Which one of the following is an exampl (;2scyuz)wwmv+ mng 1e of a vector quantity?

  Which of the following opera7frn 8ybi -s .6k3jpa*8xqwrvtions will not change a vector?

  Which of the following is an accurate sta(6k ba o o30uzg5tfk-ctement?

  The resultant of two vecy+18huqbb2k7)fn;+q :yzggp-i fj wgtors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 ji* amwep7 w.aq;j)5 qm, respectively. When thesem*e j w5ap .jqw7;iqa) two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. ueoup 1/l*9x3t)y6f1 q ytdyh Which one of the following is a possible answer for the magnitude oftuydy e3x/ou)1fy 16h9lq p* t the resultant?

  Three forces, each havingsrfuw pqtg e :3*h-a52 a magnitude of 30 N, pull on an object in directions th32 *as-regthfq:p uw 5at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown g(:pqrklr 47xlj3y 9gd81kbq, the unknown vector is

  Ignoring air resista;lprjy mvt) u;5ez05 dnce, the horizontal component of a projectile's velocity

  A ball is thrown with a vnn50 zxajd1*5 zr 3qvl9uzs8pelocity 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 a projectile's accelerati8zzoeqm*cp-s iw; 3y,onq cm;ey83isz- w,z *po

  A soccer ball is kicked with a velocity of 25 m/s at an anc2a rle+)o:l jgle 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 anti-parallel to tht9ydyv6*92c/ ihjtdt e velocity ve d9jhtt* 6vt/ydyi9c2 ctor,

  If the acceleration of an object is alwsmjd o3 m9dq70ygf2 0*a1sw qkays directed perpendicular to its velocity1d kmf qg qs2*j07ys0mad3w o9,

  At what angle should a water-gun be aimed in order for the water sd,l:hk u0 +w2oplf8a)ifn5i to land with the greatest hhi)8o5w0pk l iaud2:+ nl s,fforizontal range?

  An Olympic athlete throws a javelin at four differ3 vca*jyj49tg *ujnw 6ent angles above the horizontal, each wg4a6u wn*j j9*3vjcyt ith 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. If the b2jubael0 gp/p q., 7kpall leaves your hand with twice thequgp jp,2/klp ba70 e. velocity it 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 8.7lopdw d:vmb 68m:hw9/ lew u(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 attempt reaches its maxg-y q ,0ky+p+ df nr/fnar5ae/imum height, how does its speed compare to its initial speedep -+fydg a,rn50+ry k/fq na/?

  A stone is thrown horizontallylqqc zols4x6d i8u)); from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground below?) 68ilq;ou z x)lc4sqd

  A bullet is fired horizontally, and at the same instant a second bullet is d7wpf .w hb0psnqx8 3o)ropped from the samwpqf3ns hx70pow .)b 8e height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 117.9 m/s andk(/ 407vu xl(,v byhjhlctu:a at an elevation of 298 m drops a pack 4/xv(l(ahc vhul:t, ky7 bu0jage. 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 o*u y5- ff1fe7plw7z ctne second later a second package is dropped. Neglecting air resistance, the distance between the falling packwytf1e7 l-c z*u7pff5ages will

  A pilot drops a bomb f14r q ma74bwy8wzdnh*rom a plane flying horizontally at a constant speed. Neglecting air resist7yzhr1 4*amnwdwb q48 ance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only onmwfoah5 .) z hlvli0td2((k0y, dax)xe-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you w5 xiv zk0dxhfa(tao 0h2,.()lwd)lmy ould on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axvhup5mtci 1gnn. 4 -k)3) zqbgis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of y3-).1utiznpnb )v4g hc km g5qour car to the other car is

  You are trying to cross a rag/v7x ldho9 7iver that flows due south with a strong current. You start out in your motorboat on theagd79x 7vlh o/ 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 still water. How much time j aqok l;4akw5c*o7+, r-k 8i,rwiyfcwill it take you to move 12 km downstream, in a river flowing at 6.0 km kforwkjq7k -+*w4ra, i5iac,l yo;c 8/h?

  Vector A has magnitu):37n tuwao1 f(ngdnvu:. lgrde 8.0 m at an angle of 30 degrees below the +x axis. The y component of A isu3dtgl::7n1r(n) nagwvfuo.

  If a ball is thrown with a vej54 7, zvt9jwxbav)j blocity 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 straig5hj9lx:it nxz y/0 k;dht line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north oi; 9ktnx:lhy0x d/ j5zf east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compoa e*,:is/co) g4k 4fwdci* vbrnent of its velocity is 8.00 m/s. The angle between the direction of its motion and the xvc 4wg*/aibi) :red*skoc,4f axis must be

  A 400-m tall tower castsm8 +1b-j(0ea gihlzkvo(e p,z a 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizok,1 ae(l vb0 zh(epm+z8io-jgn?

  Two vectors A and B have components+ig(pf eqh;0g (0, 1) and (-1, 3), respectively. What are t0gei;fh+q g( phe components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3),wrm5pt/5 w s-h au kwo2sxc9,3sp.7h m respectively. What is hxcwpw.5akp m5u93t-7m h ,r o 2s/wssmagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A zlscj;-7b :hm+ B . What is the magnitude of cb-zm: 7hls;j C ?

  A car travels 20 km West, then 20 km South. Whahw+h0d xyc fys uom8 vf28y45(t is the magnitude of its displacemen+2dso (y 8w ch5vmuy8xyff04 ht?

  Three vectors, expressed in C (lv57pp a3q jswfr:ij8+.pgjartesian 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 coordi:u 3e0))y ovnz8 jsde-g yw;ysnates, 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 magni+9vk*7v3 3 ki.gs lk+iwv cvj-iioft/tude of vecto -i/kkf73+ jvct s 3i*9kglivi .+vvwor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dd v5 /.8xskzadi4 rx. ,ut1uomispla d/udk z..mtuv,4o5xa1s8xi rcement of the jogger?

  Two forces are acting on an objec eh(hzsm. +.jwt as shown in Fig. below. What is the magnitude of the resultant for s w(z.e+jhhm.ce?

  Two forces are acting on an object as shown in Fig. below. What is the d+sou8(fs i, mwirection of the re,ssuow8 m+ fi(sultant force?

  Vector A is 3.3 cm long and points along the positivda-3mt.o usymh7 *pc*e x axis. Vector B is 5.1 cm long and s 3 ya-d*pou.*mcmh7 tpoints at $+39^{\circ}$ 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 andnek s;fhu-0g 5b h;.li points at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 28 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 22 m/s from the4hskzc:g(fo 4x n epn2g)(1w*nbn: y g edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the *:ny2gsg 4wnof4n:g (zc(kpn) xheb 1bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, witha*/rf-lp4e)e l1 epht a velocity of 10 m/s, from a bridge. It falls 21 m to the water below. How far does the rock travel horizontally before ha)tlfeep1e-pr /*4 l striking the water?

  A ball thrown horizontally from a point 23 m abovv hmy1w q+zi1+7avm y+e the ground, strikes the ground after traveling horizontally a distance of 15 m. With what speed was i1ay+im vmz w +y+hv1q7t thrown?

  A jumper in the long-jump goes into thstc 7ih(b:oq. e jump with a speed of 12 m/s at an angle oht b(so. iqc7:f $20^{\circ}$ 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 14z l)vqh,2t/c py ,h,az5hfrf9 m/s at an angle of hzyv 2ph)l,h,f,f/9tz acr q5$16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 37.8 m/r2 ti3 6s)b;oa 1mdozgvdc;e-s at an angle of $14.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with ot;7 d udx.3 -kbk+zqf+f 1xfhan initial velocity of 45.1 m/s at an angle of $21.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ookhb9x :s. cg7f $30^{\circ}$ 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 horiz;6b, s :mlrwbusm,5u 1p.wxtpontally at 27.5 $m/s$ from the roof of a building 30.2 $m$ 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 0-nhp(ry 6hkpof 62.5 m/s at an angle onh rk06pp-(hy f $37.3^{\circ}$ 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 azzk(76ux3 au q0bgdi6 velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your spe36qkzuu6gixzdba( 07ed 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 Northft-+gqbapal vz* /xb5 azd vj1p.)1q., and is in a wind of 50.0 m/s to the West. The plane's speed relaxa-q1l.b5qz1/ . )+ptpvaagb df *vjz tive to the ground is

  A plane is flying duelx .-exssm+s b*pz48w South ($270^{\circ}$) 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 1r6 +ju8kk1 w-d m 1w7ovyj0s,awdi hv820 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 spee5qcse dv dp9c ;qbx1tg+,v. (bd 50.0 m/s in a forward directio(,vdb+qs xq p5gc1c;vedb t.9n $30.0^{\circ}$ 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 me,vr(fsyjkfpb v7c ,71k *y,l/s, is directed across a river with a curren7ybksf yp,*r(,fvc ,lv1j e7k t of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in stmpb;4-z-m yww0d: edqill water wishes to travel directly across a river 0.5 km wide in which the current wpq: mw;ybd-4dez-m0flows at 6.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that.6x45y herb1 y hjwp+9m6/kl. m r wf/skteuh: can move at 10 m/s in still water wishes to travel directly across a narrow straitm .srup:6k mtwl6hf 1y5e /xhh/4 w j.ry9k+be 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 wide reaches the oppositeyr0d2 z.q euef).h8bl bank in 6 min 40 s. She is swe.2byeez.qlf8 dru )h0 pt downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide rjyh4ramps ;lytycm*6- q44(wws2 / qfeaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is tf;a4 m t2j4r4cwmw*qhqsps-6 yy/(lyhe speed of the current?

  A boat, whose speed in still water is 1.81 m/s, mustaxm )1q ffcl*o8)f04;fs fzl(d p(wks aim upstream at an angle offks0xlw fzfos ()d;m *q(4)l8 f cfap1 $14.1^{\circ}$ (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)  $m/s$