Which one of the follo8 jq9zf r9fbp,vx n)s5b:)j nowing is an example of a vector quantity?

  Which of the following operations will not change a vect sc:lr1+sylc- or?

  Which of the following is an accurate statenuc c+-. m:y8;ua(rr imaz3qf ment?

  The resultant of two vectors is the smallest when theqks0ps vca:ps4)i1 k7zdp,u w6l7w (p angle between them is

  Two displacement vectors have magnitudes of 5.0 3yopdz3oirs.h;y b g f,*v0s,m and 7.0 m, respectively. When these two vectors are added, the magnitude of 0 y;fh,ryd sosi33 ogzpv.,b*the sum

  Two vectors, of magnitudes 20 and 50, are/8gclx*1l)o ; qszsd p added. Which one of the following is a possible answer for the ma1qs;zg dolc)p 8/x* slgnitude of the resultant?

  Three forces, each having aqa9; h88dsf8om j s6ha .g(wyr magnitude of 30 N, pull on an object in directions that amh a86sraygs 8d98. (fhw;ojqre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, qoip m(zigd(h ys /mmks,-/3-the unknown vector is

  Ignoring air resistance, the horizontal compozc/,js b;exf kg7oh7 qoe, .u+nent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s akt,);5ink; 4rrng6a if (3x dq pyum:nt 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 horizontal szgvuro2 oh v/txvs626ir476component of a projectile's acceleration2 2z grv 6sh6itso/rouxvv7 64

  A soccer ball is kicked with a velocityfc;g365n n26;xerr dn( geph y 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-paralle9ir i oqewr682l to the velocitqwi29r8eo6 iry vector,

  If the acceleration of an object is always direcepv,4ggj (,xxted perpendicular to its velocity x(pg4,ej,g xv,

  At what angle should a water-gun be aimed in ordeh; xe gzrv) ldj4zio5u358g)4hvh t3dr for the water to land with the greatest horizontal range?jedhv4 vgtio 8h; h53)x lrdu)4zz35g

  An Olympic athlete throws a javelin at four different angles abomgk;ho/f n-n x q9u.1tve the horizontal, each with the sam- tnkx9. 1 uhgo/qf;mne 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 forbxu3 *yy- 1bu/ltk x)x the second time. If the ball leaves your hand with twice the velocity it had *3y1by l buktu- x/x)xon your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an orp1z- cia 0ze2yiginal 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 at4,j:ov sx;u) 8 n j*irbrorrs azb4(:xtempt reaches its maximum height, how does its speed compare to its initial speed?rsbxj 4u 8)srb::4rjiz oa;o*,vr(xn

  A stone is thrown horizontally from the top of a tower at theuxbvxnonk5 )e 65lnd*u; w1-ztt):yc qv c+v 3 same instant a ball is dropped vertically. Which object is traveling faster v ncy)x)kvt+z wdn lvc*t-xnbeo 5:5;u3u6q1when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant pucsqa 7wy s-8zg;0e0 a second bullet is dropped from the same gwac;-p q7ez0u sys08height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a6r f d;u(p sr/zxfl 2,-ku;gka speed of 113.1 m/s and at an elevation of 295 m drops a package. 7.3 seconds later it drops a second paua;,zkgdp -u;rr2 kl/ffs(x6ckage. 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 d.ax wa9conn ffn)r57.g ;t4k85dz uwsecond package is dropped. Neglecting air resistance, the distance between th.ug 4rd .n 5n58kxtna9ao;fw)7 fcdwze falling packages will

  A pilot drops a bomb from a plane flying horizontally at 0vxrnwsb9263 ib vc3 op( xsu2a constant speed. Neglecting air resistance, when the bomb cn2p0 2svv69bs3x (b io xr3uwhits the ground the horizontal location of the plane will

  The acceleration of gravity o 3e sf .2wvvsyox3b*6an the Moon is only one-sixth of that on Earth. If you hit a baseballss v3v.36fy2*oe abxw on 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 a mktu:/+,bpnrvrwf84pqy; phk e k 0i 0,7yf8x straight, level road and pass a car traveling at 45 mi/h. Th hr+8b:rp8ipy; ef xqkm tpv,kuf/ y0w,k074ne relative velocity of your car to the other car is

  You are trying to cross a river that flo2 4:)m0gw 1 nf4,b tunjgkqh4ftcppm,ws due south with a strong current. You start out in your motorboat on the east bank desiring to reach tcuf qtpg:, kt4m4fmw)g4 1h,0n 2pbnjhe west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will i3d* m qa/k,yf 6gs0bf,wsbc.lt take you to mova6 3sdgksf*cmqf , b/l y.b0,we 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8b 6mbb x)kew 0.-jn)br.0 m at an angle of 30 degrees below the +x axis. The y c0)n-j.xw rkebb) 6 bmbomponent of A is

  If a ball is thrown with a velocity of 25 m/s at zvo 4fr3e+kw1)r.myt 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 northkd8 b4kimh-0 m nt+xbq83 sa;j of east and you end up 2.0 km north and sev xq-04;kk j8tmmi+ 3ns dbh8baeral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x componentkj2ce1;v y 8seh6 cgx6 of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis 612hk; vx6jyeg8eccs must be

  A 400-m tall tower casts a 600-m long shadow over a level ground.*y d4h+yv gz5 pt*if7/uxrrt6mth8, e At what angle is the Sun elx,yvet g4/trirup+5**td7 y8f6 zhhm evated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What arl:bda2uj7s.2/ aj y(w4 xj uqre the coy:2j/(7w qjdu 4lr juxs2a.abmponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. zii.tms7p4kcy(4,60 bi wq rfi5lc3 hWhat is magnitude of the sum of these two vecto ,4kir0fizswb3tlqich6p 47.iy (c5 mrs?

  Vector A = (1, 3). Vector B = (3, 0). Vecto) od-mx4i le.vr C = A + B . What is the magnitude of C lv .o4e)d-ixm ?

  A car travels 20 km West, then 20 kkjghwky)xr(o p1fkb:y/ gs-5 6bs-n4:e 6p mjm South. What is the magnitude of its displacement?)45:p1ojr(gs-w nf ebx6h k-: gkjyybmp/sk 6

  Three vectors, expressed 8qarcj6 q9dc5 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, expressed in Cartesian cootc( frzk:6a j;rdinates, 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, -8.5s 1b si+ jxxdf.dq w0 at;l6gg6xkt7nurx96- 0), what is the magnitude of vector C = A - ftssbtja rxkdx+x -x1lugnwd.65g6;6i097 q B ?

  A runner runs halfway around a circuzt ,v8ywvv1w)lar path of radius 10 m. What is the displacement vt ywv)vw1z8,of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is 6 .;kv vb et-;-jrsryqthe magnitude of the resvr-bk.6rt sv;; y-qejultant force?

  Two forces are acting on an object as shown in Fi i (0 rmpou/ynmf.9gex ug60eqv9p5f(g. below. What is the direction of the resultant g(9m9mi 5uryoxf(/6enpv0.fq0 gu e p force?

  Vector A is 3.9 cm long and points aec;n bv;71u;c(n krv plong the positive x axis. Vector B is 8.2 cm long and p rc ; euc;vpn(1kb7nv;oints at $+26^{\circ}$ 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 76 cm lonrfgt3( gfyg9 .g and points at $30^{\circ}$ above the positive x axis. Vector B is 26 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 initial spbrs;b.t mj1+ feed of 26 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 4.9 s. bmrs 1.jbt ;+fWhat is the height of the cliff?

  A girl throws a rock rdw s1--2 wbsohorizontally, with a velocity of 14 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before striking the 12 wr-s-odb swwater?

  A ball thrown horizontally from a point 19 m above the groun(p lv6-h1nolcv2t gp9d, strikes the ground after traveling horiz1hvpo( t2pcl-9l6 gvn ontally a distance of 22 m. With what speed was it thrown?

  A jumper in the long8 ki5 eso0zntden3- h2-jump goes into the jump with a speed of 12 m/s at an angle h2ient 0 dok3nesz -85of $20^{\circ}$ 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 spgi48 6jgdv5b beed of 8 m/s at an angle of d4 58bgg6j vib$38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 49.4 m/s at an p00tjh ;b1a3jfc*aza1dw1ym angle of $13.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 40.9 m/s at an angle of 6+nrj5yz mb 4s$17.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at kwl1+sf /-t2 btzw 0ulan 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 23 a(c3 kh wphkhm+ -;obz*;mi-z.3 $m/s$ from the roof of a building 64.0 $m$ 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 grou0io+ ds/kv.flnd level with an initial speed of 64.9 m/s at an an /0+i okldf.svgle of $43.7^{\circ}$ 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 at a velocityu mp6:zvi/ h-c of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows up vz6/-him:cyour speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speeru6xi z6 11nn f;z2lq 1uuuuror-j;i;d of 200 m/s due North, and is in a wind of 50.0 m/s to the West.uu i1u1nr6fuz 2u ziqlrxn1-;o6;rj; The plane's speed relative to the ground is

  A plane is flying due Soaqncuk52:nu zakj9tuq 0 3. 1xuth ($270^{\circ}$) 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 hea oiyawgc:at-2kcp6q2ju: 9xyt;*, jqded $30.0^{\circ}$ 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*u1cjkuc0a- m 8)txb s a projectile with speed 50.0 m0m* cc-x8k1 uu aj)stb/s in a forward 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 cao*w*axvcktf*,f1 ,river with a current of 6.0 m/s. What is the speed of the boat akf,favo,1 c **x*a twcs it crosses the river?

  The driver of a motorboat that can move at 1 . kcretodh05:0 m/s in still water wishes to travel directly across a river 0.7 km wide in whicdt5k ceroh0:. h the current flows at 7.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in d-vwow-a)s,q d tnswc ;bu758 still water wishes to travel directly across a narrow strait in whiad7wd- ),w5t-csq 8n;sb uv owch the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a rivera vtc47o td)o (s5-uhw 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still watsh wou(5)a4tvtd oc -7er?

  A swimmer heading directly acr)ewh28 2gi6) v mizuxkoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreaui)82)2eghm vzxwk6i m 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.08 m/p,/ .kebd/ sy u6hc+yrs, must aim upstream at an angle of uyps y 6kc.brd /e,h+/$29.6^{\circ}$ (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)  $m/s$