Which one of the following is an example of a vjbo(a5s3xrh y*7ytd /6h 5nge ector quantity?

  Which of the following oper3jp fb2nkx 9-9jcenru1 mk13gations will not change a vector?

  Which of the following is an accu 2+a ylt/a w4vt0(eg, zhrbo0urate statement?

  The resultant of two vect4/b ;ahaf *xno -xuf2hors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivev.a dq/a k.p()zhlf5 nly. When these two vectors are adde5a)nadfz vkh../ p(qld, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whichvlk1yc3/x;p j one of the following is a possiblkxy1pv3 ljc ;/e answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions tb /thwoo 5ux;/hat/;5u/o h oxwbt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown q fci8)h:e6v:fs6gi:)dito dvector is

  Ignoring air resistance, the /:qyaw5-u1f)jf a67mgm dl0e rc(lffhorizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at a2* (c1sm heoiju5 60o3eebgmen angle 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 horizontal component of a prnz(dpm ud ;c7n8wok+6ojectile's accelerationcmz+kn 76opu (wn d;8d

  A soccer ball is kicked with a velocity of 25 m/s at an angle ofk6r6z-bk /conn psnoohg9 ;-f l4u5a. $45^{\circ}$ 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 directeyc.zrd m8*ac,/tm3zg d anti-parallel to the velocity * /gm3cmrt czyz.ad,8 vector,

  If the acceleration of an object is always directed perpendicular to it mmjl777 k vrl:i.gi5ps velocitymgk:5vi.p7 l7 m7 iljr,

  At what angle should a water-gun be aimed in order for e2omo1jooxs v5qrmo880b 8x + the water to land with the greatest horimro 02vome881o +x8sbx q5joo zontal range?

  An Olympic athlete throws a javelin at four different angles above th) t ,zl7yyyj/k0jeq hnlg5)t0e horizontal, each with the s)n0hz/5 lygj tq 0ek,)y ylt7jame 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 m,oc7t3xrmt 9the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first servmrt3c9, ot7m xe) would be

  A ball is thrown at an origina7y+vaus9lsw,vy/0:uikw ja9,ky r( be z1x4 fl 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 rea7at 8ysa9 +2 qrehbw+-eyvun0ches its maximum height, how does itsaweyv- u+yaq9e7n 0s h2 bt+8r speed compare to its initial speed?

  A stone is thrown horizontally from the top of a 4 qyfbbw5g ed5f e,0i+tower at the same instant a ball is dropped verticall b4ge5i 5+w q0bff,dyey. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizonr11q4ten 4s4icu krwo *6-svdtally, and at the same instant a second bullet is dropped from enrkds6 uqwt-v*ci4r141 s o 4the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 115.7 m/s and at an elevation of 21p+yay 3acah .)fmn 05z2 m drops a package. 5.7 seconds later it drops a sefnc ap0y3+y)a.mha5z cond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, an,-rziwu7r bf9 d one second later a second package is dropped. Neglecting air resistance, ,ui 7rz-bfrw 9the distance between the falling packages will

  A pilot drops a bomb fro.a 3r,f qq.y a8rzv9bhm a plane flying horizontally at a constant speed. Neglecting qy.,afa.br hz8rq v 93air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on p:c7 fidxb:f6tm.2( zbc8zkf the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at 8fbi:7f:k cd tmfzcb.p2x6(z the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in t.8zg t:qq j9eypp s9 vap;af.:he +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car :aqg v s9.a8jpfy.9:ptpe qz;is

  You are trying to cross a river that flows due south with a strong curxns14c 0fe lo2t**l ktrent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You stxf 1en *4kl*st0 2lcohould head your motorboat

  Your motorboat can move at 30 km/h in still water. How much ti v1,0 h/pby qd:8vmordme will it take you to move 12 km downstream, in a river pv1v8/r hqd o,bm0:dyflowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees p9 z7t;e3 b75aft quftbelow the +x axis. The y compontp 9buq773eztf a5 ft;ent of A is

  If a ball is thrown with a velocity of 25 m/s at an anglb-qk0y. cq:vqaidc4( nd+ n; ie 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 east and y r vifc/1/wc9bxp;svruzqcc7z2 (88gou end up 2.0 km north and several kilometers east. How manc1c/w( vscz8 g rvqrbfu8z7;xc2p/ 9iy degrees north of east have you walked?

  A butterfly moves with a speed of 12umioa ) )xqb*..0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis xbua))q .o*im must be

  A 400-m tall tower casts aw/ 0,5zpfzzp0nloy*p 600-m long shadow over a level ground. At what angle is the Sun elevated ab,pf5zz o0*lp /ny 0wpzove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respeqmd39 wv,inuwr xudx)51krzgx+ ;py-0yp 8 b0ctively. What are the components of the sum of these two vemz)r5ugwrxibkv pdx39 d,pxyn0u8; +yw0q - 1ctors?

  Two vectors A and B have components (0, 1) and (-1, 3), resp j ab4o6c/bycu6j0 lj5ectively. What is ab cyl66ju4 jb0jc/o5magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What u1x(dx+nt -xt3 v; bt;cw(tyb is the magnitude ( wt(-vtycb;1ux3x+dx; nt b tof C ?

  A car travels 20 km West, then 20 km South. What is the)/3gn ;uofymc/(sv x9qek sz8 magnitude of its displac(x9sn )c;vgo sufk/ mq8yz3/e ement?

  Three vectors, expressed in Cartesian coor v-/s lazib/2b.y tmp*dinates, 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 coordinates4 ,v jtb qa(.m r+ ykp8zpcp9*h1uyd3z, 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, -8.0), what is the magnitu,l5ryvs e0.m lde of vesle.l rymv50, ctor C = A - B ?

  A runner runs halfway around a circular path of radiuqj awv6wzbma(6:x3 a9s 10 m. What is the displacement of the joggerwj6a9qxv 6: ( awamzb3?

  Two forces are acting on an object as shown in Fig. below. What is the magni7tzvtzj 3r**)z,ev; ty w n5dftude of the resultant force?*jwtnvvze dt)t;5*f3 7 y rz,z

  Two forces are acting on an obj t+bpc;le+yx8 ect as shown in Fig. below. What is the direction of the resucb+t epy8; +lxltant force?

  Vector A is 5.5 cm long and points along the positive x axis. Vector B is 9.2wq/sr: t4 lm2h cm long and points 4t m2: hqrslw/at $+56^{\circ}$ 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 51 cm longo-b,2 u4xy q zzx93ixq and points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 33 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 horizontally5 tz5m1 fifx m2qld5v0 with an initial speed of 30 m/s from the edge of a cliff. A stop wati 0x 5df2mm515qftv zlch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.7 s. What is the height of the cliff?

  A girl throws a rock horizon*myte q1xq(h j ,r8*fztally, with a velocity of 7 m/s, from a bridge. It falls 27 m to the water below. How far does the rock travel horizontally before striking theqrym*1 8 hf*qx ,(jtze water?

  A ball thrown horizontally from a 5to1 ka5r u8ldpoint 29 m above the ground, strikes the ground after traveling horizontally a talo55ru k1d8 distance of 15 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 angl8lb yjhjz)y/0 e 80h)jjb /zly yof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes1p9;k9atxo p nnk2p e*s o,cu7wh*w6h into the jump with a speed of 10 m/s at an angle op9khe2 pw* uxn at,sno*opk;69cw71hf $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 37.3 m/s at an an8s 2x3yown3o rsmai4 ,d -;aewgle of $26.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity ofz11z pjz5bik2 fj)uf. 37.2 m/s at an angle of $18.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an :n *vfztzz8 65sxu6 r8 6phtkdangle 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 2wg2 qkwgy6f ;tx m,e4:1wt9ok7.6 $m/s$ from the roof of a building 34.0 $m$ 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 level with an initial speed of 65.7 m/s at an cloqf:/w cl, ew-id:2angl2dwco/:elc f , -lq:iwe of $38.3^{\circ}$ 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-- pjbu,6w cly+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, the time it would take you to,lwcj p+u- yb6 finish would be

  A plane has an air speed of 200 m/s due North, and is in a 6x,ko: mv qfk8wind of 50.0 m/s to the West. The plane's speed relative to t6v:x8kqfk o m,he ground is

  A plane is flying due Sou/ av upv9*8cgxth ($270^{\circ}$) 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 lo0k)yp0o ;(f;gllvz $30.0^{\circ}$ 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 50n/p/x)q)e 4wkh/ lti qx0tt 0i.0 m/s in a forward direc /th )npkt/e0ix/twq)lqi40xtion $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stillht w )/z37y(irbzx;bz( wxfh- water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boatyb(;zh/ 73)ri f-wtxw(zzxh b as it crosses the river?

  The driver of a motorb7f)p tq,c3ssboat that can move at 11 m/s in still water wishes to travel directly across a river 1.3 km wide in which the current flows at 4.2 m/s. How long will it take to cross the rive)3q7t cfps ,bsr?

  The driver of a motorboat that can movej v-oiew8ucvp e4)( ina:g 31p at 10 m/s in 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 the driver :) 4ijp g -8 p1vea(ieonucv3whead the boat?

  A swimmer heading dire ss/7yll5pr33zvn-b -;vn0/dm mozhfctly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreamzhm -l730 bmn s5dl p;/r3ns yz-vvfo/ 480 m. How fast can she swim in still water?

  A swimmer heading directly acro2tab +e-ytlkj;of:a. ss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the cualo yj+t:tbf- ;ke2a. rrent?

  A boat, whose speed in / tx3 l,(x(uxmever p+still water is 0.99 m/s, must aim upstream at an angle of x pe(l tre3+x(vx,u/ m$30.9^{\circ}$ (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)  $m/s$