Which one of the following is an example of a vector quan yg:n7wezz pz )5sf*6il(e/br tity?

  Which of the following operaba14z.ksxwc 2tions will not change a vector?

  Which of the following is an accurate statpu thnis*9t4q6 .tf*huc k87fement?

  The resultant of two vectors is the smzs:p0d,mb3i:g .eibtmo ;7nyp s:1 rmallest when the angle between them is

  Two displacement vectors have magnitudes of 5. ,nac+a+i 6d(0 ety )oblhny5k0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of thetai+ ,e(h5bn6aykdn0)col +y sum

  Two vectors, of magnitudes 20 and rvotlziq ,a(7 6(i b4q50, are added. Which one of the following is a possible answer for the magnitude avrqi6((4tozq i,bl7of the resultant?

  Three forces, each having a magnitudwqr 0b gjie4k p7+)m*iu;hwt4e of 30 N, pull on an object in directions thi0krpw m;i jtg7 qu*bh we4+4)at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoloh)j u *e8cu+v6n cw.wn vector is

  Ignoring air resistance ia-3 ma)-uilqq 0zr;e, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an b:r k/gaw+g6qg r5e v+angle of 60e above the horizontal. What is the+ar kgqerg+:/w6bv5 g horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, them )8pkc7uoj a* horizontal component of a projectile's accelerationo7k8 )mu aj*cp

  A soccer ball is kicked wb heqh7x*jkc j;(0/akfvo e/.ith a 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 dimot 3g1u(w /nr0wjng-rected anti-parallel to the velocit0m nr unw/j3(wto-gg1y vector,

  If the acceleration of an object is always direct s,cswzq/tf ( 8f2zau4gzo8*px(l9f +:r jugned perpendicular to its velocity,,xfjz 8+g9q rfa s(u(o g8nsp2t/c4lwz*u:zf

  At what angle should a water-gun bex6rapwm0k g4x9lbx q7th,6s8 aimed in order for the water to land with the g4ltgw p6r6m,qxh k79x0sba x 8reatest horizontal range?

  An Olympic athlete throws a javelin at four diff7ws8 z- )zb 6qakt)qy04jkyl/lu-qt n erent angles above the horizontal, each with the same speed: qt))qlu4j0zsbkyl qa n-k8 /6- w7 tyz$30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for2yv k uhw8w 0/-nfjotw-5x6r i the 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) wooxn/t-8w2 6f-u5vj ihy0rkw wuld be

  A ball is thrown at an original gxx+m; ) se, g *r)pou*hz,ubxspeed 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 g1*s 6r k z do+*vpgag3 s3p9q.ecczw*voal attempt reaches its maximum height, how does its speed com s3q1*3vkrc pow*ep *zg g9z dsa+v.6cpare to its initial speed?

  A stone is thrown horizontally from the top of a tower at poqt1c).v9iu the same instant a ball is dropped vertically. Which object is traveling faster when it hits tci1qu9)p ov.the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dropgy j7vsxsk/wy0p,6 8sped from the same height. Ignore air resistance. Compare the times of fall ogvy ,y pjks/0x8sws 76f the two bullets.

  A plane flying horizontally at a sp 0angiz 3s5z5seed of 50.0 m/s and at an elevation of 160 m drops a package. Two seconds later it drops a s0g5 5 s3szaiznecond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped fromlfpfoa:t 53tv)5g (l s a plane, and one second later a second package is dropped. Negle5l :pto5)vag s3ftl f(cting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horiv limvms2 l3u6 ,,/nywf(ua2qzontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the pl,valvn um23, sf2/w6yi(qumlane will

  The acceleration of gravity on the Moon is onldoc*,1y h fdy)bft6 g6y one-sixth of that on Earth. If you hit a baseball on the Moon with the same eff,fh*ydyo)6f6d btg1 c ort (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 straigh) :i7iby ru9e0qn5 dpvt, level road and pass a car traveling at 45 mi/h. Tqr bvun)pei0i795 : ydhe relative velocity of your car to the other car is

  You are trying to cross a river that flows gr7g1l, 4z8tq lf3;sjzt+ pb bdue south with a strong current. You start out in your motorboat on the east bank desiring to reach the west b31z rzgqsp l+bjtt4gf,8 l;7bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it tak 6jl8nz y8p7vr ;wf1s2ha od7fe y;h87fsp 2nl wv86jr za1f d7oyou to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an / .osetrq9(- 1hk horpix sqez/j-g9* angle of 30 degrees below the +x axis. The y component ot e q./9(rgoh-qsx19pj z/ek -rs *hiof A is

  If a ball is thrown with a velocity of 25 m/s at an angle of4qih3 gxgjy.v 0ic1n 6 $37^{\circ}$ 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 youekuc4 1s; v1q(nf -yitr9 plz)+ igo0s end up 2.0 km north and several kilometers east. How many degrees north of ountg(f; c 4sezqip-y+)lk v s1ir019east have you walked?

  A butterfly moves with a spc gp47nsk4 gic6cow 9 o2n;0cveed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion ang;n 0ig29 pk7cc 4cwv4nsco6 od the x axis must be

  A 400-m tall tower casts a f -3 lfqdws8i:nr*ky 0600-m long shadow over a level ground. At what angle is the Sun elevated above ther0-8 n*lfyd3fs wq: ki horizon?

  Two vectors A and B h)g6ut c 3hiy,gave components (0, 1) and (-1, 3), respectively. What are the components of the sum of thest y6)3,cghug ie two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3c h5pq cf; -ndph: yt*+b-+gmq), respectively. What is magnit+bc+n:hyh-dqm fq-p cgt;5p * ude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . r e5cubj6 n on88ia9k)What is the magnitude of C ro8kjua69 n)c ni5 8eb?

  A car travels 20 km West, then 20 km South. What is the magsa q:u2auw(m- nitude of its displacement- aa2u us(wm:q?

  Three vectors, expressed in Cartesian coort0 qft) a3d0h;meg2a7pl .-y)ktm9qaw2 wso qdinates, 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, expressed49wamg6:czc z aso (:l u3t.ok6mfs6h in 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) anodu5 qxb d .zs7(qn.z;d vector B = (+3.0, -8.0), what is the magnitude of vector C n d.57(qdz.bz quxos ;= A - B ?

  A runner runs halfway around a circular path of radius 1h6z4ibdo 3q kj*d5fs5 0 m. What is the displacement of the jogger?4sk ojdhq3dz6 ib f55*

  Two forces are acting onpkg7biq3/4t2u ph(/yml;fwc 6u i z; l an object as shown in Fig. 3-1. What is the magnitude of the res3;; z yqk4w cmu/bphpu7 ( fg6tl2i/ilultant force?

  Two forces are acting on an object as shown inje7t qy(33lus+mpjf 8 Fig. 3-1. What is the direction of the re3( j37fsumyje qt+8l psultant force?

Vector A is 5.5 cm lokt6d,:j )mukuwp1e cy3)(ew n* fx1jfp.i1wl ng and points along the x axis. Vector B is 7.5 cm long and p)*ww cuit mee f)1un p(l:k,jw.fy k6dj1x31 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 long and pointsh; u4zf f5feh 2dk) cgj2h2w*c 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 spq-pa 1w*t 0hnynf /j1leed of 10 m/s from the edge of a cliff. A stop watch meashn*pj 1wlq-1n yaf/ t0ures 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 a velocity of 10 m/s, m6d s)vu1cx) nfrom a bridge. It falls 2cnu))sm1 xv 6d0 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground7shdr q.1 s51ua87rb6rsl kck, strikes the ground after traveling horizonrs61rh7a 5buldk r7 cq.8ss1ktally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes intooj4k z8z7c*ip the jump with a speed of 12 m/s at an angle ofz*c4 ipokz78j $20^{\circ}$ 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 with4atdr5u*csiy bltqd0 h ,:+n/ a speed of 12 m/s at an angle of ,:tq yrib ucahns*l/0+ d5 4td$20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an r fib);*rte8 pinitial 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 initialb q-5u hw-0 3w,xabxor 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 fix1jrb )cih;p1red 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 horizontally at 23.4 m/s su* pbb 5)lu+cfrom the roof of a building 55.0 m tacu*5p+ )bl bsull.
(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 ap*wxyda0 bc;+dsa )2mn angle of xcs2p+y0*db ;)ad awm $41.2^{\circ}$ 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 o.pl q ie17mw ej/6hu3x2n.e suf 4.0 m/s. If you ran the same race on a day when you had a con . hmuweeiq6sp2lju .7xe/ 13nstant 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 m/s due North, and is in a wind of 50.0 m/s t qtnl80 9-3tddcz.oi vo the West. The plane's speed relative to the ground iic9lo8vd0t3 -t n .zqds

  A plane is flying due 1i3p q:8rt vjoSouth ($270^{\circ}$) 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 12v rq93u5p,mhh yc8ax35 o( pbj0 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 spee;e2b8hstsj93wts,*a:t fw y vd 50.0 m/s in a forward directionaehw 2sttb3 wjtsv 89 ,y;*sf: $30.0^{\circ}$ 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 -liyqfc qz8tj01p.7 oriver with a c - qqoz8.1jlfi7tcy0 purrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that 8dv(u1w9 wezes* kjm3can move at 10 m/s in still 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 taus(mzk v 9eww81de3*j ke to cross the river?

  The driver of a motorboat that can move at 10 m/s in still wa spv,)7xvoab2ter wishes to travel directly across a narrow svx2savb,)po 7 trait 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 wide rj63+a o2m c )na5sdxxjeaches the opposite bank in 6 min 40 s. She is swept downstream 480 a xn5jx32 d6 mcjoas)+m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wilh;8s;ip kvdte -52fzde reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the ; e lfks ;t8d2h5pv-izcurrent?

A boat, whose speed in still water ixyjcio3,qm1w ,a):m is 1.75 m/s, must aim upstream at an angle of,:m oxqc ),i 3mjya1iw $26.3^{\circ}$ (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.