Which one of the following is an example of a vecme 4gl.g v))s vi9gp0n-wy2eftor quantity?

  Which of the following operations will n eigq1g:wt (f/;n5dhmot change a vector?

  Which of the following is an axd1t,g)81cs i:r qzdjsu g9 hy *5jbb2ccurate statement?

  The resultant of two vectors is the smallest when the an/ nn6rgow3 :-vkb ou:wgle between them is

  Two displacement vectors have magnitudes of 5.0 m anhlgzsd.q+wck-:i p3*an)az s*b u w5* d 7.0 m, respectively. When these*+uwkn a5g.qd: s*z)z3*l sb-wiapch two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following is(if6gi;pm j.v a possible answer for the magnitude of the.f gi6ijp(m;v resultant?

  Three forces, each having a magnitude of 30 N, pull on an object inyyj, lsnz.0.x ud 00.byu4 qiu directions that .0ju00l b yui,zxq .y.snydu4 are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tv a u2nk8na1nmj5 i:2k88yyex he unknown vector is

  Ignoring air resistance, the horizontal clehks2:l- ep 7omponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s atzn/mvqdtnumo5g t ho9yw3 bwur+:4 .w/v, q2+ an 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 horizontalfq v;b .ee;ob9+cd bmwc *.dy2 component of a projectile's acceleration;+.v*9cbe.d;qy c mo w fe2bdb

  A soccer ball is kicked with a velocity of 25 m/ss*zwc;g1c ooq 22*wno 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-parallel to the *t xw8 2kvj9 4r+sxswovelocitw8jxvs*2x+wo9s4 r kty vector,

  If the acceleration of an obk, bxp)9vk),d rwsy 0kject is always directed perpendicular to its velocity,krsy) kxw ,0 )9dkvpb,

  At what angle should a water-gun bz;uatju t(i/+0w pa x3e aimed in order for the water to land with the greatest horizot(a0 zx+ujpa/u3; witntal range?

  An Olympic athlete throwr.r (aw1ssh*e s a javelin at four different angles above the horizontal, rh *s1w(.raes 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 thez6.g(w),qc9 x gdpgv re2bh .lj4:qbq ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would qd. xc q 6rbv4()qwg:g e.zp9hgl bj,2be

  A ball is thrown at a m96y5oi-raenk /j7x fn original 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 8 ;bs1ewl b a2u pnv+8y2 .-aa-xudbfuattempt reaches its maximum height, how does its speed compare to its initial spu2 a8 -uw lu +-d;nfyabb812abv.xspe eed?

  A stone is thrown horizontally from the top of a tower at the sh89bn,rz:rgzy * m7lzr*w za/ame instant a ball is dropped vertically. Which object is traveling faster when it hits the level grozm/7,ry a:lzr nz*wr 9g8 zb*hund below?

  A bullet is fired horizontally, and at the same instant a second bullet is drhoy,t8 e-zk0f /zhx u;opped from the same height. Ignore air resistance. Comzhyo/ -t0x;z he,u8fk pare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 89.2 m/s and at an el n fzsq:nc4l,55p kpd+evation of 151 m drops a package. 2.8 seconds later it drops a second package. How far aparcn5ps qldp:z5kf, +4nt will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a kth y;app +5;f),f )g;h ispsesecond package is dropped. Neglecting air resist;it;pf)5yp ghph)ss,k+;ea f ance, the distance between the falling packages will

  A pilot drops a bomb from a plane fl:u zppn1z vch158n1qhying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground thz 1hu5:cz 1hnpqv81npe horizontal location of the plane will

  The acceleration of gravity on t000wvguaebw / 8mntn.mz d,r b7 qg8c)he Moon is only one-sixth of that on Earth. If you hit a baseball on thenz bqvwm/et00b8g8a c. r,m d gn7uw)0 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 axisw3.w tjfvoqy3gu 81 z* relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to thef83*vog z wu3wy 1.jtq other car is

  You are trying to cross a river that flows due south with a stro)6a x r4x4i)px(yet x,bqk:bp/wz3tfng 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 xb3bxwx)at yp/tf4:(,k eqrz 4pi6) x head your motorboat

  Your motorboat can move at 30 km/h in still1 mcbh bdt)3s4 water. How much time will it take you to move 12 km downstrea4t3cd)b1m shbm, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 deg9lw 2q *wpiz3y hii/,drees below the +x axis. The y component of A isdyi 2w* /zqp ,i3wi9hl

  If a ball is thrown with a vel9jb2 ;tvyzto,r2 s5 qgts5oh3gkn31hz9 y-s aocity 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 l ve)zrdferp0,6f . 4fm8 8ptnw1ym653uiidrtine in a direction north of east and you end up 2.0 km north and severart6pmuinzv4 tdf5)f dp3816 .r8m,ife r y 0wel kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velo1 c eg 7hvr3b:pswlcc3v z1+7ocity is 8.00 m/s. The angle between the direction of its motiov3 1bsl7rze1ocv:7c3 hgw cp+n and the x axis must be

  A 400-m tall tower casts a 600-m long s8a kp+)8mukab hadow over a level ground. At what angle is the Sun elekb) kp+8uaa8mvated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. i :pfob.m*k(vf.,y1khsl(m a :ffo z/What are the components of the sum b(1 af, .o/klfo szpv:kfy*mi( fmh:. of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respecti kaemfbm p ( un80w52uj,)rrqf0oz3) svely. What is magnitude of the sum of z,o qmjuf )s85ekrb m0f w (a0r32)nupthese two vectors?

  Vector A = (1, 3). Vecths.sny fy1za73,u8:nl c* pbyor B = (3, 0). Vector C = A + B . What is the magnitude of C 1z,n3l.7phnys s*y yfu :8c ba?

  A car travels 20 km West, then 20 km South. What is the mag19bztd (mtdv(:rhr k/+d8gi k-ka2k fnitude of its displacemkg-k8: 2t( r1(/df+k tazmd9kvib rhdent?

  Three vectors, expressed in Cartesian coordinate4ss r2m y((.ii cqgbc7n2.vwf s, 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 coordinaux0e(li dq;uti)v 7 n)tes, 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, 09qa: n dh,xwmoc/f+j-8.0), what is the magnitude of vecto+x: jof, n0whmc dq/a9r C = A - B ?

  A runner runs halfway around a circular path of radius gq; qoz)*4wcvw5t9je 10 m. What is the displacement of thze)o c45tjwq*;g 9vwqe jogger?

  Two forces are acting on an object aps v.rf,r1uk9 s shown in Fig. below. What is the magnitude of the resu psrku9f v.r1,ltant force?

  Two forces are acting onihs/f87jp6rn 4*u5p9 tgp q lu 5unxy) an object as shown in Fig. below. What is the direction of the resulhljf 9g ui57 5rp8 u t6/ppx)*nsy4nuqtant force?

  Vector A is 4.5 cm long and points along the positive x axis. Vecq( 2/4n77c rutzozlmh tor B is 5.3 cm long and p 2(ortcu7lz hqnm/z 74oints at $+53^{\circ}$ 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 75 cm long and points at koc g r.g04e)ln3o-7zvp;b/u jyes1k$30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 45 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 alz7 lhgnj +ao*3, fnn -- dmyl45oczy+n initial speed of 27 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 4.4 s. What is the hozh n a*gmzc-l f+d yn+7ljn,l-oy543eight of the cliff?

  A girl throws a rock horizontally, withj9a obywvbt1jhrk 7ew8 2hf18d)hy- rt.l 3g* a velocity of 15 m/s, from a bridge. It falls 15 m to the1y. f-w8r j9t73l1)e* h w8 j2dhbhytkv aorbg water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the k xu9u 9n 18h)-wjzqyiground, strikes the ground after traveling horizontally a distance of 15 m. With what yui-9 1knwh9 xqjzu8)speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at a9 er5zyltj bz8z(6 8mtn angle of tb(zz 5e8y6r zm8l9tj$20^{\circ}$ 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 spem (v 8q(my4fj+8 acuf6 ki.ljled of 10 m/s at an angle ofu f8aq46(j mljvl i+8m( f.cky $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity s8(q gww9h ma0of 44.0 m/s at an angle of $34.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initiawz tksj;3 t0j cuyag v;+vf//-l velocity of 27.7 m/s at an angle of $32.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired acu39j jxd1 bb9t 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 shotrkp4b 4xwt3;r vnfs/q05 pqw5 horizontally at 24.4 $m/s$ from the roof of a building 31.9 $m$ 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 67.4 m/s atd; xrgbo3;b3 /or4d az an angle of gzo;;broda 3 / bdx43r$46.3^{\circ}$ 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-m race at5wh, rd6c )pgu a velocity of 4.0 m/s. If you ran the same race on a day when you had a constu h)6w dg,5cprant 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 s ark ke+e7v e3ze(*yaa3sw5v2peed of 200 m/s due North, and is in a wind of 50.0 m/s to thew5 ka2*+v 7v ysr3 ezk(ee3aae West. The plane's speed relative to the ground is

  A plane is flying due South pbv.1za7y167ze0xanfky 7* uwh 2gkd($270^{\circ}$) 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 i-a ox6/hb 2l9gkph-exk+ fnv :s 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 5l 08ad.x c)wy.hqrl8r0.0 m/s in a forward dire.qd0lh.cr wxly8a8 r)ction $30.0^{\circ}$ 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 /cro 11.ukuba :wczjm;r(p rn* x*u3 bacross a river with a current of 6.0 m/s. What is the speed of the boat as it crossrxbw *:zc1 3nrcu(aukm*u /b1 roj;.p es the river?

  The driver of a motorboat that cano p*qge89v/ku9v h( rn move at 16 m/s in still water wishes to travel directly across a river 1.8 km wide in which the current flows at rv/9vu h* op9kq 8egn(4.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move atpvi ,0vp0dv3ro3 ya4i 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 sy3 0irovvp ,43p ad0ivhould the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches thkd 5 bajqfvm7ut. iw435+qu .je opposite bank in 6 min 40 s. She is swept do .5+ 3f.5jq d4vubum7qajwkit wnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rive.ad8uh s+tvx5mo l2o4r 200 m wide reaches the opposite bank in 6 min 40 s. She is swept ddvh m5+ltx2 a8u soo4.ownstream 480 m. What is the speed of the current?

  A boat, whose speed ng;h 5pt..ry oin still water is 0.99 m/s, must aim upstream at an angle ofygp nro;.th5. $29.6^{\circ}$ (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)  $m/s$