Which one of the followin2)9;v;ily.dhl(ciwe eakj+og 9x; xc g is an example of a vector quantity?

  Which of the following operations will na s aiprbcpa3hzt:8v k-s;075 ot change a vector?

  Which of the following is an ak:1+beotnn-cm ayw ,*ccurate statement?

  The resultant of two vectors is the smallest when the angle bayku;jqj4:j p,n +*k getween them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, rev sfz j(n8 y*bzqh0/d2spectively. When these two vectors areyzhnf (8q bv02/*sjdz added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 5* 26rir /sfchy0, are added. Which one of the following is a possible anryf*/rc 6shi2swer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull oy 44yh6vcc)eixz px27n an object in directions that are p7iv)44 eyh cc yxx2z6$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the u5aqu9di,y59ad ejso 3nknown vector is

  Ignoring air resistance, the horizontal component of a projectil *jbh972qlap v. o:wvye's velocity

  A ball is thrown with a velocity of 20z/ 36n bl,wx lm b:)aqh:i2*gidb zym) m/s at an angle of 60e above the horizontal. What is the horizontal component of its instantaneous velocity al)wbmhy/: zanx2:,mgbl i6 3) zbqd* it the exact top of its trajectory?

  Ignoring air resistance, the b5xx8d9p/9jui-vb5y ur-fz e horizontal component of a projectile's accelerationb p5 fjrbyx9 e xv/zu98i5-u-d

  A soccer ball is kicked with a velocity of 25 m/s zbhv -*pcnuyrk/xcb5 qv).-m2 1wju/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 anti cjol*j: c6c twk49xjqqz-c3/a4le) t-parallel to the velocity vectorjcct*kjl x w:ca4zt-q/ 3jeq64 )9clo,

  If the acceleration of an object is always directed perpendicular to its velo3+l 8zbr9e99 aej tnao u0fp7ncity,eana7 +eo9z bjrl 0unft3989p

  At what angle should a water-gun be aimed in order for the w54 99d vlh68udq((iins voramaiga87 ater to land with the greatestla( 8hmvgou9n v 6id(4si8iar qd97a5 horizontal range?

  An Olympic athlete throws a javelin at fom:x zqf4+7fi2u) ae teur different angles above the horizontal, each with the sxaqzi: t2f7f4 me e)+uame 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 time. If th4yud oio(km:oi4e u ob(a+(h2 e ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first servmo :(huo o4+oeiy4 bik(2(adue) would be

  A ball is thrown at an original speed of 8.0 m/s at sx (*nr2cww8i; -ufbcan 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 reach**s n9x2 rm/zd sp,l-kfrje5 ca/ait, es its maximum height, how does its speed compare to its initial speed?z,f5r*cd e,/ 9ls-i / ns*apr ma2jxkt

  A stone is thrown horizontallk(z0bnco r2 ,wmovt 9;y from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground b2;rz0bwvnmo (9okt ,celow?

  A bullet is fired horizontally, and at the same instant ej6k .n zws*8va second bullet is dropped from the same heightne jw.6z s8vk*. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a1 gvawgl4*gv( 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 apart will the two packages land on thevggwl1gva*4 ( ground?

  A package of supplies is dropped from a plane, andz 1q /ye,x6t wr ia2rne1t ;.bdd(9miv one second later a second package is dropped. Neglectinn;(v12ei/91td xzie6. dq wm,ryrtabg air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally aq1lkx97 ,,t i(fq tjhdt a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the planej ,qfttid (q,hk91l x7 will

  The acceleration of gravity on the Moocai4(jeii 4nu i:01qi)z t +rdn is only one-sixth of that on Earth. If you hit a baseball on the Moon witqiic 0it:ed jr+ni)14 (ua4i zh 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 axis relative h9ow ys5l),e vm)1mdqt2men3to a straight, level road and pass a car traveling at 45 mi/h. The relative velo9m ewm1n,styvh)ld5 3 2qe m)ocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong cu1;pln-bby ys9 rrent. You start out in yourp 9bb l;y1nys- motorboat 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. v a1 (u02ezohj How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/ (z ejao12uhv0h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. wyu57hl*q485 d-uw )hh.uvt0c j yomh The y com ym ycjhqhl*duuuhh w-o0w8)74t.v 55ponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of f5d g,omn6gx6$37^{\circ}$ 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 z.,ax6 -e kwz, k9xan8 icdqpw )kll9nrre928 east and you end up 2.0 km north and several kilom 8i lqcekx-kn , aze dk)8rxr9p6lznw.wa9,9 2eters east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its s ,frgg-ly )t6.ede3kg)n w(gvelocity is 8.00 m/s. The angle between th gk,-get den3 )6.lgrg )(yfswe direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m;b7 gx9uuua ,s long shadow over a level ground. At what angle is the,x ;9bgua usu7 Sun elevated above the horizon?

  Two vectors A and B have components (- ix 9+qnno/3rilw ;9bu 7kzo h9u+lbc0, 1) and (-1, 3), respectively. What are the components of the sum of t +9nw-oz 7qbb l/hkn+9uiuico9r x3;lhese two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. ljcmc ;aq2 +d0j:x qc9What is magnitude of the sum of these twx qjac;:j+d2c0mq9c l o vectors?

  Vector A = (1, 3). Veykn1/-j4jcxi1e t-w r ctor B = (3, 0). Vector C = A + B . What is the magnitude o w-n/14xikejc j rt-y1f C ?

  A car travels 20 km gjw2/);qsi snff(+:irts 4yoWest, then 20 km South. What is the magnitude of its displaiyn4 o2:;/ (fsfjw)tsqgi+rs cement?

  Three vectors, expressed in Cartesian+,+vqm kmmz.s 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 Cartesiwzt/; : fwjxfrwms;1 8an 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) and vectob*em pt q751adr B = (+3.0, -8.0), what is the magnitude of vector C qm*b1 7da5tpe = A - B ?

  A runner runs halfway arounsrj6lmjj- * rw4f5.)z )fotn sd a circular path of radius 10 m. What is the displacements6nj rlfr-tjso .m)5 z wj*4f) of the jogger?

  Two forces are acting on an object as shown in Fig. 3-1. Whatdhr ,,mdlj0bg8 me/g / is the magnitude of the rj ,e0rdb , 8/glhgdmm/esultant force?

  Two forces are acting on an object as shown+z*5xllei: g07d vj by 8xd7ch.4lsq w in Fig. 3-1. What is the direction of the be:xg 4iyc0sl7w d8l *z5jvqhdl.+7xresultant force?

Vector A is 5.5 cm long and points along the x axis. Vector B :ha0omxs y-tfj 9/ zgevf4z,0 is 7.5 cm long and points at +30e to9v jmx-g:, 0fzs/e4thfz 0yao 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 pointny, x ))si)2* u.xmhmeq/08libmhzlhs 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 mm h) +cg w3aid-(hyae9/s from the edge of a cliff. A stop watch 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 +acg yh)m(9hd e i-aw3cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridvx:q +ob6 .oka8n4xsi ge. It falls 20 m to the water below. How far does the roc :.n ok i6sqx4xvba8+ok travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, sm3;t5 u di2.bqodjmj6 9u je/btrikes the ground after traveling horizontally a distance of 18 m. With what spe/ 29qij 5edobumju 3djm;6t .bed was it thrown?

  A jumper in the long-jump goes into the jumvr5vij9 k15)yv; kslw p with a speed of 12 m/s at an angle ofwyjv )kr 1siv;v95l 5k $20^{\circ}$ 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 jubw0p5t4dlru si- ; ft(mp with a speed of 12 m/s at an angle 0 d4-;sfltp5bi(tr wuof $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initif968w/r i9x:uzi0(jjd jzz rd al 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 atexzu1c 7peuz4ddvk2 isdj16 r2sd*+4 an angle of $30.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an2gpd2d 9,sby b *mdam6 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 m/s from the roovy03q83pahm6d *n)v u4tinsksjzv 0,f of a building 55.0 mp8n)t svs a*0,qy03i4m6v k dj3hvnuz 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 an initial-9p m4pvu z +qfv70oxs+wd 8jl speed of 55.6 m/s at an anqv w48 x+fs7lzduomj+p- 9 0pvgle 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 rac7v i)fo0 h (urr3d4uxge at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constgfd0uxrv43 oih )u(r7 ant 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 vh2bw)ip-5 zhm/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relihh2bv )p- wz5ative to the ground is

  A plane is flying du(u obk02 xdva8u+ k+kve 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 is hr2 kq45-p w rlzo*yvs.eaded $30.0^{\circ}$ 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 wiickltv84-,)l1h b2 q l h t.vvxw0dpn.th speed 50.0 m/s in a foq)t 1.tl h2xv ivlw-l4vhbkndp, 8c.0rward 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 dire-z),jkg iu8n t1yj-s/y lb7zvcted across a river with a current of 6.0 m/s. What is the7 lysz--gj8n/)iu, vbj1ykzt speed of the boat as it crosses the river?

  The driver of a motorboat that can mog+2 jmlr x(,m y/vi4x0 c5kbicve at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in whiccv4g+bximxr,m/0 2icj ly k( 5h 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 j1s8a dw3b+8i3c4m gk .zbbq bwater wishes to travel directly across a narrow strait in which the current floi.ga1 8bbqmzw3skj+ db4b83c ws 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 opposite baffk254d 3eu o7ojqnydefc cf,5 9o ;v1nk in 6 min 40 s. cf 9o ;o1 34okvfjed7u fen2qf5yc5,dShe is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches +ncjh:xq wz1vb6cp- tvo,4 /b2mm0o jthe opposite bank in 6 minjbvo jc+v4:m,b1otm2p60 n/w-qh c xz 40 s. She is swept downstream 480 m. What is the speed of the current?

A boat, whose speed in still water is 1.75 m/s, muwreaphu0 x28 .st aim upstream at an angle of xawr h 8u.pe02$26.3^{\circ}$ (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.