Which one of the following is an example o /dat d;7w-g n)bdyi:gf a vector quantity?

  Which of the following opers9/6n)t sg ee jeif.e7ations will not change a vector?

  Which of the following is an accuratpo1 g99fjamj3e statement?

  The resultant of two vectors is the smallest whe 3qw qpa9tik60ec(vm4 n the angle between them is

  Two displacement vectors have+ rv9jvrh oc() magnitudes of 5.0 m and 7.0 m, respectively. When these two vectorh 9rjr) c(+vovs are added, the magnitude of the sum

  Two vectors, of magnitudesn)t-,qkq3z m vji8j+-7w nizrxf;zg; 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the -r3n8j;; q kw-n7z) qf,jtxz + mivgziresultant?

  Three forces, each having a magnitude of 30 N, pull on an object in who1n g0zp*k b0,eo;kdirections that ar 1k ;,n0ebo z*goh0wpke $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, 6iem0zwk9 uv or+1 pt1the unknown vector is

  Ignoring air resistang2 pkazmeh:4q8ic e2 :ce, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of 60e above the hori; ma kr:b,x/9taris/vzontal. What is the horizontal component of its r9tr /i s/a;:avxbkm,instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the ho9u2gsij2z zh96 0kfb irizontal component of a projectile's accelerationjzfui6ki9h s 9zb g220

  A soccer ball is kicked with a velocity of 25 m/s at an anglit 31fp4gybb ,vq nc9+c :t8sle 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 u6 cj 0mv0.pv8 h1hjvfou( t36qt lh:tto the velocity vet0:t8 u lv( 361thvv c0.oj6qjhufhmpctor,

  If the acceleration of an object is al.hbc u g*opikw8sd ++xhl ,7n8ways directed perpendicular to its velocitycs, hnluiw88 k+p7+ .x* dbogh,

  At what angle should a water-gun be aimed in order for w mkr 0rr+((pv. 1cbdcthe water to land with the greatest hov(+wr rbd 0m1r.c(c kprizontal range?

  An Olympic athlete throws a javelin at four differeni qvnu71tkrpz):ix)tnouv 97u*8 s .zt angles above the horizontal, each wi i*vt: zuotqi s18vu.p7)nn9zr7 xk)uth 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 theh8lm x,um4mv;cxeh ,, second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would bmm;c,uhm4 x,x8eh, lve

  A ball is thrown at an original speed of 8.0 m/s at an angle o 79eclr4 -rzf4xb :zgssq+ m,yf $35^{\circ}$ 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 yq hei/gj32wg 5wr ,, il*sn1yattempt reaches its maximum height, how does its speed compajh*r5 /n12isygywig lq,e w3, re to its initial speed?

  A stone is thrown horizontally from the top of a tower at tk 4+,(33 mvjonu w6s8 rfcjrethe same instant a ball is dropped vertically. Which object n6vsc4f3r8ek3 wumt j+,or( jis traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a s(.rrh y0j3a aaqo;vxx xa/83fecond bullet is dropped from the xf;3a0h(xyaojx.vrarq 8 / a 3same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 50.0 m w oiwib+81sm2f/l zk,/s and at an elevation of 160 m drops a package. Two seconds later it drops a second package. How far apart will the two packag8k,ilw f is 2bz+/wm1oes land on the ground?

  A package of supplies is dropped from a plane, and ohofi8ugc0.7u8 g diz1ne second later a second package is dropped. Neglecting air resistance, the 8gficzi81.h 7uu0gd odistance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant 3fd i mxsllsd)*8zg4-speed. Neglecting air resistance, when the bomb hits the grzid3sxl)4-* 8 fdl sgmound the horizontal location of the plane will

  The acceleration of zma.bz2d; 6hpgravity on the Moon is only one-sixth of that on Earth. If you h; z6bpz2ma d.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

  You are traveling at 55 mi/h in the +x axi + 2xu-t:r*0+1)izfqeg k dp3rf*klq :kaylgbs relative to a straight, level road and pass a car traveling at :f+qg:r tyukp2ql* eazg)-fx*b1 dril 0k 3k+ 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows du)k tl xp.*)pe j0myk7ue south with a strong current. You start out in your 7eky k*j.0) ut)lxpmpmotorboat 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 time +w6y/bocd xszg,b87 jwill it take yswg/b+8 zd7,ox bcj6you to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an anglenfo vp , kbp8rnhf38blg9l*8: of 30 degrees below the +x axis. The y componeoklg, l: 8vhpnb rn*9ff p83b8nt of A is

  If a ball is thrown with a ve( ( 4qdqqweu cb2/kxz0v(ndg(locity 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 northfuqy73b8gc d- of east and you end up 2.0 km north and several kilometers east. How many degrees north of east u-f3cq d87bgy have you walked?

  A butterfly moves with a speed of 12.0 m/s.h5r gs9*kt9ect 9kq0f The x component of its velocity is 8.00 m/s. Th*t59gk9chq9 f s 0ektre angle between the direction of its motion and the x axis must be

  A 400-m tall tower castn vj*v k0emypt(. x3t2s a 600-m long shadow over a level ground. At what angle is the Sun elevated above the ht kyv(t.*pmxe 2njv 03orizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respecajrv18can ,p*620poah oh 4y ktively. What are the components of the sum of thesen8026hhv*, yo1r4pocka p ja a two vectors?

  Two vectors A and B have ol4 ngb:yjin in.-h), components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of :ni l)n b h4oj,gniy.-these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What ise(wwfv08 t6.hqo +lqa the magnitude awq ot .e+v l0(w6q8hfof C ?

  A car travels 20 km Wesf y2 a0:u9ytott, then 20 km South. What is the magnitude of its displacemey yfu:ot0a29 tnt?

  Three vectors, expressed inxu18hy-s . s3z cjvbe, )4kvjv2rh1ph Cartesian 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 Cartesi-itc,09 vx6q j(gp ve gpnf4,man 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) a e,jz b4.1+h w:rergldnd vector B = (+3.0, -8.0), what is the magnitude of vector C = A - ,ldj+ee zwb4h:grr.1 B ?

  A runner runs halfway around a circular path of radius 10 m ( sudbyacv41-x-al: b. What is the displacement of the jogg4x1lc a d:-u-yvab sb(er?

  Two forces are acting on an object as shown in Fig. 3-1. What)1 d7uics+t+ejbc o. m is the magnitude of theuts 7)i+c+o dj1c.bme resultant force?

  Two forces are acting on an object as showivc 4s+ j6p 7pu-5ml6rw kdi9wn in Fig. 3-1. What is the direction of the resultant forcep9iwuj 54 wcl6m+6kdir7ps -v ?

Vector A is 5.5 cm long aes2f.r:gz/ a h28xk 8qt+m:p1i- mpa v-hzgt snd points along the x axis. Vector B is 7.5 cm long and points at +30e to the negative grzx2tte1+gq am 8 - 8kmh v:zs:ash2.-f/ippx axis.
(a) Determine the x and y components of Vector A .
(b) Determine the x and y components of Vector B.
(c) Determine the sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Vector A is 75.0 cm long ab07mdrw;mt38saix w :nd points at $30^{\circ}$ above the positive x axis. Vector B is 25.0 cm long
and points along the negative x axis. Vector C is 40.0 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A .
(b) Determine the x and y components of Vector B .
(c) Determine the x and y components of Vector C .
(d) Determine the sum of these three vectors in terms of components.
(e) Determine the sum of these three vectors in terms of magnitude and direction.

  A stone is thrown horizontally with an initial speed orguy xv)y, *e8f 10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the 8vy,y)u grxe* top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontallp/pjx7d3y b*j5g 5hwhy, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. wj pj7xh35yp 5dhgb/ *How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, strikes the groun5 ala wrkjkwc0/ .m71sd after traveling horir0/ a.c 1wklaj7sm kw5zontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the n9+;/zx 3 fq5pm o+l6gxgtnw ljump with a speed of 12 m/s at an angle o5z+ glno6nx/x9mw;+gq 3 t flpf $20^{\circ}$ 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 speedb tymk. h,4qh+ of 12 m/s at an angle of,hm+ q. hktby4 $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an* bdvij3nj8u* initial velocity of 60.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 60.0 m/s at an an9q91 ggkc 83q zyfwh+uq o)l+rgle of $30.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle8qrzf:- -q tbe 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 horizontally at 23.4 m/s from the roof ofuuymksb n,k.9mk6q z1;,s5kqmtzl cu:4f 2n . a building 55.0 m sy.n,k5zku c 6 u94qu;k m .12mtn,lq:bksf mztall.
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of the building that the projectile lands.
(c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

A projectile is fired from ground level with an initial sfu 3dy55ywz8j ow b50qpeed of 55.6 m/s at an an5bwfzqo8dyj yu055 3wgle of $41.2^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.
(b) Determine the maximum height reached by the projectile.
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height.
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height.

  On a calm day (no wind), you can run a 1500-m race at a vp)bterj: wuv. 3,e yso9-klu- elocity of 4.0 m/s. If you ran the same race on a day whenw9lv.u, se: te ubp)j3ryk- -o you had a constant headwind which slows your speed 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 m/s to t/ ae-6tb.emyqhe West. The plane's speed relative t -yb.m/eaqte 6o the ground is

  A plane is flying due Sos 8x(-ge92 ( iowvfpiouth ($270^{\circ}$) 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;1bm+s) vw9legy521idgbqn s20 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 p/hk/ )zs5g ajxrojectile with speed 50.0 m/s in a forward directions/gxkza h )5/j $30.0^{\circ}$ 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/s, is directed acros3tg38gbc o0(jf m2cx jh1ovo3s a river with a h1g(ojg0 b83ovom cxj3tcf 23current of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorbtyx ctg+t*e5ep(tp23yo, y( aoat that can move at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in which the current flowx yeepop(,a t5t*+ty(g3cy t2s at 5.0 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 water wisheom hztvi5;gn w9p3 +(frni28f s to travel directly across a narrow s5 irzmgt(f v9i+wnp8 hf3on ;2trait 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 opposi 8**w4q(v*vpts, r uau0er kfute bank in 6 min 40 s. She is swept downstream 480wr v, ket v*8(0s 4*u*uqfpura m. How fast can she swim in still water?

  A swimmer heading directly acrtj,h7qcxw2b +d)c.qh nym5 d+ oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of thjdd) yh,+mn +.cqxwh 2qbt c57e current?

A boat, whose speed in still water is 1.75 m/s.ji rn-.8 cjq.4sj) jqldtl1s, must aim upstream at an angle of1i.. trj48l)nqjsj .qjs l-cd $26.3^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.
(b) Determine the resultant speed of the boat with respect to the shore.