Which one of the following twgx (m 43ye,ais an example of a vector quantity?

  Which of the followidug r ogw0y;0 ;o5dklx*o63h yng operations will not change a vector?

  Which of the followingmsb) *3dm ttb7g plm01 is an accurate statement?

  The resultant of two vectors is t4*f f opo; *n0dzerpc9he smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 mzwdz1x6x3s58vqusy/;ccw zx4 s p .:d and 7.0 m, respectively. When these two vectors are added, the maspsq; xc3vzzd4ucxw8 .s:d61 yz w5/xgnitude of the sum

  Two vectors, of magnitudes 20 and h7 z:jkxw3e(h 50, are added. Which one of the following is a possible answer forhx7jzkew(3 h : the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an obcvm *k:rtkw z(h 0c4,aject in directions that are (avk :,t0c* mzkhwr4c$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec,f j)vt4l3+vhup4 rgptor is

  Ignoring air resistance, the horizontal compj*h:jxd h:v6 qonent of a projectile's velocity

  A ball is thrown with a velocity of 2t: .)cnh)uptadqk 1/u 0 m/s at an angle of 60e above the horizontal. What is the horizontal co:au/utcn). )tph dk1qmponent of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's accen5k,mic r0kh *leration*n0hcr mk5ki ,

  A soccer ball is kicked with a velocity of 25 m/s at an angl;o0f e+k. jqsne of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration l/-9e1tbzua i65ah lnt9he d1 vector of an object is directed anti-parallel to the velocity vect9hnie-5tbal/h1u 6ez 1 ald9 tor,

  If the acceleration of an object is always directed per.x t)n9.: dkuvctnl2apendicular to its velocityxdv kt.lnt:a.)u c n92,

  At what angle should a water-gun be aimed in order flp)d n5; o(z+v mvpubfs75t:oor the water to land with the greatest horizonl)ou z7;pv(t d 5:fsom5pv+bntal range?

  An Olympic athlete throws a javelin at sei9ng6l3qn ) four different angles above the horizontal, ea)e inqgsn396l ch 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 time5xw,dh dmh x.lw7:l+ s. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal ra m: .+xd5 lwx,dhlshw7nge R (compared to your first serve) would be

  A ball is thrown at an originp0prvkdttq lv,k 583; al 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 attempt reaches itd+)t/odbbv- is maximum height, how does its speed -o+ t/bv)iddb compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same in49:eavx8eygl stant a ball is dropped vertically. Which o :gv 9ayxl8e4ebject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second buy7rvng3.9l5gd ejki 8 llet is dropped from the same height. Ignore air resista y v l57kigdj.g839nrence. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of kp)h g9 dynewn)f5 0e/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 package d5nf pe9hw)y 0/gekn)s land on the ground?

  A package of supplies is dropped f,d6( mdozj wi6rom a plane, and one second later a second package is droppio 6zw,d6dmj (ed. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constantaio*gfkf.. yx 7qu39ia5 jlr 78c2sct speed. Neglecting air resistance, when the bomb hits the groundo 2rfagqc*s ay8iu.5k39if 7.c ltj7x the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixt4k dsn 7,iv) zxrwftc)q 72cy)h 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 would la)fcv,wckntr x 7ys))42 iqz7dnd

  You are traveling at 55 mi/h in the +x axis relative to a straight, level7nm)/v, po;,f ruba co road and pass a car traveling at 45 mi/h. The relative velocity of your car to the otherc,novm pfra ,;/o)7 ub car is

  You are trying to cross a river that flows due south m3 : 3 kqs)wh9 u8*x)cvmdtnejwith a strong current. You start out in your motorboat on thntk))j*:udc 38m h swv3q 9xeme 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. How mucha/n51 wm( iqpk time will it take you to move 12 km downstream, in a river flowing at 6 (m5n 1/qpakiw.0 km/h?

  Vector A has magnitude 8.0 m at ag6 n 18 z-a1okijsemt+n angle of 30 degrees below the +x axis. The y componee 6-on gkimz1j1sa +8tnt of A is

  If a ball is thrown with a velocity of 25 m/s at an ang*wxtt0f yt8 q+le of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight l:pc:)c y 3rdmdine in a direction north of east and you end up 2.:cryd:d p )3mc0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a s*q y 2eli q9spa6(n(lcpeed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angl9nye 2* l aqcsiq((p6le between the direction of its motion and the x axis must be

  A 400-m tall tower castsc3l n2ro+3 o hmz 7,yxxx8sea, a 600-m long shadow over a level ground. At what angle zx+xl7c y,oo 3rm28xeans,3his the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), 3/ kxphuyrtqxr 82e,0 respectively. What are the components /2tpe08qxk uyrhr3 x ,of the sum of these two vectors?

  Two vectors A and B have com1 srp jm ;0at 5x+tx9 vdj,2)razx:tv/ej. hsgponents (0, 1) and (-1, 3), respectively. What is magn;2t 51gjjevsjarxx9 v 0pa )rx +sh,/.dmttz: itude of the sum of these two vectors?

  Vector A = (1, 3). Vector Btbk0lp:8 m4n ,(b. eba hfu1ol = (3, 0). Vector C = A + B . What is the magnitude t:4,ha1 onlb8k l.0pbum e(fbof C ?

  A car travels 20 km West, then 20 km South. What is the magni f31 pz,xrt241mnmfng tude of its displacemef1t 2znmgmx43p1nf r,nt?

  Three vectors, expressedo k b tcr, 14 t).asluv(/xhbr4rc+hi) 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 1a3x/ 9w4h d hjwh)rmtd)ry7d 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, -k tf*r733uxwege :bk5hjsy) .c on6d )b++hfn8.0), what is the magnitude of vector C = A - B+:3dtb )on b7)ke53gfw 6e+.h*f r cxnkuyshj ?

  A runner runs halfway around a circular path of radius 10r 3otp-;*rrme m. What is the displacement of the jrom-*t r3rp e;ogger?

  Two forces are acting on an object as shown in Fig. 3-1. What is the magnitude od n)nur7kafv*l j5- 6fm u,,rzf the refr rn-ndfjvm7 )ula56zu *,,k sultant force?

  Two forces are acting on an object as shown iimt cw27c1 v3f*g8zesn Fig. 3-1. What is the direction of the resultant fs 3c7vtg 8wmzc* 1ei2force?

Vector A is 5.5 cm long and point.*rhte : rq sd5zbnxf7g1x9 qoh(79 cws along the x axis. Vector B is 7.5 cm long and points at +30e to the negaorq7hxw c dt7(: shrb 1qfe5.x gn*z99tive 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 (lbxd(whd* f wf(s9l6y83nl ylong 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 fromvv1+hk -wny r.9z1uw p the edge of a cliff. A stop watch measures the stone's trajectory time from the top y.-v1u 1p 9wzvh+rknwof 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 1vch; ev8gb+m 8g0wq 1i0 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally beforh vic+mq808e1g ;bwgv e striking the water?

  A ball thrown horizontally from a point 1)b*yaib ,fxb 24 m above the ground, strikes the ground after traveling horizontally a dist1i *)ybx ,bfbaance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle dg2b* ( 70bnccwfu9h 4l0krk q; 3goswof ngw 0f9k*bu23rgscolc40(bkdw;h q7$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes9 3un*t8nqg4n4mo bxg into the jump with a speed of 12 m/s at an angle of 4 nmxgo3tqn8b 9gu4n* $20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60.6f:ep.t 5-4o,)dg1b gqvbe) gtf zqke 0 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an *wv+ay r, y20h /mdyot1dk-.) (na zoklr*xwzinitial 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 an angle a9zid3- an) gmof $30^{\circ}$ 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 roof of 2i)cz r0de fl/a building 55.0 m t0/ricldfe)2 z all.
(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 froc- qjfb c2je(u mh1(ksi),wu, m ground level with an initial speed of 55.6 m/s at an ah)ju1 ,2,(q mj-w(ufkcecbis ngle 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 velocitt )3j.hqfj:oy nz:e 2ry of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows3.zrqf oj:): htny2 ej 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 ya*mhpma jlnc nbd7-fm)+(54m/s to the West. The plane's spee(-lf bmm* nmna+5h c 74)pjydad relative to the ground is

  A plane is flying due South n1nn5.xw,rl jpf 5dc) ($270^{\circ}$) 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/4io x6nsmw 2x-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 horizontlb*.foe35r*dw7kb2b egbm 2 rally fires a projectile with speed 50.0 m/s in a forward directg23lfb be eb**.rk wb52od7 mrion $30.0^{\circ}$ 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 directem w*e9ijt+-eorv , (hed across a river with a current of 6 (mor-t9ej+ei ew hv,*.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 stz 9 hozd+ib4p ,3p-z87d anuheill water wishes to travel directlyez ,zd- d7h84n+9zap3opiubh across a river 1.6 km wide in which 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 water wishe84db7x (zffm(xz,zkyv 7 t vz3s to travel directly across a narrow strait in wdvb3(8( kfzfzx zzyvm774 xt, hich the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a skxcb./ vt5 )v p)gs+jriver 200 m wide reaches the opposite bank in 6 min 40 s. She is swepv/ksvt ) cbgp 5+s)jx.t downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank a7id6wm3 o6 9kn7trswrz6n3dv cj3 7kinm j7wks 7dckr3wa63nn9r63 i 7doz6 vt 6 min 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, must aim;-epzsq 3 x4j:tq9fc k upstream at an angle of cejqq -p t:934kzsxf; $26.3^{\circ}$ (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.