Which one of the following is an e/ggpw m 9bwsa x9rduq*7c6)/gxample of a vector quantity?

  Which of the following operations wilfs.j a 7lsjkpae53 wc.)d s ay jil7c19p+0pd(l not change a vector?

  Which of the following is an accurate statemnc :9wcg .ac ntvt(2lkw,0y (sent?

  The resultant of two vectors is the sdja7 n3j9f6vf mallest when the angle between them is

  Two displacement vectors h *0gw8 )xmj2g *y e3:cagcdrltave magnitudes of 5.0 m and 7.0 m, respectively. When these two vecg8cg xe) r :2y *tjl*0ga3dmwctors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. 3n*v;k(m:fiux r.y yv Which one of the following is a possible answer fo( k3nvriuxf.m;y y *v:r the magnitude of the resultant?

  Three forces, each having a mag d*3b /(bqk9e1yw9 8iq xbfowfnitude of 30 N, pull on an object in directions thax* d1wbbikq 8/9 9yfewobq3f(t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowow4ud)3v.a d 8e f 28c)ma;rtrf gf5nkn vector is

  Ignoring air resistance, thdc y w*uk xvn/j,v,um)8v 2vi/e horizontal component of a projectile's velocity

  A ball is thrown with a velo msq+c,2)/d,l mypkovcity 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 horizontal component of ak5 ,86pcglo pp5,/w6 jrl:- lqgavxcn projectile's acceleration lnpx 6, go/jpl5g:6 ckpv-q,58lwcra

  A soccer ball is kicked with a velocity t9-vb6h2hjo 84gxrd pof 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 di /stxk5h5 gsy1*wm+ p+ a njgcn*;lqo:rected anti-parallel to the velocity vlt; 5 opswsn5k xcqm +*:y*nja +1ggh/ector,

  If the acceleration of an objecte , 9vjq*xvnf 66it-dl is always directed perpendicular to its velocity,* nij-d66qtf9x,l evv

  At what angle should a water-gun be aimewv 5f0llbcwqfy5.0 ) td in order for the water to land with the greatest h5w0tl.q f0l cyfw) 5bvorizontal range?

  An Olympic athlete throws a javelin at four 3qak6 ryn ovn9cz:3/ mdifferent angles above the horizontal, each wica 63m3:oy/qn nrvzk 9th 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 for the second time. z,y45ryhylt 6+1/ rz)suk jj oIf the ball leaves your hand with twice the velocity it had on your first throw, its horizontal rangou ,6yj+jhkyy/z5z) l1rt4rse R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle of vr,pqa :u3sc+ $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a gt 569 zaga+.,dwiolswf* 7 kv/fqwg 8field goal attempt reaches its maximum height, how does its speed compare to it8/+6zgwfs.5 wwf qait ggld,k*7aov 9 s initial speed?

  A stone is thrown horizontally from the top of a tower at the same isop3/ow3cl w,gf :* hyxgindvq:v(ddf) 0.l5nstant a ball is dropped vertically. Which object is tralc wwdp3gix gh(f.fqldvy):do3:n/50*vo s ,veling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second qkogaf15 jprm+ut7y.u 3k276clf ,mcbullet is dropped from the same height. Ignore air resistance. Compare theak612tfqmr.l 3cou7y kf 5jp,m gc+u 7 times of fall of the two bullets.

  A plane flying horizontally at ) so *;- h6 yskgu57* y8dqw*eufvaifva speed of 106.2 m/s and at an elevation of 139 m drops a package. 3.4 seconds later it drops a second packagyoky f8h;*e f-d6s5v7ugu *awvsiq )*e. How far apart will the two packages land on the ground?

  A package of supplies ub 6p+my6xitsx2k+ lp)iixuz8p /v .+f qz: 9ais dropped from a plane, and one second later a second package is dropped. Neglect ki896:xszi++uaxtu plpf +pqzy 6i.2xbv/)m ing air resistance, the distance between the falling packages will

  A pilot drops a bomb fromr+lrzqep/ v d94b**xo a plane flying horizontally at a constant speed. Neglex*9*qr/ ovr4b +pzdlecting air resistance, 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 v4t)+/j fbtmr vu:fsj.jvrp):+lj b +that on Earth. If you hit a baseball on the Moon with the same effort (and/) lpvvvbf jjuts.:mtjb4r:+ + )jf+r 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 straight, levelve48qos ;k-et 4wx hk nx)/t qa(3q7nr:bk9 ii road and pass a car travelingobk4 n: n4s8kxtek(/-q3 i wirqv;q9th7) ex a 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. e9),:bspv fgu You start out in your motorboat on the east bank desiring to r9p fe:sv,g) bueach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stytpfyy( dp7l )sbx-;8 ill water. How much time will it take y-ys8lpd bypxf)7yt ;(ou to 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 thnm (7hww(ls0j+lrp be b,rx:8e +x axis. The y cosb+, (jm : x wlbhe8r(0npwr7lmponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle ofyq9/tz gvqy4 yoo ii ic2.:k3) $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight l j5gc+, xd)z2kc8ge8 ohlcn( (m jqk(yine in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east j2d5qo(c zl(+hkk),ecgmyjx8c g8n(have you walked?

  A butterfly moves with a speed of 12.0 v)q sxvwejy/ gzx4o.).*y*wdm/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and theq.w* xg j syy)v*/zvw.o 4xed) x axis must be

  A 400-m tall tower castp3 siucsna/qm/qyfi35r ;+0 ps a 600-m long shadow over a level ground. At what angle ici ssa3/ y/5 pfpu0irnq+ 3q;ms the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1wjpx;.qydc7 /) and (-1, 3), respectively. What are th7.ypdcjw;x q/e components of the sum of these two vectors?

  Two vectors A and B have rly uz45)y9gps) ov.dr 2-lnucomponents (0, 1) and (-1, 3), respectively. What is v us)d rr-9p4n yu2go5lzly.)magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + ksj9)v2: ervo B . What is the magnitud9 v:jsvkro )2ee of C ?

  A car travels 20 km West, 4kaza/s u80c;c 9xxyj24 rzfo;6g bx vthen 20 km South. What is the magnitude of its displacemrsf 28 vc/; xz4uo 4x0kga6ajbc9yzx; ent?

  Three vectors, expressed in Cartesian coordinah/oavk6s dq;w/ch0ux9;e;t sf n(f2 ttes, 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, expresseh ld9tz 1(ul f.l;tou/d 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 i/pk2l;x+pxk +w*0 fnj qljow9 s the magnitude of vector C = A -+ /lplww k+x;pkj f90n *oqj2x B ?

  A runner runs halfway around a ci+w +6hzynn0thrcular path of radius 10 m. What is the displacement oy hnwnz+0h+6 tf the jogger?

  Two forces are acting on an object as shown iqn8 e8- pa7.xsx4v*hrd mc 33rugzn2 kn Fig. below. What is the magnitude of the resultant force.cr 48uhms xe73zg xn82*rav -pdn3q k?

  Two forces are acting on an object as shown in Fig. below. What isw*r( y 0kkx g83 ; cob6m2coyhl2d8u7uo-jwy i the direction of the resultay oy8b0wuxo3gioljk;86 2k2-d hrc*7m cyuw (nt force?

  Vector A is 3.5 cm long and points along the positive x axis. Vector B is 9.57o .4, ; d 8tfkofwvpz.y2xswv cm long and poiod s.o4tk,vwf;.w7 pfv z 82yxnts at $+50^{\circ}$ 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 88 cm long and points ahksx5wyj.7o9e(0w4hgji p45c c 1rss t $30^{\circ}$ above the positive x axis. Vector B is 24 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 x, 8q i-bv2rjnn6by6s15 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 2.3 s. What is v 6rqnyx,i 8-n6j2 bsbthe height of the cliff?

  A girl throws a rock horizontally, with a velocity of 16 m/s, from a bridlea f,v3( hho+ge. It falls 26 m tla v,(3heho+ fo the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 m above the ground, strikes the grounv e*q6-att 29ha ykm,zd after traveling horizontally a distance of 24 m. With what speed was it thae2*9-v6zm ,qh at ktyrown?

  A jumper in the long-jump goes into tbm h73*m wy+)waftob7vd5fa 0he jump with a speed of 12 m/s at an angle oaw3) m57awm t7bfhv0bfdo *+yf $20^{\circ}$ 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 with a speed of 13 m/s at an angl,jhu6zc5 l88q(po*mdb ha d)f e ofb*(ja 6,8d coh)5 8zmlfuqd ph $23^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 4u;hhxph2u6,vs9 y5 bj3.2 m/s at an angle of $36.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 48s ; ze0ti h5h9vje0zy2.9 m/s at an angle of $48.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fire+i/ vij, 2meir nkc 0h7a2je8qd 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 ho 1a68m nx1kr*v,(k,q dsmd goarizontally at 22.3 $m/s$ from the roof of a building 54.1 $m$ 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 r2 um ulz,w.1grfwhzetde0:y: ; *w2rspeed of 43.1 m/s at an angle ww;zrwrum uhg:0 ytf2:rz2, d1el*. eof $39.1^{\circ}$ 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 v4;tdq4ar/u;0k. 5bo orl s yguelocity 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 timslyq/ugdaob4 kr 5o4r u;t0.; e 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 50.0 m/s togl)(kg.z* rea the West. The plane's speed relative to the grounl a.)k(*gegr zd is

  A plane is flying due d /foeqh9m/s )d* z-djSouth ($270^{\circ}$) 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 1)b wq.e4baflec3h7 ex) :i5 vu20 km/h 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 with speed 50.0 m3enrf-k7n)o) h8 fpo x/s in a forward direxofkf)-3onern8 h) p7ction $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stqu0uu1;6 hbs8so.gw4g3t w(ztzlqu5 ill water is 8.0 m/s, is directed across a river with a current of 6 qz51;w.o(tuu3g0 wuhs6tus8qb lz 4 g.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 12 m/s in still water wishes to h19faqh(w,n xtravel directly across a river 0.7 km wide in which the curre(af w9x ,nqhh1nt flows at 3.7 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 water5u; wa am1zxr: wishes to travel directly across a narrow strait in which thrmaaz 1uwx;:5 e 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 wi6 ep aqry32-fbe 7 dlpin6xp5.de reaches the opposite bank in 6 min 40 s. She is swept downsf2d5 bxa7- 6 e lrp.i6ype3pnqtream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reach/-bdaeka3 /cgy8a81 + lu gcnwes the opposite bank in 6 min 40 s. She is swept dow1/aacl8gcgda8y/ 3nk-w+ beu nstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.12 m/s, must aim ga u8pux+xbngs8 5bk 52f20 frupstream at an angle of 5supaf8x+5u f n20g28b rbkxg $16.2^{\circ}$ (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)  $m/s$