Which one of the following is an examplzqt ltkup;,h)k 4 2s/jctp r)ygug.- 9e of a vector quantity?

  Which of the following operations willmfbf: k 47jjhk1ovr0- not change a vector?

  Which of the following is /l xmo57sii u 5rfn, wh,l;v3zan accurate statement?

  The resultant of two f cn9-)l r2hohvectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respective/p ci4jch)7 i2cm e7bmly. When these two vectors are addem7m ci472/)jepchcib d, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addx4xcs76fzm ga:bx-2x ed. Which one of the following is a possible a6 2xm:c4ag7xz -x xsbfnswer for the magnitude of the resultant?

  Three forces, each having a mp)/q2as ob .qtk, : y9euebitywaf)*+agnitude of 30 N, pull on an object in directions that arebty b aieay:2w)+/t p)sukoq,f.9* qe $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown ve bp6x3xh3 r9xgctor is

  Ignoring air resistance, th;t.:gs v0m e caj29 fpyi1msa-6 7ihxte horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of 60e above the horizont4 33:phva5wb m+l d k8u9vtuisal. What is the horizontal component of :ul3s mv3b+v 8 5dti94uwph kaits instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectilphu, )4+ 3aghbsy008)gw m8es shuz kae's acceleration03es4 h+us8 ghzyhg),s8mpku)0 aw a b

  A soccer ball is kicked with a velocity of 25 m/s at anoj6* iz0ytp.r 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 directex w;v3sqpon6-wdi * e+d anti-parallel to the velocit*senv;6w3xp -+wqidoy vector,

  If the acceleration of an object is always directedx15h.5 swzu 1c yuq lbo8dhwzjn) .+,d perpendicular to its velocity,c )b+zdx,l1 hu1 jh8uqswoz5.w y.n5d

  At what angle should a water-gun b8 o,vn+u(o)r5 r+a vkv/l lftxe aimed in order for the water to land with thekf x+rv5v, at8vno/+)(r olu l greatest horizontal range?

  An Olympic athlete throws a javelin at i rn0dw q8f4/mfour different angles above the horizontal, each withfn/r0mwi 8dq4 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 o0g 2ztwoal1tnb/1 9dme. If the ball leaves your hand with twice the velocity it had on your first throw, its horizon o l za0n92d1bo/t1wtgtal range R (compared to your first serve) would be

  A ball is thrown at an8zdln24a7g:o, jttm i original 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 gwdyso2 (vdhg2ak; /0 ooal attempt reaches its maximum height, how does its speedyhd(so;220kg ao d/w v compare to its initial speed?

  A stone is thrown horizontally from the top of db a14l qs2 :x9w.)njrcs2awra tower at the same instant a ball is dropped vertically. Which object is travqar rs d41.cwj sxnlb92aw2:)eling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet ,giy/76zh 6tbm /veg ais dropped from the same height. Ignore air resistance. Compare the times ofy/6v hita z e/7gg6mb, fall of the two bullets.

  A plane flying horizontally at a speed ogu1qnwc.umf+nd 3e n*vg12o/ f 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 n/fu1e3gnogwm1cd. v* + nuq 2on the ground?

  A package of supplies is dropped from a plane, and one seu0sq n21byh.ri1 re5;zm xyn)cond later a second package is dropxrq 5emyn0zn; ih21 u y.r1)bsped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally atnqm0k m:4u k v:*m9fdv a constant speed. Neglecting air resistance, when the bomb hitkmf : qkvmn 0ud94mv:*s the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on E-wcai /8 ksikt0fx3;j arth. If you hit a baseball on the Moon with t- k;cksix/ 8f0atj w3ihe 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.kz8jlsnt*0lfa xi8s nom9v t2):ya 1 axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your cartm in) a0szy. s2v9a*jo1fxlkl 8tn:8 to the other car is

  You are trying to cross a river that flows due .ba0b1k -zaurha zxs .2 1rg8 aej2j(xsouth with a strong current. You start out zbrs- .1 (1axka2jaea 2bgjr hu0zx8.in your 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 st. ta1w 9u:fk puul0t3jill water. How much time will it take you to move 12 km downstream, in a river flowia1uuw0tk.lpj93u :f tng at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angc*3pmtr .9.x2h3jsgo4 qkp d wle of 30 degrees below the +x axis. The y c 4xk3m32d.gpj9pq* tcro s.whomponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of f- 6yt*75wjd7 odcsxq $37^{\circ}$ 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 t/w0mehe7p f4b2ekc 9 4w6hrmyou end up 2.0 km north and several kilometers east. How many degrees north of east have 4 2kc6prhw0thbmee9/ 74emfw you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its(3ydhu io:0 sa velocity is 8.00 m/s. The angle betwso:y30daih( u een the direction of its motion and the x axis must be

  A 400-m tall tower casts a 60v bbqz,7i4k:zo(yn/xot z8-pwu/ )s g 0-m long shadow over a level ground. At what angle is the Sun elevat vnt4 : yzg8) qui,7obokz(xs- zb//pwed above the horizon?

  Two vectors A and B have components (0, 1) and (-gl r9s/tw 91jc0d-j87 ip crdv1, 3), respectively. What are the components of the c cj1w 9l/9-tj0vdd 8g7rrps isum of these two vectors?

  Two vectors A and B have componentsst b0dn8kx 2y; (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vecnt ;y2k8sd 0xbtors?

  Vector A = (1, 3). Vectol(b-+kgtrf. c r B = (3, 0). Vector C = A + B . What is the magnitude otfb.+ rlgck( -f C ?

  A car travels 20 km West, then 20 km South. What is the magnitn.:; j)nr qit6 gvyezxgin0/.jskr ,9ude of its displacement?0;yin/nq k)t: 9v6jizx.er,nj . sgrg

  Three vectors, expressed in ecqjfg7* a)bfly+8k8 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 in9njl:r5 2- tquxbrd3v Cartesian 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 vector B = (+3.0, -8.0), what is the mm6dvo10xiqt lb ek-7vg/0kf5e*gd q7 agnitude of vector C =7/07qve5f*0 6 ig-dd gxk emvk1loqbt A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dispe-o74 gbj pib+lacement of thep-b ji eob+47g jogger?

  Two forces are acting on an object as shown in Fig. 3-1:q e7 (rkrd uaycx,)eb)* jy:q. What is the magnitude of ther) 7:)c :bykaxy,uerj * dqqe( resultant force?

  Two forces are acting on an object as shown in Fig. 3-1. What is the directic/4q6 i j)mdyyon oq4/j m6)yydicf the resultant force?

Vector A is 5.5 cm long aau 4r6to pwris+cb 3x;59( kbdg(yif5 nd points along the x axis. Vector B is 7.5 cm long and points at +30e t 5wcs xb+ar p6gfyiokri ;549( 3(dubto 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 x m+ux l3fd 9sl-nl39nu kuvpvma,4*d2 b:(ojlong 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 1 41m;*knk sofyl d7g-6m;kt0fhf (bqt0 m/s from the edge of a cliff4d6o*f-fg 7q(n ;sy0thtf1mk bm ;klk. 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 cliff?

  A girl throws a rock horizontally, with w 7pfr*-4 cif.1zayy qa velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far doiy7 .q1cff -rpyza4w*es the rock travel horizontally before striking the water?

  A ball thrown horizontally fr0ojfo qli-kthh. :8-zom a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. Wz:qhl-0o.t i8ho-fj k ith what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s / iz7;1a gg na*+woeziat an angle ofa17a zo+ ziig*wgn;e/ $20^{\circ}$ 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 ax fdjgo1q6- n5l2b0ob w4 ljc- speed of 12 m/s at an angle ofjlwq1-c5 4-2bx6d nl o0g ojbf $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60.0 m/s at an lmf esysw-/)8angle 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 at a.k2 twufkzf/e+q hf-2n angle of $30.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang7u5,h3 d do8eltb ordl2wv5k: le 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 horiz5,h5g w6vax5om va w(nontally at 23.4 m/s from the roof of a building 55.0 m tall.n 5(v ,o max56ghwav5w
(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 ovrm+y+v op2e/3 +ghp m/s at an angle ooroyhv3 /emp++ v+ gp2f $41.2^{\circ}$ 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 4.0 m/s.g rgf2fzigaz,p98 r ldc c.sy62m0+n* If you ran the same race on a day when you had a constant headwiz8arnpf22*f9y. gicc+z 0lgd,sr mg6 nd 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 m/s due North, and is in a wind of 5077 wiz0jf3 msd.0 m/s to the West. The p7zi3js w0f7dm lane's speed relative to the ground is

  A plane is flying due Sou. e(z0w* /wl*1; sntbbxuda frth ($270^{\circ}$) 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 swq -okp q+ h *q7uhnfi*7m3zz-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 movingg tj-;oy hz)-wy3q1 b tsftve41 qk.p8 200 m/s horizontally fires a projectile with speed 50.0 m/s in a forward direcp)kqzs3 o- t bt4j8 yv. ew-fghq;11yttion $30.0^{\circ}$ 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 directlx6/ v8hya6v daz 0:ooed across a river with a cul8/ay:hv6o6 dox vz0 arrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in stil5 ytjs,xa*3 rtl water wishes to travel directly across a river 1.6 km wide in which the current flows at 5.0 m/s. How long will it take to crostrasy j,*35xts the river?

  The driver of a motorboat that can30)diw w 8mp cl4 ee89w s(z.zblmt8eo move at 10 m/s in still water wishes to travel directly across a ndzt. (bmp8 3c9e88 4l0moiwwl ezs ew)arrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m w, x/f.xie*mx,bon :zride reaches the opposite bank in 6 min 40 s. She is swe.e /,r, bfxi nxmz*x:opt downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches thkif4 sh,km2,e e opposite bank in 6 min 40 s. She is swept downstream 480 ,,me ki4 kf2hsm. What is the speed of the current?

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an anglc8qsuz f 4a *.ot-vsewbp(f6: cid:b: e of ovs8f zui b*.acp4 df-6tbw( c: :eqs:$26.3^{\circ}$ (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.