Which one of the following is an example of a v 1hqsj.f h6thwbz,ga 7x-gpgk;7qs , 8ector quantity?

  Which of the following operations will no3s;u1vban*9g,zk6vb xnqf q3o+4t fqt change a vector?

  Which of the following is an accurate statementu6r7o ds.bbgql r(+d/ ?

  The resultant of two vectors 2wb odj*8j-g/v8guq/olp- i*;p ts5:mhos oais the smallest when the angle between them is

  Two displacement vectors have m7dbe(y c-fsi e8 cq7)vagnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are a7ve(fseib)y 7-cq 8cd dded, the magnitude of the sum

  Two vectors, of magnit3)6p cu,v rqiuudes 20 and 50, are added. Which one of the following is a possible answer for thv3 ) 6cup,irque magnitude of the resultant?

  Three forces, each having a magnitude of 3qg 9y. +6liqp,kdgo7k)uwm b(0 N, pull on an object in directions thk69p o )dqb,+ lgw. 7ykuig(mqat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thvsi* tm)l3k(yay3:zpe unknown vector is

  Ignoring air resistance, the horizontalkfa 4u:452hpu5ls6so2px oe h component of a projectile's velocity

  A ball is thrown with a velocity k/co .cy4t u3gof 20 m/s at an angle of 60e above the horizontal. What is the horgt3 4.kcyuo/c izontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's accexw m0ddh**xa. lerationhw0xm*d *a.dx

  A soccer ball is kicked with a vel6a- wevilbv1 , k-j8ihocity 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 v6 7q*+w2cdtqilrx1 dnu;d n wfhv27b1 5-zeovector of an object is directed anti-parallel to the velocity 2q-cenuv2t; *5+bhd z6 fn1rid lwq7vod7xw1vector,

  If the acceleration of an ,- .o wez h +,zcd/nnod,p4ornobject is always directed perpendicular to its velocitn.,cd +, roo/nw4de- noz,pzh y,

  At what angle should a water-gun be aimed d z7f-tnh1cw)e :5owgin order for the water to land with the great)17: otn -gcde hww5zfest horizontal range?

  An Olympic athlete throws a javelin at four different angles above te)sxabdfwiq6. m* ;z3 he horizontal,m.x s ;azfei )q*b3wd6 each 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 ti;8vgbuzogyq2 -t8ar / be5+ye(aur s.me. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal/q5t+rrzaebo. 8 -y(;yvbg8s2gue u a range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/srm ua 5/od 2/tldori9iaim1 // 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 attempt reaches its maximum height, h o(rd :v4 v2cnu d 54o4j3uaqmlqehkywg.:4j-ow does its speed compare toa.3d :uy2gkvn4vjeru d445 :mhjl c(wqq 4o-o its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant au973kis t v5kr ball is dr9ivskr3tu5 7kopped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the ,qqt j 56nm* kpdtlv*3same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bqv*,j* knp3 t5tq6 ldmullets.

  A plane flying horizontlvn6v (nkxh jh*) r5(oally at a speed of 50.0 m/s and at an elevation of 160 m drops a package. Two seconds later it drops a second package. How far a l(nn6h(vo)kh *j vr5xpart will the two packages land on the ground?

  A package of supplies is droo-;7tg4f/ *auph g- crld6wrg pped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between4ltu* h;g /rr7f-6dga o-wgpc the falling packages will

  A pilot drops a bomb from a plane y umpy9*y/u7 4wuj4z +jqw7ggflying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane willjyy* 7 4 wj7z9 4+yu/pqgugmwu

  The acceleration of gravity on the Moon is only one-sixth ziw q.u)wg44y06xn86rmymygo 6djy6 u4;vp i 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 wouldpdm yu on 4j.6uvmwi rqwygg68 6)4zxyi0;4y6 land

  You are traveling at 55 mi/h in the +x axis relative to a ,3hwdutde0k. rym v+ (straight, level road and pass a car traveling at 45 mi/h+ k,d(wd3m.eh0utyv r. The relative velocity of your car to the other car is

  You are trying to cross arilc ,--i7l ej+yp8i y river that flows due south with a 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 shoulil+ cyy 8ri-pj,7ei-l d head your motorboat

  Your motorboat can move at 30 km/h in still water.or8 k w)d8-ptj How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km8wdojr-kt p )8/h?

  Vector A has magnitu*,9ep1u 1 s -lya*/ktaprd sbhde 8.0 m at an angle of 30 degrees below the +x axis. The y component of /ess*d btp kalp-r*a91huy1, A is

  If a ball is thrown with a velocity of 25 s8wp2x py9/:*gi7c eb r7dndum/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 lifxkx *cwqc*es4*,p s0 ne in a direction north of east and you end up 2.0 km noxs*f4*pcks ,qw* c0xerth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/nj6e4 mi *2ngss. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the 2sinm4*ge nj 6x axis must be

  A 400-m tall tower casts a 600-m lon 40(+ s f7b cy+ppo5z9gq4s aau8bnau;z*maimg shadow over a level ground. At what angle is the Sun elevateg7a n4pf* y8a4 9apcozs+ia(q 5b+ umuzs;bm0 d above the horizon?

  Two vectors A and B have components (0, 1) qxtl-2q9s*d-mlvs+ *n3kg6jx e4 + gwb s zbm9and (-1, 3), respectively. What are the components of sl3jw sg4b tx-x9 eqn*ds-mkv 6b+2qm*gzl9+the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What-47ytwck-;ncakc rr7h 8q (oe is magnitude tqrkr7c(-;ncc-84o 7ye kwha of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is th* vyg 38:rdo-d2muaq ne magnitudd2*au-oyqv m 3n: drg8e of C ?

  A car travels 20 km West, then 20 km South. What is sc7j *n*auo-0f sl9d gthe magnitude of its displac7 -d0jl*c*nua sfg9soement?

  Three vectors, expressed in Car0du 6*)gib 0(5r-qsd,njsis vaj;u mbtesian 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 coordinatesuux tc0jcprm ,-:v9dq ewsoat; , 7/b)fdbk-(, 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, v70p ;w h5i3s;syhhxk. kjo9 d-4.0) and vector B = (+3.0, -8.0), what is the magnitude of vectohs3wsokd 9 xkh i;;05.pvyh7jr C = A - B ?

  A runner runs halfway around a circular path of radiusu/rxkkrb98 gkz(zkfp h9773)qq3q k s 10 m. What is the displacement of the joggerk3kp8 kx )g3kbuqk(7z9q/qr7z hr 9s f?

  Two forces are acting on ahb)6a6t l:o i xi hw,ljif/4i0q lh-u)n object as shown in Fig. 3-1. What is the magnitude of the rflt/ihla 6u4, h:6hwbl -x0)o) jiiqiesultant force?

  Two forces are acting on an object as shown in Fig. 3-1. What i qw/nx; qb6.vr*xxii5s the direction of the resur*ixv xw/ qix q5n6b.;ltant force?

Vector A is 5.5 cm long and points along the x axis. Vectox5i ybcx ,,g 0y cq6u2ct3kg7fr B is 7.5 cm long andgfqu,26y370ci5b c,yt c x kxg points at +30e to 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 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 lo*ciaxd8ueu(u 9mfx 0.50 qalmng 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 initial speed of 10 m/s fr/ mfd89dus0 psom the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the clifu dpd/ sfsm908f to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, from qz 54:smn2 vqub5ucy -a bridge. It falls 20 m to the water below. How far does the rock travz-u4 cm5 vy2nsuq5bq :el horizontally before striking the water?

  A ball thrown horizontally from ilur/qdy 5x(rc**z3h, b zr,la point 24 m above the ground, strikes the ground afte hbxyd/u5lz *rqr r*(c 3il,,zr traveling 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 zv2r6uy rpq dvox5gfa4v 2h3 : d7ar24of 12 m/s at an angle ofv: 4g5 23ayrv frdo var6ud7q 2z24xph $20^{\circ}$ 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 w: axu. t h wbu,zjenq;fh+/*q*ith a speed of 12 m/s at an angle oqu n t*b;qfaze/,hj*h+:u wx. f $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an in(lcfk34rko vnr u+ j+0itial velocity of 60.0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launchel(cry o c71g6kd 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 an6u,phj a*ay 7w 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 at 23.4 ula0y3n8k7jk m/s from the roof of a building 55.0 m tall.uak3l7k0jyn 8
(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 speed of 55.6 m/s at ):sr icvd8p0 2agc l9 *ndx4ykixy;u( an anx an 8)4cvdi(s9:; u*rp2 kyxdcgl0iygle 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 velocity of 4.1f.ooar3ehj*jd2-c 4uar mfqg-fxv o y0 b.(00 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 would take qca--ovjh1j3f2g0r yd. 0 fora um*o4(xfe. b you to finish would be

  A plane has an air speed of 200 m/+ n .: fih2v;:tdhopr;pn)eix s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground ix ;+p)2tr.oihn id ;:vn:hfpe s

  A plane is flying due Souq/990t7stf 0 vc m5a3ntbvjklth ($270^{\circ}$) 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 :eep5z7i+q h nu4y o+s120 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 movins1 ,9q;fk1se segxd9 rg 200 m/s horizontally fires a projectile with speed 50.0 m/s in a forwad k9eses9,r1s x1fgq ;rd 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 river7 a fxofo:j(/p with a current of 6.0 m/s. What is the speed of the boat as it c:xp7f jf(oa/orosses the river?

  The driver of a motorboat that can move at 10 m/s in still water w:rb7,rz p 1l (j2frfjeishes to travel directly across a river 1.6 km wide in whicz:pjlrf21 rb7 ,(j rfeh the current flows at 5.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that ca bfjj82j2e+ w f kpp59x/yuf0in move at 10 m/s in still water wishes to travel directly across a narrow strait 5fwj+0up x kiyb p8e/jf29j2f in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acry80c6z, ig8:xqen b y0;s kewgtaf4k; oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stckq, ky ;eseat4yx6n8fg 0:g z;0ib8w ill water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank *n):lvzop)k n0yve:o ek 7 +of6 yw(fydq(dv8in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?zql o)7:) npy(vkf*:yk w8 do(y6+ oe f0nvedv

A boat, whose speed in still water isz seequ); 5/ )p6x0zu5 z1i)lsfrctay 1.75 m/s, must aim upstream at an angle of 0s/ip6 1qs )cla 5 u)yrzz5euxftz)e;$26.3^{\circ}$ (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.