Which one of the following is aim 1o t0u0*ee0v.rrqhn example of a vector quantity?

  Which of the following operations wi3:-x kbmi5pdse*iww6ll not change a vector?

  Which of the following is an accurate statement?un0-clb3snrg k .f /)y

  The resultant of two vectors is the smallest when the angle between t) c- ) v n2tl:my;s)fbssi)mnchem is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivw/5x*kg)1r e6vtf4ei o:ffq yely. When these two vectors are added, the magnitude of the sumyxfgw o 1 tfve f/ker4i)6:*5q

  Two vectors, of magnitudes 20 and 50,0v /dk j4fesjw:xk0s+ are added. Which one of the following is a possible ans/sjjw: kvkdf 4+0xs0e wer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions tgug(g 8tpnw)q 66 f8)zy jv4gsd/zm9 mhat are) wqggjt8f4s96 uzzpd 6nvy mggm)(/8 $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unlp/5 vi4wfyp+ known vector is

  Ignoring air resistance, the horizontal component od;70nnh ke1x hbgjl)c3i12ed9x zgx -f a projectile's velocity

  A ball is thrown with a velocity ofhg: doo):w9-fk 4 u-wt5cbxjn 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 l*:coc myi(ghs5g3ac3e 6)zf w 4kt7kprojectile's accelerationi (wg cszo3c7ht y:3g6*ak4 lmf ce)5k

  A soccer ball is kickfdy ck 1zq/;7 ocr)ph1ed with 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 vector of an object is directed anti-pv2wsndx +8zt j4+af6oarallel to the velocity vecto8j2vt4d6+xsa nfwo +zr,

  If the acceleration of atfa4; 7u ,y-ee ip;vh.pt adepv).3xtnrfh6.n object is always directed perpendicular to its velocity vith3fht7a)n pp . u4..vepe- 6erat yfx;;,d,

  At what angle should a water-gun be aimed in order for the water t:(b4edqu:)(gmkz n q z1 uone;o land with thequdz:g 1:bkuen ;o)nmqz((4e greatest horizontal range?

  An Olympic athlete throws a javelin at four different axtn :ko,m:91 sgt;b ggngles above the horizontal, eac :kg9gtom :ns;g,x1tbh with 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 ba sxnlxij9ohkg20 rm )idq f4p5y0;+9qll leaves your hand with twice tfglqik 2d ;j)mhq0x+x5o9 ns9 r p4i0yhe 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 8.0 m/s at an angcxc -)lq3ks1 sle 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 reache9a0/bl+aioi6vy w7 vaff 301tqq3bfw s its maximum height, how does its speed compare to its initial 9/yi+6w0faovb1 af7v q 3tqwa0l3 ifbspeed?

  A stone is thrown horizontally fro30da6k sl fvzyd:wv6 m sys /f.;+vy*am the top of a tower at the same instant a ball is dropped vertically. W/3a szy *l0df swks:66da ;mf.+vyvvyhich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instantwmg.9ej :dtf d55fkz4 a second bullet is dropped from the same height. Ignore air resistance. Compare the times owz5d tm.5 f 9k:jgde4ff fall of the two bullets.

  A plane flying horizontally ak,l 8qh 2wp0bnt a speed of 71.8 m/s and at an elevation of 265 m drops a package. 3.2 seconds later2h8qk0w ln pb, 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 s(lh/3jwb9 4kkg7 bkuabbt l;yo l( s;1econd later a second package is dropped. Neglectinaw; 7klb o3; lth4lybbu/ jbg1(k(9ksg air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horixha1m/vpt16 m oitz( -a: h+fzzontally at a constant speed. Neglecting air resistance, when the bomb hits the gi ah(ft61tmm:/ zhapxzo+-v1 round the horizontal location of the plane will

  The acceleration of gravisci8* 6-qm8 (cfxnjzv ty on the Moon is only one-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 would on Earth, the ball would land*6 vx8c8 m(sj-fcinq z

  You are traveling at 5o3k3eh p59s4k8 h+wako.d h7 zua jh)w5 mi/h in the +x axis relative to a straight, level road a) hu95kzs 3jke.wh734h + kop8adowah nd pass a car 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 duxep986g.vlm r e south with a strong current. You start out inxp6g8 vrml e.9 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 fmcln,w*ndz.ao0,js2r p9 / .s ;lwxwmuch time will it take you to move 12 km down z/pmn,wnd.f wo ; .rxsljs*0c,al92 wstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 dv r h8de4z/kb79l dz9g)i5 d d+mc6mnfegrees below the +x axis. The y 7fmn/5 8c+ zdmbd vdrz 9i 4)9khlgde6component of A is

  If a ball is thrown with a v9u(si ,ac rjv19jggo,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 easnp6;hcf cf7 s4v ./kftt and you end up c.thfk s6c ;p/v7fn4f2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed ofma ocd42()c6t nmp, fg,luhr4 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the directi,cho )nl46tufa p,r(2cm m 4gdon of its motion and the x axis must be

  A 400-m tall tower casts a 600-m u2u*a 6ir d(vdwip;(clong shadow over a level ground. At what angle is the Sun eleudi6 (w*(u ir 2ca;dpvvated above the horizon?

  Two vectors A and B have 6y2-ysz ka)-sq.kk jhw. bpmt n/,.clcomponents (0, 1) and (-1, 3), respectively. What are the components of they2 y)qnt,lm-6.akph sk b.j sc/zw k-. sum of these two vectors?

  Two vectors A and B have c gtr e(k:sl -:.:iwkxmd qt0k;x0 8ybkomponents (0, 1) and (-1, 3), respectively. What is magnitudek tg0 xxltqd yi( k0b- k:m8:;s:kw.re of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + lr+07rtvj v,q4n*i wpB . What is the magnitude of C ?it*,v0npqwrv7r l4j +

  A car travels 20 km West, then 20 km South. What is the f 2b7vsqt:;d g;ez1fv dvnr)*magnitude of its displacfv1;fe* dsq72b)v;d t rgnz:vement?

  Three vectors, expressed in Cartesian coordinatesljhc;54do k2 1)sgxj t, 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 co(yvsaf zrq;qvs l()8* ordinates, 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 1 jb90zvkn*pu vector B = (+3.0, -8.0), what is the magnitude of vector C = A - 0bu* 91pkzjv nB ?

  A runner runs halfway around a:n/y ywkh1),g r 5lm7 b8kzjzl7vb)jr circular path of radius 10 m. What is the displacement of th l:y17nz,h ry)jlzr/jk8w 7m bk)vg5be jogger?

  Two forces are acting on an object as shown in Fig. below. Whatpkg)lxi-web 3qwj ou*u- 4:0o is the magnitude of thej3*u-4 wi q o0)- kge:bopuxwl resultant force?

  Two forces are acting on an object as shown in8hvhup:4u.ohc:)xgi* tw v9a Fig. below. What is the direction of v8*:tiv o:hwx4g )hu u9.ah cpthe resultant force?

  Vector A is 4.9 cm long and vvfvq147ijfbe 5.. a2au)m63pqw i uxpoints along the positive x axis. Vector B is 6.7 cm long and poi.e.2p6aij bam7 5vxv q fqifw3u)4vu1nts at $+53^{\circ}$ 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 68 cm lon/yi,sd1kyg,43 s yn bjg and points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 27 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 horizobftn*lp w *l6z.ut 04vntally with an initial speed of 22 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 be06t.v t*ulnlpwz f 4b* 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a bridge;m.rz*dntlj5ddh )g,vy0bzqwt76 * b. It falls 14 m to the w5hjb * wd,7ydt z b d6t)0z;m.lrnqv*gater below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from f2g5ahh t q19za point 23 m above the ground, strikes the ground after trave fhzha 1qgt925ling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle f)bl1um( vmb(+ kl8vb o f8)1b+m( vu(llvkb mbf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into xw kzk4m8 ztla j(0((qthe jump with a speed of 15 m/s at an angle qxw z(tm(4 ljakzk08(of $38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with w7y e6ts*mt beq(k/c)kgpq2g u-3 m)dan initial velocity of 47.5 m/s at an angle of $21.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 28.g krk (c+i4ah*;tw 0lbox qhl ,w9-,dq8 m/s at an angle of $12.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle o. -xnq* (s8gmsl-foe xf $30^{\circ}$ 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 horizontallypxz2*8ps)oh2 h z s 4zxwm36mcaf3 oe: at 22.1 $m/s$ from the roof of a building 32.0 $m$ 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 mu8rh 2d* /th: nh,vvsground level with an initial speed of 53.6 m/s at an angle vmnh thhr vu*s,2:8 /dof $45.6^{\circ}$ 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. If w a n7,6s3 pabo-xpe(fyou 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 take you to fin7 6psn,o(pw3 aafx eb-ish would be

  A plane has an air speed of 200 m/s due North, 2ljnj( vm8/+; i ei0bs8 bhu9pud rvf)and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grounvin(+;/ er0buli29 jumsb )pj hfd 8v8d is

  A plane is flying due South (y+q7nsh ;d6wy$270^{\circ}$) 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 sp 3 6z f842hkfi:nnwkzig;*wz meed 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 movinlcq(8jks0ak1p q 53e pg 200 m/s horizontally fires a projectile with speed 50.0 m/s in a forwardjkq l80( kqpe c35a1sp 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 wat l8et.bd 342wlq 5)gg42gxowoj z) nlaer is 8.0 m/s, is directed across a river with a current 5bwj)o4xg zgqgn. )lae d3lw l2 t24o8of 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 11 m/s in still scxmh,6+ywj/hdcsay) 6- ,hxwater wishes to travel directly across a river 1.9 km wide in which the current flows at 7.9 m/s.+ c cashw,ydsx xmh,6-yh6j)/ How long will it take to cross the river?

  The driver of a motorboat that can mo+wp/89 poc- oyryp2zu ve at 10 m/s in still water wishes to travel di8/wuyp+p-y cro zo2 p9rectly across a narrow strait 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 w8l ,n ,d81jyfaodwcv-e dp +u-ide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she jddow 88n,le1-cf dpa vy+u-,swim in still water?

  A swimmer heading directly across a river 200 m widelo1+bh:tki 9 c reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the ci9 ch1k:tb o+lurrent?

  A boat, whose speed in still water is 1.22 m/s, must aim upstream at a*yn9yhqvg8ce8x 9c;wn angle of g98 *yc h ny;v8cqxew9$17.0^{\circ}$ (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)  $m/s$