Which one of the following is an exam*6r3,5 yaoc78)z njmpe duyiyple of a vector quantity?

  Which of the following operk m;hu;;: 6ybgt6pstoations will not change a vector?

  Which of the following is an accurate statemenuk2 5tx(q gk.:kv8tbet i7 4odt?

  The resultant of two vectors is the smallest whnf twci7juz; 5x;d7q(en the angle between them is

  Two displacement vectors 2q2wr/f) hcud ju 2v3rhave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude v32) 2jrh2u drc/wu fqof the sum

  Two vectors, of magnitudes 20 and 50, are added. Whichcg2wx v,- /1tsb3lj-sni e,/ipk1hbu one of the following is a possible answer for the mas/ ,lwesg1inuh2,1p3tj i k/x -bvc-bgnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an of2ore5 /ot /g+l gaz;wbject in directions tzlg5t+o ; /wr2aeofg /hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, 7d/, y sxx*ilu q3.dchthe unknown vector is

  Ignoring air resistance, the horizontd(nx 7fg ty61val component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an anjh4t5e172x ur( .em onc *ktef2pfm(e:0 soafgle of 60e above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top omo 5xo:*f fpesc((e.htkeu an 1r02e4 t2fjm7f its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's acceleratio7 lnl6e5pu x*xnux76ex llp* n5

  A soccer ball is kicked with a velocity of 25 m/s at an2e ob) /;fdlub 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-paralle6w de.(0u ; (d x/ketk(pcvezxl to the velocity vect uxt. wvcd(k0(;ee(d/e6kz x por,

  If the acceleration of an ob7e0dk g 8rvrp7 adewg aai;.l2z8;8flject is always directed perpendicular to its velocity,id. a8a ek2wpgra8vl7;fdze8gl7 0r ;

  At what angle should a water-gun be aimz( -w xd qwikns2)b /t*rs8ekl8p5nt(ed in order for the water to land with the greatest horizontal range? 2i x)*8dkn(wsetrkzt/5 (8 s bqp-nwl

  An Olympic athlete throws a javelin at four different angr e7ukk6h+ta7; dq6ag- q nxj;les above the horizontal, each with the same speed: aa;6gq kt 7-h qj6udx7renk+;$30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second cuezcrl,yn,h1j ;2 xir+(+wws,5ohm time. If the ball leaves your hand with twice the velocity it had on your first throw, o ,rew uhslm+z 1i5jh,yc( ,n rxcw2;+its horizontal range R (compared to your first serve) would be

  A ball is thrown at an or0 5di7xil9vfv iginal speed of 8.0 m/s 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 k fc2i2a sjl5ep y,)2oattempt reaches its maximum height, how does its speed compare to its initiall,scfk 5y2ij2p2 e )oa speed?

  A stone is thrown horizontally from the top of abb d )7dkbx(utw,+or7 tower at the same instant a ball is dropped vertically. Which odb7 bdxwkr)u+7ot ,(bbject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same in- 4 vdtdhur ;u+j;ag;bj+bs5mstant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of thev+bhdud rga s; j t-ju5mb4;;+ two bullets.

  A plane flying horizontally at a speed of 50.0 m/s and tu 4bv w,2;clkat an elevation of 160 m drops a package. Two seconds later it drops a second package. How far apart will the two packagb c k24wvt,;lues land on the ground?

  A package of supplies is dropped from a plane, and one second later a sec7vbd0gs p2 a;6 6hjt:prt.cu)g3tl qhond package is dropped. Neglb7p )htgrh3; lq2:t.du6 s6vt cjp0agecting air resistance, the distance between the falling packages will

  A pilot drops a bomb frhba+o ; 9ajo ncyjwi(c5b6mh(st/ 8 y0om a plane flying horizontally at a constant speed. Neglecting ai8;+o5ay c(j b/whocyms(hn6iba 0 9jtr resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of tha i,n 8r;ste-,m sz4pmrt on Earth. If you hit a baseball on the Moon with the same effoepmtz r4ns- ,ismr;,8 rt (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 axis relative to a straight, iflp.d)d77 t6s rq ygx( 6,unklevel road and pass 6t6g 7 xkr(dudpisfl7 ).,yn qa car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a rjm8m-: ehe3 bgoab g: 8s/xpn4f fol:-iver 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 should head your:hm/xg-alf 8jbfn:eep8bg m4-3o os: motorboat

  Your motorboat can move a3bl01)/2 ecxcd cz- nud)ri xwt 30 km/h in still water. How much time will it take you to move 12 km downstr/ -u1)lec xdnz) cd03irxcbw2eam, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle ofh4v+i p6gll61 z omrk4 30 degrees below the +x axis. The y component of+vrk6lm 6oi hzl4 1gp4 A is

  If a ball is thrown witote8 /y; )bqxne6d 49h*v-x9bqbr-ns n/z wfe h a velocity 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 wcbms 5ch9- e,north of east and you end up 2.0 km north and several kilometers east. How many degrees5,mwec schb9- north of east have you walked?

  A butterfly moves with a speed of 12.0 +rc9(* unok/z 7y qm-fz;h(f ur0 czgim/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis mustnir; 0y q+zu(*r7ozgcc /hk(9fzm uf- be

  A 400-m tall tower casts a 600-m long shadow over a level gr mq t7id0.o/zwound. At what angle is the Sun elevated above the horizo/o0d tmwqiz7. n?

  Two vectors A and B have components (0, 1) and (-1, 3), res5 ob( eob3y7yupectively. What are the components of the sum bey b37uoy5(oof these two vectors?

  Two vectors A and B have components (0, 1) an(zu6lt4 2. upfsg 3sdtd (-1, 3), respectively. What is magnitude of the sum of these two vp t2us4dt3su.l6( zgfectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector,cx)w-g byl e84 j+myd C = A + B . What is the magnitude of) g 8m4ewyb dj,cxly+- C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of ,g)phaug-ktp ) 0r vb5its displaceme h)5ta) vgrpgbu,0-pknt?

  Three vectors, expre*z2je( 4fukll yk6x, lssed in 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 Cartesian coordinat3 u*)vwwhq1s wkytv)3es, 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 = (+3.0, 5o;nxsi ma0k:hqlxg./qnb tlm85 w- ,-8.0), what is the magnitude of vectbmx0, l -:gi85on w5ts./x;k aqhmqnl or C = A - B ?

  A runner runs halfwabkuxglq o*r49i+ 4( rey around a circular path of radius 10 m. What is the displacemei* o9l r(qu4xe krb+4gnt of the jogger?

  Two forces are acting on an object as shown in.uvfa,z v69:zqxcy a9 Fig. 3-1. What is the magnitude of the resultant forva,yzc qf 9:x.uv6 9zace?

  Two forces are acting on an object as shown in Fig. 3-1rjt3 n0mjpv+ 4. What is the direction of the result+3pr0 tv4 njjmant force?

Vector A is 5.5 cm long and points alo lhpo:akbn-*6 ng the x axis. Vector B is 7.5 cm long and points at +30a6*h:n-kbol pe 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 long and fil h*idz0 0j:d)m)b7cdhwn t6kb g np.+x05upoints 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 from the eorhmtg.aqx5x79 5 6uedge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff xtheux9 7.m5o6raqg5 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 ab /h0yh ov,cf1 bridge. It falls 20 m to the water below. How far does the rock travel horizonta hc/hyv0o b,1flly before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, strikbh3r/obvu 0-tax 2ma-es the ground after traveling horizontally a distance of 18 m. With what speed wa-a3b u2abv-/x htmo0r s it thrown?

  A jumper in the long-jump goes int6nrmt1wq m(kg )rboz03 9txo( o the jump with a speed of 12 m/s at an angle of q3b )6nomrk 1 gzwo(r(tm 09xt$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long i5):je pmjjtx.q;o76vph*wm-jump goes into the jump with a speed of 12 m/s at an angle of j t6i) xe :hjwm7pv*qm.p;oj5 $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60.0 m/s at an angle of im00 / efeu4uh$30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launchef(y 6:ufw9 nxud 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 fire11 ) abehcxdoc63 ir.td 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 hsznt5fhxei.g50x c 75h3x.ht i8pf;m orizontally at 23.4 m/s from the roof of a building 55.0 mpg t.t.hi ;n5efs 5xzh7f0cx8i3x hm5 tall.
(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 o,b pask )/)btan initial speed of 55.6 m/s at an anb)t)o/ sbkp,a gle 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 ra*.v6png* drigce at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind whipvgr6.i *ndg *ch 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 ;wi*f - b cy xwmaeu 7mpk).355l9fndxa wind of 50.0 m/s to the West. The plane's5xfn7l593* u -f;m .iwkybmax ewc) dp speed relative to the ground is

  A plane is flying due Se: trgkc5 ie g:i1krf cv88)e0outh ($270^{\circ}$) 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 is headed16ftrbj mit.-f wn7l +jt2w xw*c()ze $30.0^{\circ}$ 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 kul,b 7 lgj-.tu+n*nzprojectile with speed 50.0 m/s in a forward j-z+,. g7u *knublntl 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 acrofbt 1*tt;zh 9sss a river with a current of 6.0 m/s. What is the speed1ttb*fs9th; z of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water wis3)2kl *q1zl:hhy svt h djx/i1hes to travel directly across a river 1.6 km wide in which the current flows at 5.0 m/s. How long will it1/vdh 2)1t:xhi 3jklhlyz *sq take to cross the river?

  The driver of a motorboat that can move at 10 m/s in su.u/wt kg;bd8 till water wishes to travel directly across a narrow strait in which the current flows at 5.0 u/;kbg 8.dt uwm/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppo ;qdbn o,r9ib7otb18w,o /hi8o/vrs usite bank in 6 min 40 s.7 o1o,bw8o/is;n brr,i9oq / bhdu8vt She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches th6+s5z/ca d1dvqp t5yi e opposite bank in 6 min 40 s. She is swept downstream 480 m. Whatt+vqzys1d/ c55 dpi6 a is the speed of the current?

A boat, whose speed in still water is 1.75 m/s, must aim upstre7/qa,rt*,eip ,su set am at an angle of /s,a iqes,r ,tet p7u*$26.3^{\circ}$ (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.