Which one of the following is an example of a vector q-.bx+n a 7vnto-oks+kuantity?

  Which of the following operations will+r a.zat68q tt not change a vector?

  Which of the following is ajlnh66jc4 8fwl(myy5/ dfn wf/4-klf fc eh+(n accurate statement?

  The resultant of two vectors is the smallest when the angle between themvgmq vfr. /+yuji/5 s4 is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 mcmv8wg rv8x.gwk;(m2 , respectively. When these two vectors are added, the magnitudm(;2gmv8x gwrc .vw8ke of the sum

  Two vectors, of magnitudes 20 and 50, are adds.k0i fhyr -7,qwlyx1 t8khy(ed. Which one of the following is a possible answer for the magnitud7tk (y 8-,xi h yq.1skfhlryw0e of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directo4 j8u*lilja) ions that are ao4juj8* ll i)$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, th..ay 4)z llmske unknown vector is

  Ignoring air resistadevzqp 8nzw.*sn*7q/ wl:i )s nce, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s a l68 pkn4;xd 2xk(1shknz2kgdt an angle of 60e above the horizontal. What is the horizontal component of its ilz4k2s1kpd6;g( x8knnk2 hdxnstantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horikz;)cc6djc *gzontal component of a projectile's accelerationj 6)gc; dzck*c

  A soccer ball is kicked with a / :r0;shdmqnycyu:* b a52pwa 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 an w1ixx 6ajl9o6 d2jokr9n* kr/ti-parallel to the velocity vector,6a x26rkjo 99*rljnod/i k1wx

  If the acceleration x ut lrilev;be01*p3 :of an object is always directed perpendicular to its velocity,rxi u13beptvel:;l* 0

  At what angle should a water-gun ;5ez /uzvly4o be aimed in order for the water to land with the greateslzv o4/5 e;uzyt horizontal range?

  An Olympic athlete throws wm rg75rmpuwz /g:m .4qh.. cpa javelin at four different angles above the horizontal, each with thez/m4q.7 w rmgcr mgwh5p:u.p. 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 tstkd 72vv-f;:x35ql/slat s(cdpc2ahe 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 vcdvdc; qxsl - p(2t235ls/k7a:taf s be

  A ball is thrown at an original speed of 8.0 m/s at vwk1,z6 evx 0n)8gthh 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 xfa88 uo ch gdbh) rv7v(s,57qfield goal attempt reaches its maximum height, how does its speed compare to its initial bg7xd uh7h sqacr)o8(8f 5,vvspeed?

  A stone is thrown horizontally from the top*be)5sq 0 yc(qx 9 qxai7dqgo) of a tower at the same instant a ball is dropped vertically. Which9o) sq)*bq0xeqy(qgdx 57 cia object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a sec6s qw( 8 .*xhbyhivci3ond bullet is dropped from the same height.q b v3shy*i8 w6ixc(.h Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 50.0a vcmklxy ,m)m(uw 2al0uh/93 m/s and at an elevation of 160 m drops a package. , (2vmw)mhyuaukma3/l c90x lTwo 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 one seco. 1vunc4sy/e+paxt m5 nd later a second package is dropped. Neglecting air resistance, the distance between the fal a 4/pmxt.sn5yuc e+v1ling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neg3pu hnwlr +q*6.8 npiglecting air resistance, when the bomb hits the ground the horizontal location of the planepu*6p 3r ig +.h8nnqwl will

  The acceleration of gravity on the Moon is onszylh9 ./;lc:c. sqrily one-sixth of that on Earth. If you hit a baseball on the M.lh/s9i rzs yql;cc. :oon 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 +xx7dcb4 gwk -j4 axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the xd-bg44cw7 kjother car is

  You are trying to cross a river that flows due south with a strong current.3ttl8 ya)pmv k-:xrnt0e )vnjc 8gd33 You start out in your motorboat on the east bank desiring to reach v3pkgn3dcm0tjy xt :l 88rta) ve-)n3the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. h c*19m3iw.ve e qyal.u4emhjn2ri1,How much time will it take you to move 12 km downstream, in a river flowing 1c*, haw3m4ee1 lyrmhjviuie q2..9nat 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 dle* uq1:aeca;e, bs *5uhz5oe r (:pyeegrees below the +x axis. The y component of z:r q echea5u(p;o ,1:*es*ybeu5eal A is

  If a ball is thrown with a velocity of 25 m/s +9w kd chq( ;qla2qc5gat 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 you. a:m-l r+ai6xk-jyj3q dnxyo*6hhf5 end up 2.0 km northd5- fak63o.x-a q:hny rjmil6+xh yj* and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves withlhd5t 8zx 9 *csox 79mc0elc8o a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the xzo l95 xx*987s8thc0cmecld o axis must be

  A 400-m tall tower casts a 600-m long shadow over a level groundsr6 i:3cg8fxdc1l0uo. At what angle is the S:3 sig0dfx6l1cor 8uc un elevated above the horizon?

  Two vectors A and B have comm+0 h pb6nz/ vrd.5vwbponents (0, 1) and (-1, 3), respectively. What are the components of thehv5mwrz6 p0nb d.+v/b sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3)4j/(qof;kch zbk)2 zb7bto3 r , respectively. What is magnitude of the sum of these two vec7k r );cfj /zb3ook(2hbtbq4z tors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is th/r+z wfghwi6tlv 2r:,e magnitud,flhwg t:26r/r+wz vie of C ?

  A car travels 20 km Westk:p0w/y l w.fy, then 20 km South. What is the magnitude of its displa.k pf0: ylwyw/cement?

  Three vectors, expressed in Cartesian co +q 2bfmyw)w6dordinates, 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 coordinat q7cys.9(yo ;zkbj n9ws c*iy/ 5(ycnfes, 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 txbj 6mhm5:o 6-kb/wx b6pcr0 = (+3.0, -8.0), what is the magnitude of vector C6wo06kpb6rb- :/c mx bxjmt5h = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the u7a1/nmgritpa :v .e5 displauap.ri /em:7a5n1vgt cement of the jogger?

  Two forces are acting on an object as shown iz ww/ yb1v-d3en Fig. 3-1. What is the magnitude of the resultant fov/zyww13d be- rce?

  Two forces are acting on an object as shown in Fig. 3-1. What is the direc/ 4bhj(l ,f p:hll-jwxj;nd5ation of lhlh jp/-:,j5 j4wf;xlan(b dthe resultant force?

Vector A is 5.5 cm long and points n0c2h4,r1i rf6fxgq,.hu tphalong the x axis. Vector B is 7.5 cm long and points at +30e to thrh 1 6xntgu0f qhp,,.ic2hfr 4e 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 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+wvlm ic rx3,k;byg:- 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 initicf k8vgeh wx3 391j0ap bj:jw(al speed of 10 m/s from the edge of a cliff. A stop watch measures t(xga 19ejj3bw:vjk 3c f0w8hphe 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 horizontally6 fx)i;e*hksn , with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. xi);sknh 6*ef How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above th5x0vh qf:wrvu vev3/-r 8w z/ie ground, strikes the ground after trarv wv :xe5uwv3zh //vri-8qf0veling horizontally a distance of 18 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 9+hzj ysrm;cmo *uc.2an angle of *uys9hcom;. mrc2j z+$20^{\circ}$ 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 12 m/s at an angltas *j::s+: w qcpd)xoo6ol6ee of o:sd6 oxe l+w*sq6p)a :o:ctj$20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60fqt5- /w+d:5so dwb4pinp y +x.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launana2q u vrpxej3g8)je x/8,r) ched with an initial velocity of 60.0 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 fired at an nfl.st a tpl, c78l)c.37kfrgangle 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 of a buibjel+-2 njk(re tzhwtj ) .*:ylding 55.0 m tall ey *r: bj+-l2twht zjjke.)(n.
(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 ayth*5c gwe8*oqeq x//n initial speed of 55.6 m/s at an angle ofgh/e8ex* qy5 /cto* qw $41.2^{\circ}$ 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 velocity of tvvl- l/ce6 om);l7vl 4.0 m/s. If you ran the same race on a day when yovo m7lcl/6l l-; tvv)eu 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 ot;zc8(11hl-n0 xhix nok xzw9f 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the groundtx 1 81w(ixn klozzh-0cxh;9n is

  A plane is flying due,i9:chg81s3 rcxc :nmxkt j0h 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 s*c.bprq; esj*)j 3rrq34ndz c peed 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 speeb )m,ut: a v0m,1u/kpqmcl 8ijd 50.0 m/s in a forward duqtbu)m a1,v:m,l mk8/ 0pj ciirection $30.0^{\circ}$ 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 r4k 1p6998j vbpbmdv kra i56p8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it cross 6v8 rm465kb jp1pkr a9pdibv9es the river?

  The driver of a motorboat that can move at 10 mn4ed5v d15 ei 7ep rdd;e5ort(g 8gc7h/s in still water wishes to travel directly ae7tvdeip7enhdo;(g 4e8 rc d1 5 d5rg5cross a river 1.6 km wide in which the 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 water wishes le,: a b6 +myx,um0qf6llmf:e to travel directly across a narrow strait in which lq0blmx mml ,fyefeu+6:6, : athe current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river ,n8hf5yfy1nb 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swi8n, fn1hyfby5m in still water?

  A swimmer heading dire f,s wcqv8fu003 p--ayz4/chs8llhbo ctly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 44fc/ qv--3 0buoals l, zpcsy8fw8h 0h80 m. What is the speed of the current?

A boat, whose speed in still water is 1.75 m/ e3pxc82zz. ;7c;med t*wvarq s, must aim upstream at an angle ofx2*ptcz 87mce . vqar3 z;wde; $26.3^{\circ}$ (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.