Which one of the following is an example k93v lz7e 7-necmk)hu ycux5*of a vector quantity?

  Which of the following operations will not change a vector7*)tfl ia uddqqaa sa6// o 3l1ifz2ywb34r0c?

  Which of the followie3f,r* 2id /*wbe5e sjpzpo n3ng is an accurate statement?

  The resultant of two vectors is the smallest when the angle between them +, ++715sm*k jptfpgfh xtkum is

  Two displacement vectors have magnitudes of 5.0 m sx2y;7je uc0 +iena: rand 7.0 m, respectively. When these two vectors are added, the magnitude ofnaxj+ysr i:u e20;ce7 the sum

  Two vectors, of magnitudes 27ev.+w,vus 5un q ccadluk 2-(0 and 50, are added. Which one of the following is a posne cd.qc 2sv+vk(wu-7 ,u5ual sible answer for the magnitude of the resultant?

  Three forces, each having a magnitudecn2yn liz t8qw+14f9j of 30 N, pull on an object in directions th wt9cj qnyl 182n4izf+at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector i:yo hmr-) ph4bvmx3p ;8 eluk7s

  Ignoring air resistance, the horizontal component 6cpf bmg5m ;*oof a projectile's velocity

  A ball is thrown with a velocit:ba.rf ge+ 6yay of 20 m/s at an angle of 60e above the horizontal. g:eb a+ yaf.6rWhat is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal corx+b;dcdd)r4omen ,;kna 8*bgm 7e:qmponent of a projectile's acceleration abkd4,n r*8n7mc:rqex;bgde +;m do)

  A soccer ball is kicked with a velocity of 25 m/s at lc bjo9 (6rno,tz64ti 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 gnlotetq - c kv5w(g r8i2)n05of an object is directed anti-parallel to the velocity voiggnqrk )t2t 5(- 08 lcnve5wector,

  If the acceleration of an objl8 r1ktyy5l7yect is always directed perpendicular to its velocityl 5l7 y1ytry8k,

  At what angle should a water-gun be aimed in order for the watn0n/ pl)q)rfwer to land with the g)l)rfnqp/wn0 reatest horizontal range?

  An Olympic athlete throws a jaytpya 5,h80 x :cupxm4l 9;zpqvelin at four different angles above the horizontal, each wi:qppmp , c8lz0 5xuhx4ay;9 ytth 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 balw y2qdd v6j69ll for the second time. If the ball leaves your hand with tdj ldv2y6qw96 wice the 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 angle ef4)s3y *vrbq r 2)baaof $35^{\circ}$ 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 maximuih8phty9i g)) m height, how does its speed compare to its inii)i t9h )hgyp8tial speed?

  A stone is thrown horizontally f8pf0wveu.j- - jx*cpjrom the top of a tower at the same instant a ball is dropped vertically. Which objewv f *0u.8-j-jjpcxp ect is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant rvdetas vus(xos u98 s.lmjys.m,.j7z 5k*53a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of. z ujs9dss3jv.s v*om5a87xe.(y 5 ,mu tlksr the two bullets.

  A plane flying horizontally at a speed of 50.0 m/s and*lt dvwvo7uk0+ *qgtb 7lr.8 x at an elevation of 160 m drops a package. Two seconds later it drops a second 77xlvtu bk 0o*rv*ltdqw g8 .+package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and onp 4o kk dwnou-w* ik- dh*,s898ztxbc,e second later a second package is dropped. Neglecting ai89s,4i zck *nwkbxud8ohot*pd-wk - ,r resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. x2z m etoikb/9 b,0db5 Neglecting air resistance, when the bomb hits the grdo0i9 ebz/bx5km2 ,tbound the horizontal location of the plane will

  The acceleration of gravity ql +9.u6ssuy won 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 lan .6us9+ywuqs ld

  You are traveling at 55 mi/h in the +x axis relative to a)-dcpwe(4noh k u8(rl straight, level road and pass a car traveling at 45 mi/h. The rw(l r h(denucko-p8 )4elative velocity of your car to the other car is

  You are trying to cross a river that flows due south with jo 81w 67u:gim2qcgkna strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorbwgk86ujonc:qg i7 21moat

  Your motorboat can move at 30 km/h in still water. How much time wizi37 sd(fy / lb+0isefll it take you to move 12 km downstream, in a rive0si(fbdf +7zi /s3lyer flowing at 6.0 km/h?

  Vector A has magnitude1kn8 fql* hx7p9n/dl2 f5lxus 8.0 m at an angle of 30 degrees below the +x axis. The y component of A isnh8/nd 9lxffsu5x p7*1q l2lk

  If a ball is thrown with a velocity of 25 m/s at an angjl7z u1lk )9r,sua /n(o,mmhkle 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 directionv i0c+) :uvbadp *vgz6wbn)fd0u (9vb north of east and you end up 2.0 km north and several kilometers east. How many de 9bvvdvd*baw :fi + ))v (znu6cu00bgpgrees north of east have you walked?

  A butterfly moves with a speed of 12.0 msuq(l*khl * 1s(zk2qss z (w7x/s. The x component of its velocity is 8.00 2wlk *szz*k (hsu xlq(s1(s7qm/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m 1 (l2opf(tg7+ifwxvx long shadow over a level ground. At what angle is the Sun elevated above the horizox fox vpwfg7(12 i(+ltn?

  Two vectors A and B have compoy xzn.1c/o +v1cy(fxhnents (0, 1) and (-1, 3), respectively. What are the componen1+yhvyccf1x /on.x (z ts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivqte2*s*t h7p nely. What is magnitude of the sum of these two ve2*q sent*t7ph ctors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Whain :dh f--3dv brpjf(q q0p68at is the magnitude of C ? p06-id83qa(bjn:- rvpq hfdf

  A car travels 20 km West, then 20 km South. Wh+f6wli dxp9v.y9hy4as/-oho bm ,h:xl+go)h at is the magnitude of its displa)fhsp+xw.ivamly9: - o46ohxhl y ,d gobh9/+ cement?

  Three vectors, expressed in Cartesian cv;rm-kt-j4lf r5h;1 qcs4qko oordinates, 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 coordid-cp/ zm7aak-nates, 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/*zwdc*sh .gdmly e8ni( dd(7 ) and vector B = (+3.0, -8.0), what is the magnitude of vector n(h/e*mc(s d8i.ydw7 gd*zdlC = A - B ?

  A runner runs halfway around a ,nshr)2ghy 0i :bk*hh circular path of radius 10 m. What is the displacement of the jogg ki,hhnr)hbh 0:y g*s2er?

  Two forces are acting on an object as shown in Fig. 3-1. What q(2pog+l, blzhy7sg )is the magnitude of the resultant fp2gh s( zb)l+y7oqgl ,orce?

  Two forces are acting on an objec pw2 hxiee sj(*(l8w8:elxg n7t as shown in Fig. 3-1. What is the direction :8ew 8l (h sglpenxx7w2ei*(jof the resultant force?

Vector A is 5.5 cm lr9.pa vdcc) c:chd 5*ye1w*ww ( 2dcezong and points along the x axis. Vector B is 7.5 cm long and points at +30e to the nega yz9ev * )cr1ec:wdd.(c5wchpwd2c*ative 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 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 2bb ho,e eql(4long and 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 initiaavkmj2 isn*,/l speed of 10 m/s from the edge of a cliff. A stop watchnjaskv* / 2m,i measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with *fyk896t)a4caba akyv7ja* y a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rocafby a78a* yavt9 k*4)aykj 6ck travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the 2abgs: i9) s8yc+-nwb tmo;or ground, strikes the ground after traveoom9ab8+t :r ;gb cnyis-2ws)ling horizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speedd tzp( 61 sgw+5/cdqybu0* bum of 12 m/s at an angle ofg(bdzs 5tdu10c6/+pmy u qw*b $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpi0*mh-jfn+ f o;zif1eq. y*sb goes into the jump with a speed of 12 m/s at an angle jhse-* i1f*0oy. +zbqnfi; fmof $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launcho h x34(;grm3iuyjzw.:zfjsql 5hl) :ed with an 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 6 :j8zmcn9 2g-p0o uz u2flbq/f0.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firq) jqb yk 98ts4b4yguml(: /yped 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 horizontally a v,:t9yrq6zqt :g3nwz t 23.4 m/s from the roof of a building 55.0 m talz g,ynt3zqt r:w 69qv:l.
(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 .kbj,-0b8nyjh ,m gra speed of 55.6 m/s at an angyj08mr ., jk ghab-nb,le 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-) 66 7bix5q cr e7p-la7ltnqugm 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 speed by 2.0 m/s, the time it wo 7q6-7a)ibexlq ng67ucr l5tpuld 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. 0w)25gn j8jkr z4)w.jx n.lahqq j2ah0 m/s to the West. The plane's speed relative tlg nh wh xjk2azj2.08wa .5j4q)q)jrno the ground is

  A plane is flying due r:/4 jo y juudyek0 (ulw0o/m*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 120 km/h itc03l5,uh gzkpy;fk l 1/x 2his 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 horizon xl x.osq+re+j o)la -ya,0ib4tally fires a projectile with speed 50.0 m/s in a fysx le+o.-q,a4 ioj x+ra)b0l orward 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/s, is directed across a rive +xeu.l(bmkg -r with a current of xl( .+-e mubkg6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that c6 pty05qu :qxbr3fpo.n ;8qxwa*v:scan move at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in which th6r cbsw3 p* yp08 fa:xutvx;q5. qn:qoe current flows 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 way xq p8hxe 6miq 3h3o2 qt;oqt hx)gg308p:4qster wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what anglyhxx3 :ph8 ip )q3e80q;qo2g4qx3 qmt hsg6ote upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches yp ap)x(mhk95r -. xrdthe opposite bank in 6 min 40 s. She is swe9dphkr (m pa xr5-y)x.pt downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reai6lsy0oa b 5f3ches the opposite bank in 6 min 40 s. She is swept downstream 480l y5630aobi fs m. What is the speed of the current?

A boat, whose speed in sti;7hq ;/buub enll water is 1.75 m/s, must aim upstream at an angle of q/ b7h;unebu; $26.3^{\circ}$ (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.