Which one of the fol iph9f +*xrze)lowing is an example of a vector quantity?

  Which of the following operations willu:3 77naqx.wu/1 g vlo hjwu0;ftjbf4 not change a vector?

  Which of the following is an accurate statem91z:i8 h9 jt4 rp bl;cvyz+mhient?

  The resultant of two vec gr9b ngbk3;u3u61/cr.h mihltors is the smallest when the angle between them is

  Two displacement vectors have magnitclg+bw6;wm l t /p2l9zudes of 5.0 m and 7.0 m, respectively. When these two vectotm+;/bzpw lw6 cl92glrs are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, ar :jqu.,y)ra szg jqs*,e added. Which one of the following is a possible answer for the magg: szsu.)*y,rajjqq , nitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objectl*ger :j50uhzss.m il (d4y.lc g+kd8 in directions that are :s(szer5 +j.hd y*8 4k.llmlc 0duggi$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,yuskf+ :s s7s3 the unknown vector is

  Ignoring air resistance, the horizontal component of eeij7js5*rdf.h4 vk 4 a projectile's velocity

  A ball is thrown with a velocity of 20 mc kp)y rxr7hpq9 484snp1t mh1/s at an angle of 60e above the horizontal. What is the horizontal componhrx1mcp4q ks7h498y 1p) nprtent of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal component of a projectile's accelerationpw -7d) +ejnwac kyksg( ,r+wwc g-r9a/0dj ;d0gw )+g- cy/r, ;r(jda7kc nd 9-wwdkej apws+

  A soccer ball is kicked with a velocity of mq41r+p)n r;pyua-m j25 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 objectfprxk lz e*ga9yk6h; d)2la 70 is directed anti-parallel to the velocity v ;kpxfdrhay0 7ge)6*lk29a l zector,

  If the acceleration of an object is always directed perpendicular to its velocib ci *1vfuri,5ty,1 *i,rf ibvc5u

  At what angle should a water-gun be ,a79lsnv:du oaimed in order for the water to land with the greatest horizonta,a7o dsnl9uv :l range?

  An Olympic athlete throwst wdc9qga/p ypb46a -1 a javelin at four different angles above the horizontal, each with the same 9yawpg/abcq 46p- 1dtspeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 the ball leave,uqob 7bb271z3s , gtf, oqoovs your hand with twice the velocity it had on your first throw, its horizbb731vtbooqg o7 qf ,,u2zs,o ontal range R (compared to your first serve) would be

  A ball is thrown at an original speed ofhhjw-:hw5-as5c (ak f 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 its vbl*edr -(+ren9 ezk8 maximum height, how does its speed compare b8r+z(-n eedrk 9vel* to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a bo 2ruqqn3m-v8v ed:-r all is dropped vertically. Which object is traveling faster when it hits the leveln23vqrrqvu: dm- 8eo - ground below?

  A bullet is fired horizontally, and at the same instant a secw,j fled;;zb1 ond bullet is dropped from the same height. Ignore air resbjzf;1e ,wl d;istance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 50.0 m/s(7p17i4d j* zytf8egm fj7ykc and at an elevation of 160 m drops a package. Two seconds later it drops a second package. How fmfyj(t 774pc ef87ig1zk*d y jar apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, andjape,c a .9g;g one second later a second package is dropped. Neglecting air resistance, the distance between jp.ge g;9,aacthe falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spee hej+6 ok9lfkf.z*z7e d. Neglecting air resistance, when the bomb hits theefkh9 o+6 ke jz*lzf7. ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is ourixz*0) nx4d8ghbs+sn0l +n nly one-sixth of that on Earth. If you hit a baseball on g xxr 0n*++sl8hz)04buindsn the Moon with 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 to cd( 4bpby9 zb1a straight, level road and pass a car trave4dpzb c yb(91bling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows p6umcmn(3j(2gxmdr+ .s4 ifkdue 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. Yofxjku i4(dg2m3 psnm(r6. +cmu should head your motorboat

  Your motorboat can move at 30 km/h 8/ r6mn+g olgtnq6t w9in still water. How much time will it take you 89o6ngt+wnl r tq /6mgto move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angleitxq flv*-(e + of 30 degrees below the +x axis. The y component of -lqi+fv( ex*t A is

  If a ball is thrown with iz du 7j0ylt8;ve-y9e 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 north of ea(d.xs;b5*c1kcz (hfwv au os- st and you end up 2.0 km north and several kilometers east. How many degrees north of easwf sc(ua* h.bkvz -;1s dco5x(t have you walked?

  A butterfly moves witj7bgozt p,rzu04 1:k/dc7cu ch a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its mo/:co1z77jz gucu,4crdtp b0ktion and the x axis must be

  A 400-m tall tower casts amzw rpjg04 m k)9vo95h 600-m long shadow over a level ground. At what angle is the Sunhm 4ow09pzgjm)vkr 95 elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatycpo1m l9(hf) are the comp9o(lm )h1fypconents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivelossgx*o(,9yznotn5 g7 l-)reln))jny. What is magnitude of the tlnnnoyro,o- ) )ge7nl*5)x j 9zssg(sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vectoft+hute.+anv8w,*0 s 4q6b8uk we ru dr C = A + B . What is the magnitude a8f,*q k4dvu.0eet8b hwrt6s+w+nu uof C ?

  A car travels 20 km West, then 20 km South. What mzd .)(y2z*zab,lfh e is the magnitude of its displacem)bmzz ya,h(e *2 fzld.ent?

  Three vectors, expressed in Cartesian coordinat (ayjeak6: q7m2tdom1es, 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 coordinates, akilbzmk x mv,sie743pl36 0 /rre
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, -4.0o0/e2i (kit;srzf ft 0) and vector B = (+3.0, -8.0), what is the magnitude of vect/ikf z;f e0 02ris(ottor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. gr4c4wite- ;fe8 f do7 What is the displacemenw48 ff47t;-oidgcree t of the jogger?

  Two forces are acting on an object as x jl+56hq6 j u fdf) uh13(yfaeh,lqk8shown in Fig. 3-1. What is the magnitude of tq6 ky3h)5f8qah6uj j1 heu(x l+fl d,fhe resultant force?

  Two forces are acting on an obje7bshpi7 0j4qb r/ fxk9kg7vd7ct as shown in Fig. 3-1. What is the direction of the resultsk x47jdib r 0g f/pk77q9bhv7ant force?

Vector A is 5.5 cm long and points along the zob g8,mt,/n vma -)bqx axis. Vector B is 7.5 cm long and pointsnm,b, tm b -8oag)z/qv 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 a1)t-ltcmx + nund 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 from the edge o*.;f3j vqda l*nv5rujf a cliff. A stop watch measures the stone's trajecq3*n.rvj ad; jf5*vul tory 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, from a bridgn; n7dk)bn1hsp n0x 5re. It falls 20 m nxp)7h;rs bn d 01knn5to 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 groxtllplp2v/id*d x juq5 n9r/ .8tb00mund, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it throp98bu pdjv/q/. 5 ttr02*xl dxlmn0liwn?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an anglegu f / 5nxvl98jkk wqy6bfw-3(3ry t)q j txyqf86)/k 3 w k-gyl(f5q9nv ru3wbof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-ju nbcr8z w5e5zlq8 0xd7mp goes into the jump with a speed of 12 m/s at an angle of n5cq08zd rlx8ezb w57$20^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 60.0e6fud:cm 4mgf ld8 /fp/a /-th 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 6t9u v t;zzdc.tbwh5+ /0.0 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 anzbi(2y00/o06rn2po rog0 vb r(i f mtbgle 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 roof of a building0z(s klf- f2bwb9 qivd*2nqm6 55.0 m talb*z v22 i 0qqnf- bs6l(9dmwfkl.
(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 fz hdf5 d0lw36wrom ground level with an initial speed of 55.6 m/s at an andd65zw lf3hw 0gle 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 +b y(kj/hga3p1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s,/3+ (gpjbkyha 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 5+c v4 3)gx +kfc0lufpo0.0 m/s to the West.xfc0c+vg f+ uk4op) 3l The plane's speed relative to the ground is

  A plane is flying due South+ uce7,uorhnfa6t: 5u ($270^{\circ}$) 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 l,zi3mzq, tp25h )a)r )yziuf120 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 *ml k3r +hmk(nwith speed 50.0 m/s in a fomhm( *3 rnlk+krward 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 across a riv 14tm ;,yhuh dt4fo0fiphn58ver with a current of 6.0 m/s. What;uhpm ,y504h1h vfdfnttio48 is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water hmo 40naed6g :wishes to travel directly across a river 1.6 km wide in which the current flows at 5.0 m/s. Ho eod6:n4amhg 0w long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stilugele zy+/j uw5d5+o(l water wishes to travel directly across a narrowzu /5 loe5w+yug+ ed(j 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 wide reaches the opposin dm 6tvr+hh*(te bank in 6 min 40 s. She is swept downstream 480 m.v+dr6t ( *hhnm How fast can she swim in still water?

  A swimmer heading directly across a river 209axhxt0o,wn 70 m wide reaches the opposite bank in 6 min 40 s. She is swept downstrea,woax9 h0 n7txm 480 m. What is the speed of the current?

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an anghb,. .srm nsmyh :yc++le of m.h., rcbh :++ sysymn$26.3^{\circ}$ (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.