Which one of the following ismcbex, z5pfs 6t:8mktl 6 ;bd4 an example of a vector quantity?

  Which of the following operations wi1kcyu2b+2 dy cll not change a vector?

  Which of the following is an acc(4i 4k kqc1gbcurate statement?

  The resultant of two vectors sndlhq jrf2yg qv-ws,70b( 1 /is the smallest when the angle between them is

  Two displacement vectors have magn bg 1 ukgh5j9rl2k*t3uitudes of 5.0 m and 7.0 m, respectively. When thesutkkb1*rg35lh gj2 9u e two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and (9w+ohn62 k2cwrzp2 xhaqc np -nlv8u;,4 ujx50, are added. Which one of the following is a possible answer for the magnitude of the rqu,lh 6 8hpjc9u+ -x2nvo2p kz(wwx; 2rna4ncesultant?

  Three forces, each having a magnitude of 30 N, pull on an object 0 x tb)1r6 n3x6:9jg 1r-xa-zh1 uk ksamhuuxfin directions that arru)j sz6ub9a1 ta-1m gr30uh16xhnk x: -xfkxe $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownt l50a1r* aty-4xylsj , the unknown vector is

  Ignoring air resistance, the horizontal component o2, wunarpg2h7 +n46lyyr xur /z1nr;kf a projectile's velocity

  A ball is thrown with a velociv gi),b:b;zdef*3l 5b) z( 7yz uvtfdity 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 h +eo;e,ddo rthef6 ;)uorizontal component of a projectile's accelerationd rf+ e)ud;oeoh6,;et

  A soccer ball is kicked with a velocity of 25 m/s at 1b6fe7q;axw9zn uql )l4cz+k 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 gl07, kwc:l, :o*mt dl jij7xnof an object is directed anti-parallel to the velocity,t7gjxm no l 7ijl:d,*lwk:c0 vector,

  If the acceleration of an ;p6c)vq ljxt/ 5jhh 4eobject is always directed perpendicular to its velocity,) jlh;e5/jxqtp64 vc h

  At what angle should a waterbz iwo j,1pntd9y+0)j-jz/m e-gun be aimed in order for the water to land with the )i, 9jjjd z wtom+/b-z 0ey1pngreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles abov5+k cfctzh zx:0,lrz0gl3se3 e the horizontal, each with the s3 c+l: hkr zzz0f,l3se5xcgt0ame 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.wynek 3e x(o.oo,n291 yfjgn . If the ball leaves your hand with twice the velocity it had on your first te32 1 ,owyxognjnk. ey9fn.o (hrow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an originatrasi+q i8 n2gy )nj;j8v5ex5l 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 attemppug1,b7a v8i 5:h nelyt reaches its maximum height, how does its speed compare to itlbpe u1: ih g5an,vy87s initial speed?

  A stone is thrown horizontally from the top of 7ytvhphw-5 jwzu (xt 9/h*tm+a tower at the same instant a ball is dropped vertically. Which object is travelinuvw/h z9* mj+twxtp7h( t-y5h g faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second b 39rt jvm7l.bh+wymh-ullet is dropped from the samerty-9hvw h j3m+bm7 l. height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 71.6 m/s and at an elevati/y,+shelt6xu on of 187 m drops a package. 7.9 seconds later it drops a second package. How far apart will the two pac+,ut lx/ yesh6kages land on the ground?

  A package of supplies is drop3 j2xzoa3)ki:vvg , pfped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between 3k:3av gfpx,voz2i) jthe falling packages will

  A pilot drops a bomb from a plane flying horizonta /7zukp6qrjy63l 3ib31 nbevro5l:e klly at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the p1:urzkv e/3qkrli l7on6 ybbe3 p35j6lane will

  The acceleration of gravity on the Moony tij4m5+m, 2v*j*wxn sxwohjgwc7 90 is only one-sixth of that on Earth. If you hit a baseball on the Moon9,h vi*wcytgmjo057j*xn 4+mww j 2sx 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/hqp)0(s: xzulf in the +x axis relative to a straight, level road and pass a car traveling at 40zq)(f: suxlp 5 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 cuqiic eu d/ mvvdbh2heu-/b.qzf2+- 6;rrent. You start ozbqd ihu+b 62 . vud-qhc2ef;vm //i-eut in your motorboat 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 still water. How much ti8zfqvi2:)xcopz) ,e, a uztu-me will it take you to move 12 km downstream, in a river flowing at 6.0 km/h t,)2zi)uvz-xc foq pa,e z8:u?

  Vector A has magnitug ul 6p,jmtfbb ul sd(,xe9646de 8.0 m at an angle of 30 degrees below the +x axis. The y compot(u6u9 jlgp6 b e6,4lbfmx,ds nent of A is

  If a ball is thrown with a v (r;b5uhhd rf;elocity 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 yoax4zq7 hgzx :0u end up 2.0 km north and several kilometers east. How many degrees north of east have you walked7qxg:z a0h zx4?

  A butterfly moves with a speed of *8 gbbjdu8- .wqx r1 (w7hquel12.0 m/s. The x component of its velocity is 8.00 m/s. 7wlegqbud1* h(w .q xjur8b-8 The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over , qzuj;v*:u s,b(um)mjg il:ya level ground. At what angle is the Sun elevated abov*iqm vy,s zb) j:g l(,m;juu:ue the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whardaku*8l;8j qe q-zs3l)zjdsj i +o:* t are the compon qr:*d;)a-le*3 zqs+s okj8luzj dij8ents of the sum of these two vectors?

  Two vectors A and B have compkn0 dthk-gbba2ts vps;31s0 8 99jvwnonents (0, 1) and (-1, 3), respectively. What is h sa-swd3jbkb08;n20vs9nt9tvkp g 1 magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0)le21 s5dq/y iv. Vector C = A + B . What is the magnitude of C qe i1 v5ld/y2s?

  A car travels 20 km West, then 20 km South. What is the magnitudeu cr-m2zg53tc of its displaceme rc3gut25mzc-nt?

  Three vectors, expressed in Cartesia uag6ri 75w(,w5nn9 v vxgljx8n 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 coordinates)ek ne*gehb1 5yu0(th, 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 vaz1q 6bbg:r mg6r) f8uector B = (+3.0, -8.0), what is the magnitude of vector C = A1g6 fz)b86 gq b:uarmr - B ?

  A runner runs halfway around a circular patl ,5q*jwfx4m1dp x uy9h of radius 10 m. What is the displacemenwx d 5l9,fmqx1pj*4 yut of the jogger?

  Two forces are acting on an object as shown in Fig. belowyua(b lhli:p+yt/b1: dwf5u f qn8qfm a525a+. What is the magnitude of the resi( d: y qfw5hlbymb/5tf+a8ual2a+f15 p: q nuultant force?

  Two forces are acting on an object as shown in Fig. below. honmcj)g 6+er fp*kf+ *jfn9* What is the direction of the r++c*j9f*nhm pg*fe6o j r )nkfesultant force?

  Vector A is 5.4 cm long and hih hw5y4 orp02*jcx5 t yk2pmr.jx0. points along the positive x axis. Vector B is 8.8 cm long and poic0x.2mh 455ij opwx yhhp2*0jrtry. knts 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 61 cm long and po a 8r kodb+h,unfpi67+ints at $30^{\circ}$ above the positive x axis. Vector B is 22 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 20 m/ss81coi 4h mv7b bo(1pvrx7hf0 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 3.0 s. x0 71ob4fbo( mvv7h c8pr1his What is the height of the cliff?

  A girl throws a rock h1j 5;q6hus1 md1gls+n-owkrr orizontally, with a velocity of 19 m/s, from a bridge. It falls 10 m to the water below. How far does the rock travel horizontally before strikqr51u -h+ 1wdomg;j6l s 1nrsking the water?

  A ball thrown horizontally from a point 22 m above the grounzm9 j0bpoj;sjk:k 68 md, strikes the ground after traveling horizonzs jk8 mb9;pm0j6j:k otally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spembsyfqw ulc+)d z t(.52pj; t-ed of 12 m/s at an angle (j . 5q+spl b-y)2;zfdwucttmof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump f-gs lw 53lo * ;jj98oozbo)srdfay2,goes into the jump with a speed of 10 m/s at an angle of g,3o2fjzfo*by 5 jad l- )8 or9o;lssw$37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launx f,75uz)vjp bched with an initial velocity of 53.8 m/s at an angle of $14.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 22.2 m/s at an angle ofgbu ej6u 3(n 9.vx2kme $19.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of )vmx 6pzrb nx,io27,uhdedra0 22y :l$30^{\circ}$ 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 atnpvamtt-,bcz5e3rj h9. t7d/ 26.1 $m/s$ from the roof of a building 48.7 $m$ 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 1p 3vr/)gyt2 h:yctbo speed of 52.8 m/s at an :/vtp )1oyyt2r cb gh3angle of $44.4^{\circ}$ 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 wi1nyzx7b uj3x;nd), you can run 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 speedx;u3bj 1 yxzn7 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 50.0 e98 owjfl ec*)m/s to the West. The plane's speed relative to the grounw*eeo9jfl 8 )cd is

  A plane is flying dums jriqxl/90m/ogws)*cmyx *z o 26-i e 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 sv .obi2z, 3suupeed of 120 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 )5xymkobzcihs1 4olz a 20abl:tr-3..0 m/s in a forwar1 lo ml3 :zc5 .i2 4-xbozybrkas)h0atd 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/swi:kbpue2e5 6 , is directed across a river with a current of 6.0 m/s. What is the speed of the boat as6u:i pbk5ee2w it crosses the river?

  The driver of a motorboat that can move at 8px,lwvx:z6 *huw 5s p2x.qx:n m/s in still water wishes to travel directly across a river 1.3 km wide in which the current flows at 4.3 m/s. How long will :z .nw5svx2qxpx*6xwh: ,p ul it take to cross the river?

  The driver of a motorboat that can move at 10 m/hw,v) xq7; f6r,pgbjm3ee8wqs in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At w )jq8p fg73 ;bwemvr6,exq, hwhat angle upstream should the driver head the boat?

  A swimmer heading directly across a rivh v8ymo7*/wu,- dsm3kvc ac 5ier 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still k ac wyc8/,hmuv*3ovim-sd 75water?

  A swimmer heading directly across a river 200 m wide re+m6m k a5.byd0(n9gk,6 fwihitaqg z:aches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is tf n ,bwyht:ga.gq( d zk590k6m+ 6iaimhe speed of the current?

  A boat, whose speed *m19 avbb6do1 t fecf3in still water is 1.18 m/s, must aim upstream at an angle of 1 tbdfo1c3b e69fv*am$21.9^{\circ}$ (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)  $m/s$