Which one of the following is an example of a vector quantit: ;83sywdqklvripzy 5;(s3 zqy?

  Which of the following operations plipcukc9 y6+ v8wy73will not change a vector?

  Which of the following is an accurate stsij9 /p qqvl37atement?

  The resultant of two vectors is thg1. ;gsia;fx de smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, re7;vu3-n ov6c;pm ug(a wv+nt yspectively. When 6vvu;+n;pu 3g-( vtcy7anmo w these two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the foz;qxq( ,8zpnjf82zb 0 dnhnq5llowing is a possible answer for the magnitude of the resuljzxq fnb52 npdq08(znz ;hq8, tant?

  Three forces, each having a magnitudyra9pv 69)oqge of 30 N, pull on an object in directions thao 9v y9agrpq6)t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown l)5 ;gn.zw 9y5zp/qbovtj d)2bpn7xkvector is

  Ignoring air resistance, the horioiay7 p m,6xrxf, 3i;xzontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of t-kwl;i e0mcsbe41i0 pv 5y.d $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, the horizontal componelmyg3.x -)s ri6zt i9v8/u2jg vr hlj6nt of a projectile's accelerationj g/2h6 ry- jiv9r8sluz.l x m6)i3tgv

  A soccer ball is kickeo*d55k tb+amvmls )j 3d with 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 directed anti-paralle,yhja sd.asu /m n 56t9xmuw93tr1ka.l to the velocity vecto3ak9 us a s th5n.d9ra/yx.m6mtw,ju1r,

  If the acceleration of an object lz7n hq0nibp3 dn *07ris always directed perpendicular to its velocity,zlq *3n dn770brn pi0h

  At what angle should a water-gun be aimed in order for the wat7bo 8w-vudq/6z, xj qper to land with the greatest horizontal rangb o7j-qdpz q86vw u,/xe?

  An Olympic athlete throws a javelin at four different angles above the he 1l tls s:o5 1:ti5rv,hppuf9orizontal, each with the same spfsvo:h:1u 9sl5il , 1teprt 5peed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time-a p)0h*q fkh0kkly3a. If the ball leaves your hand with twice the velocik 0qfalh-0kp * hyka)3ty it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed hhs;t 0 -bl67 zm+vwpmof 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 att3bj (((s ogsbjrrs1i 2empt reaches its maximum height, how does its speed compare to its initial spes(r ( bsbojj2(r3gi1s ed?

  A stone is thrown horizontall f /0yk,m 6:idondmfbx8xp.+pxi ,e4by from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground belobf 0kpy io4pi/:xm +8fe b,x.m6nxdd,w?

  A bullet is fired horizontally, and at the same instant a second bullet is drope +x hol*0iyqc j91av-ped from the same height. Ignore air resistance. Compare the jva19x y0+i-q* e hlcotimes of fall of the two bullets.

  A plane flying horizontally at a speed of 110.8 m/s and at an e1m,ug f8)yk xqy325e.4lkseki* 3 .dsh work olevation of 281 m drops a package. 4.7 secondd1 kyo2 5.lugwmsk3x,. *ye)eo3kr sk4qfh i8 s later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped ;x4se: q3 j i(csht2opfrom a plane, and one second later a second package is dropped. Neglectips43shqe oc :( xtj2;ing air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flyixz:v1 gzs /xw4**fhwhng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the pl**/szwxf wxh4 z hv1g:ane will

  The acceleration of gravity on ther 6i98 ylvohuu ln5w j ehb;+ub)s915d Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same 5 )b9l8vb hjuisdyw 1n9+lehr5u6;ou 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 r-s-s l ra9*pfuelative to a straight, level road a -s9- pu*alsrfnd pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a riqlvt: 2f4m;qw ver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly weq lwv;4m:t2q fst from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time :j7mo b5hawuw0q s0n ,/tu,qbwill it take you to move 12 km /,ntq7ua0,w0wu 5jhbsq ob: mdownstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thk: n,fqby9 6eue +x axis. The ynyqb f9,ke :6u component of A is

  If a ball is thrown with a velocity of 25 m*hg cdzc4f8.gwf,jjl:(m o 9j 1p lna8/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 eas7d)f4*ew 3c yxr eg2 t-tnqpj2t and you end up 2.0 km north and severaltd3x7q ft 2pe e)nc2-wyrg*j4 kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The c5yymzn,dfuj6i9 h5 ,x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must b ,f956jnuh y5zdy cmi,e

  A 400-m tall tower casts a 600-m long shadow over a level boy8rdu bb -ib3pg . ug(* 7yy2g0;yczground. At what angle iscd-y zbg;boruyp bug( 7*i gbyy08.2 3 the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectr1pl -n/z *tdcw o,psq -f;9xyqfcmwz:/ l:j (ively. What are the z/ls-j,:*pztfp-om(ld / n q:1ccy9x;w rwfqcomponents of the sum of these two vectors?

  Two vectors A and B have components (3* jkalv):b ag0, 1) and (-1, 3), respectively. What is magnitude of the sum of thes3j*)ak alb:gv e two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C w4 xc )4vgcw 2+zobk-dkj:4 zp= A + B . What is the magnitude of Ck cz:44- z+)v4dck2pxwb jowg ?

  A car travels 20 km West, then 20 km Sout/347 oo;.r ajaoc2tq m/splfeh. What is the magnitude of its displacem 2fo;3/rjpo 7/l4 aoe.tqsmc aent?

  Three vectors, expressed in Cartesian coordinates, xpx2zuj -o)/ .f1itqmare
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 Cartocg47nr/wwyp7o 8tg -esian 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) mwi1n)jw8k3 sehop; :and vector B = (+3.0, -8.0), what is the magnitude of vector 8ow hnk isjp)m3 e:w;1C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What isis0to0hl.5mrhyvkk*) w2ni/8d 1iq tsgl+ v+ the displacement ki2rvl8sd /slwtgq o*m0nihv5y t). + 1k0h+iof the jogger?

  Two forces are acting on an objec oh e2b*:tqp6vt as shown in Fig. below. What is the magnitude of thepvq2e* thb6 :o resultant force?

  Two forces are acting on an k2;r 9zgytnl( object as shown in Fig. below. What is the direction of tyg;k n(2r t9zlhe resultant force?

  Vector A is 4.5 cm long and points along the positive x axis. Vector B is 7.5 tr5vx3w ll, s*eyo1p( cm,x3rloltvp eys*( 5w 1 long and points at $+34^{\circ}$ 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 85 cm long and h76kno:cm.c q w6p6ejpoints at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 49 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 with an v1qs)bbsp. fjt,.no 2c,da z+initial speed of 15 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.7 s. What is th)af .vp 2,qdo+bsn,bc zt1j.se height of the cliff?

  A girl throws a rock horizontally, with a velocity of 14 m/s,(8 qpce 18mqcdwr9t2w from a bridge. It falls 10 m to the water below. How far does the rock travelq 9wt8c(mr2qd1 w8 cpe horizontally before striking the water?

  A ball thrown horizontally qs8: ze)48i p0cdjx zvfrom a point 27 m above the ground, strikes the ground aftezvq edz:8ps ic4x 80)jr traveling horizontally a distance of 20 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 an fza, .trtdh bu4rd987gle oh7 u bdr,98 r4attzdf.f $20^{\circ}$ 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 1d b(k3*hzn1q(6 nknnqrv:f n44 m/s at an angle o 6rf4h ndzkn(q3(k*v 1qnn:bnf $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloci6j n9bezp2 em/ty of 38.1 m/s at an angle of $14.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 25.8 m/s at an angle of xzu8mtnk+f 9a7oq)r3azk .*q $11.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at ,rbcw9i c3:ruan 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 horii zik l2;82:;yby +acfsvc3xie,6j cjzontally at 23.3 $m/s$ from the roof of a building 30.2 $m$ 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 level with an initial speed of 41.3 m/s au n -o,l hs7tt2rpc;bo ng9i+kii7x01 t an angle o og;0ix+ 71il9-sh27unrni pbttc,ok f $41.0^{\circ}$ 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 can run a 1500-m race a2 /rl1 g.nmldat a velocity of 4.0 m/s. If you / lmgr2al n.d1ran the same race on a day when you had a constant 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 -u p3fnj,6hgts n c1y73cre /p200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed rs/p ,1gh3rtfej 63 p-yunncc7elative to the ground is

  A plane is flying due So0 shez.2eu c+buth ($270^{\circ}$) 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;)nzc;u/i+:lih a7u+qqhm ii 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 moving 200 m/s horizontally fires a projectile with speed 50.0 d nu9 0z5kh.x;xbrb)jm/s in a forward directio05rjbu dk;. xbn)9xh zn $30.0^{\circ}$ 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 riveeb aa/r v8j9h)r with a current of 6.0 m/s. hav e/jra8b )9What is the speed of the boat as it crosses the river?

  The driver of a motorboatbuugdpo dxm 170e i/ e-r(k4)u that can move at 12 m/s in still water wishes to travel directly across a river 0.9 km wide in which the current flows -d )xuopr0 eebuk4 /7u(gd1im at 7.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that ca m rz32a)cpcbi4 bz./qg ( epe9n6bd*bn move at 10 m/s in still water wishes to travel directly across a narra.mb pz/qi2 g3*c(cb4 b)9rn 6dbpeezow 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 ah6 ,3t/hua 5mhxl6omriver 200 m wide reaches the opposite bank in 6 min 4l6ah 5hu,tommh/ x3a60 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 zpf 49qkhbq, 24a,akogv 6td*m wide reaches the opposite bank in 6 min 40 s. She is sbfo,hv49d ,4 q*kq2t zk6pgaawept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.37 k8b8t(fqu gj 0 3,kvzmm/s, must aim upstream at an angle of f80 t mqkub(g3z,8 kvj$29.9^{\circ}$ (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)  $m/s$