Which one of the following is an exaix9 qvtn5poaa-)8 /j cmple of a vector quantity?

  Which of the following operations wilkfr;7. shds9 zo z;y(dl not change a vector?

  Which of the following is an accurate stateme/k/ 3pr wx6owzwr5:d znt?

  The resultant of two vectk8u)os.n m,qn 18*qfp zyjjs+ ors is the smallest when the angle between them is

  Two displacement vectors hav e-)qui/k5x5iyqb i2oe magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude ofyiu5/ok b)iqe -2q 5xi the sum

  Two vectors, of magnitudes)wyj3qv igh10 v a65kv +j3wer 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultant?jk1 5vv0 q3jhgar wvw)6+3eyi

  Three forces, each having a magnitude of 30 N, pull on an object i d7l-huq2eok( lj(lqfi4+o k4n directions that a l+k-h(j4llo4q 7uok(d f2q iere $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vm*20xx nx:* ur zishi6ector is

  Ignoring air resistance, t hngx3w0p*1baj60ygt he horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an a8,pxu ifz0*s 9tkpv *x74orhongle of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horifg pc2t1h:5 * vvsvcz)zontal component of a projectile's accelerationvh5c1v*)2 :s ptgcfzv

  A soccer ball is kicked with a velocity of 25 m/s at au4myhvdg z.f2sy1/,xw06 nt bn 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-parallel to the v::iorjxm 3l2zolo 9h4 elocity vectlhoo:r9i3lmo2 4 :x zjor,

  If the acceleration of an object is always directed perpendicular to its velocitopofb6-okad )4 jnn2.y 2bpnja )oodn4k-.f 6o,

  At what angle should a water-gun be aimed in order forb cht7ffc*5or6zod e 4u/a8 3/do e0fy the water to land with thfo */h f748ao6cfe03ru 5bcy/ zddeote greatest horizontal range?

  An Olympic athlete throws a javelin at fonpr,69*wes)7b m+j od7fi whour different angles above the horizontalo6 , +w 7d)bp*sh7 inmfrej9ow, each 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 time. If the ball fidxh(/ftu*h fc22:aegx ph z35n r/) leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared2 /pe3hx*t(aux) hnh52gf:z / cffird to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at aj r36yo 9-be e-,lpn2 *qocylwn 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 maximum height, how does it e( nb6.4y .p1;oj7c(rwqlp-9xjhts mxyob4eshbe 6y( c7bmolq;-p1x 4te j.9 np 4y.(wxsroj speed compare to its initial speed?

  A stone is thrown horizontally from the top of a tojc* qlj(g,w53y-a jb6ckai 1bwer at the same instant a ball is dropped vertj5cli aya g (k,qj163jbw -b*cically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizomcbje,n*) t8.tca 5u xntally, and at the same instant a second bullet is dropped from the sam) m.5t*jcxteun bc,8 ae height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a s;t7u1w ddimr 6ioz 6.bpeed of 63.5 m/s and at an elevation of 253 m drops a package. 4.5 seconmidz6i1u d6w.r t;7b ods later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a seconow 4qyr2u 0t,xd package is dropped. Neglecting air resis24u,0qxy rwo ttance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a conkfa ul9y(3q0oi jrld.fm3 cs;6s:0dk stant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wil;s0mdal0i 3dq9fjf:y r6l.(k3 sku ocl

  The acceleration of gravity on the dqr) 5ft/ry+bl/td8b Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and ay/ 8 r+/lqddtbbft)5rt 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 aoblh k04jvek 2dui0 5z8qy1gxxe -(k, straight, level road and pass a car traveling at 45 mi/h. The relati0g e0qy ( dxkkz- 1bo254v,xujl8hke ive velocity of your car to the other car is

  You are trying to cross a river that flows e1, eaohg) ,)iqhvs5or q)pp-j+ 4yyj due 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. You should head your moth-jrgaeh41 y,,)+e 5yp)vspq i) jq ooorboat

  Your motorboat can move at 30 km/h in still water. Ho y5srf:u 8v8qtw much time will it take you to move 12 km downstream, i s5yu:8fvtq 8rn a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +;h*-bb+werl ro :7)*gkzphq fx axis. The y component of Arp;gkh)7 :rfl*-z+o e b *bwqh is

  If a ball is thrown with a velocity of 25 m/s at an angle tx7 puzjkf5 86q400j)wqox qaop o9 3rv9x7pdof $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in lqemboo a268( esci13+s :qdla direction north of east and you end up sa1oq38el: i+e do6lqs c2m (b2.0 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x 5 b:a2 kz)8(qhiu bnpjcomponent of its velocity is 8.00 m/s. The angle between the di bkph5a)n8:b2 jz q(iurection of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. 8 bodt1ad 2m*rAt what angle is the Sun elevatao m1 b*8r2tdded above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivmqf 7w r2wr6+kely. What are kr 762wwfqmr+ the components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivel0 la+hivcboij/ t/xjy 8 916w0jsh qj4y. What is magnitu j0 /ha ywvci0lixj+9sh8 q/ job4t1j6de of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C -1fqv65(sbx nympx.j= A + B . What is the magnitude of C pfb(xnm.qsj-v y165x ?

  A car travels 20 km West, then 20 km South.32lvvv az /kso6 u(*qlhnn( +q What is the magnitude of its displac(3lu /svlvn +*hoz2q (qvank 6ement?

  Three vectors, expret.a93q0ek fwq8ara havv5pv6n2( 6p dssed 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, expres a .zd-a5 vi8oylrv(/xsed 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) and vectorip /) sz- j6kahz75w1kn1u xsh B = (+3.0, -8.0), what is the magnitude of ve-/ k)uaz67z1p1hx 5 h nkwsjsictor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the w5iy (9dn5g;o5.dz c iktvhx)1 jm6z hdisplacement of the v .6 m5;j()cny9hxdt5z1w gkihoz 5 dijogger?

  Two forces are acting on an object as 8q7o4qnhk/ r .jfw: giqa8ej9nw;w3 qshown in Fig. below. What is the magnitude of the rew7nje34qo ha8 qq.rn:gf w9k ;8iqjw/sultant force?

  Two forces are acting on an object as shown in Figbj)tjnk byf4r)4eb,*/drx . y zoyq3). below. What is the directioy).terfo )b4/) jy 4 ndq,3x jz*yrbkbn of the resultant force?

  Vector A is 5.2 cm long and points along the positive x axfwd 0dqq3:mj e8.-pyxis. Vector B is 9.4 cm long and poin0 p .dd8fwm:qjxqy3e -ts at $+38^{\circ}$ to the negative x axis.
(a) Determine the x component of Vector A $A_x =$ (数值)  $cm$ and y component of Vector A $A_y =$ (数值)  $cm$
(b) Determine the x component of Vector B $B_x =$ (数值)  $cm$ and y component of Vector B $B_y =$ (数值)  $cm$
(c) Determine the sum of these two vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(d) Determine the sum of these two vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the posive x axis rotated in the counterclock wise direction) $\tan \theta = $  (数值) 
Please only fill in numerical values in the above blanks!

  Vector A is 89 cm long and points at,gzpwy ngj v70zb8b kh9t: le19p33ir $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 31 cm long and points at $45^{\circ}$ below the negative x axis.
(a) Determine the x and y components of Vector A: $A_x=$  (数值)  $cm$ and $A_y=$  (数值)  $cm$
(b) Determine the x and y components of Vector B: $B_x=$  (数值)  $cm$ and $B_y=$  (数值)  $cm$
(c) Determine the x and y components of Vector C: $C_x=$  (数值)  $cm$ and $C_y=$  (数值)  $cm$
(d) Determine the sum of these three vectors in terms of components. $R_x=$  (数值)  $cm$ and $R_y=$  (数值)  $cm$
(e) Determine the sum of these three vectors in terms of magnitude  (数值)  $cm$ and the tangent value of the direction angle (measured from the positive x-axis rotated in the counterclock wise direction) $\tan \theta=$  (数值) 
(Please only fill in numerical value in the above blanks!)

  A stone is thrown horizontally wazo8bq t1v 2x7)z6 n d3o,onbnith an initial speed of 28 m/s from the edge of a cliff. A stopaon7xn q3z bn,v)b1to2z 6o 8d watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity( pmb/ve y:/: sc2mgez of 7 m/s, from a bridge. It falls 2/zmc mgbep:: ey2s(/v7 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontalhrizohz b svis8-.ow:pwtzo 5t:63)5ly from a point 27 m above the ground, strikes the ground after traveling horizontally a distance of 12 m. W5t5.6sbw3: zsp ztvo)r-zoo i8iw hh :ith what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spawkv+er /v(r 2eed of 12 m/s at an angle ofvv2/ke(+ a rrw $20^{\circ}$ 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 a speed of 9 m/s at an angf 3z 18 ps6yqlu 9mc5mzi7jwf3le of pq51 zjiym78csfz wu 33f 96ml$18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched wvmd7gib(9.5ht-u)x8vwh. q ck,/wgn vyu /tuith an initial velocity of 51.0 m/s at an angle of $23.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched win3tv e/rm3d9fth an initial velocity of 42.0 m/s at an angle of $43.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired mkrr4 aecw6 9: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 20.wbm+e vvv 0*(eca9sh 98 $m/s$ from the roof of a building 44.0 $m$ tall.
(a) Determine the time necessary for the projectile to reach the ground below.  (数值)  $s$
(b) Determine the distance from the base of the building that the projectile lands.  (数值)  $m$
(c) Determine the horizontal component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$
(d) Determine the vertical component of the velocity just before the projectile reaches the ground.  (数值)  $m/s$

  A projectile is fired from ground levelsiclwu)rb+5u0 oody) ) z p0r7 with an initial speed of 53.7 m/s at an ay0r5ozps0lr +c diu )ob)7uw)ngle of $46.9^{\circ}$ above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.  (数值)  $s$
(b) Determine the maximum height reached by the projectile.  (数值)  $m$
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height. horizontal:  (数值)  $m/s$ vertical:  (数值)  $m/s$
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height. horizontal:  (数值)  $m/s^2$ vertical:  (数值)  $m/s^2$

  On a calm day (no wind), you caha fo:+zvp kv3)z 1+zgd w;1lts8qm w+n run a 1500-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, thezhlv:z g 1f3q1k ma +)sptwo8; z+d+vw 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/sa 9e 9jdl/l 9lx4.ohre to the Wesrxloela9eld/ j .9 h94t. The plane's speed relative to the ground is

  A plane is flying due Southvrl oz;0 2y2bufg0azb5nn5t , ($270^{\circ}$) 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 headed bo2+jc,q y1ns epl- 8s$30.0^{\circ}$ 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 movi/ bq+rs jm;6efwkac(y 43v ms;ng 200 m/s horizontally fires a projectile with speed 50.0 m/s in a fos br4m(vsfcyk; 6wqa+;j/m 3erward 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/slnij,h u(d( c.z7chr (, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crossesur(nh(j(7 .z c,li dhc the river?

  The driver of a motorboat that can move at 17 m/s inv 8;n -n9f-jbuaxx s:p k/y1hm:2wda y still water wishes to travel directly across a ri;xk/x-:j2pd my1hsf ayvu9n abnw : -8ver 1.2 km wide in which the current flows at 5.8 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s inzys1lr9 a ;jb is3etq9 d*wl54 still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should t iba9 ;qr5 jysz t31l94lwesd*he driver head the boat?

  A swimmer heading diro*v.2+ 6 nawb fwzhaz;ectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreh6+2vwo zb*.n z f;waaam 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches tkwv 9ur 3.ft4n2v))vjtf .aqehe opposite bank in 6 n)v .q)4w39uaff t2vtjvk. remin 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still wac *:v(y bphkr1dz/ z/qter is 1.86 m/s, must aim upstream at an angle of (p qv1d*y bhrck /:z/z$20.8^{\circ}$ (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.  (数值)  $m/s$
(b) Determine the resultant speed of the boat with respect to the shore  (数值)  $m/s$