2 1le of3 hf1 dcw:.srceff 3a2 $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jum* pnt- 8ozzw4kh)+fabp goes into the jump with a speed of 9 m/s at an angle of tz 4-)*z+n8hwpk fao b$16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 33.0 m1)b0wq) zgpmb-4gaw s/s at an angle of $21.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launche-0 dp)jv)uqj5 axz-aoz b0gw2d with an initial velocity of 44.3 m/s at an angle of $43.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at20 j;9r j2 3gjtffvxjb 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 horizontkg,mt:wlf 8 u,y/6 tjtally at 27.4 $m/s$ from the roof of a building 52.3 $m$ 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 ground level with an initial sp 5t-m90n jdxzs umus,9eed of 49.9 m/s at an angle 0sxm t,nuu5mz-ds 99j of $39.2^{\circ}$ 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 4.0 m/s. r39 :y.n2lmh3kr vu xoIf 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 it would takery:kv3h x r9ln.o3 2um you to finish would be

  A plane has an air speed ofkv )z1tl5jmb aw 9*b-02qydp7z- cvjj 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relat0-y d7)zzjvb-qp tva*1kj2m5 j b9wclive to the ground is

  A plane is flying due South (o/k89hepr/ oo8hlap ($270^{\circ}$) 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 hm52j sn(ijih 0jdu96m pq 26gyeaded $30.0^{\circ}$ 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 with speed 50.,ossnm9cd 02 f0 m/s in a forward direction soc9dn,20msf $30.0^{\circ}$ 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 watr*rgg g27r f 4fb*py4x3f(4 7y xr0e*odbiwh ker is 8.0 m/s, is directed across a river with a current of 6.0 m/s. Whate4rgf7b rgpyx4rhw od4y07 f(r*gbif2**3xk is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 13 m/s in still water wishes to t i,8ki 0e.cn4jo48jnj zy*)wc/vhbl a ravel directly across a river 1.4 km wide in which the current flows at 5.9 m/s. How l ih4kw.*jez/j i 8vl0y n)bjona4c ,c8ong will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still urt4b srs+v8 2water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angu+vs 8rst42 rble upstream should the driver head the boat?

  A swimmer heading directly across a rive: fw dx8x8+xe bax7t(ur 200 m wide reaches the opposite bank in 6 min 40 s. She ieb faxw+tx x8x8 d(u7:s swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m widt7i,94 jt kuk4; uxke j,zj)jue reaches the opposite bank in 6 min 40 s. z;xt9 , u t4ukj7jk,4kuijej)She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in 5ijn6+6 hittkr.n:jt still water is 2.01 m/s, must aim upstream at an angle ofr5: 6i knj+ttjnh 6ti. $16.0^{\circ}$ (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)  $m/s$