Which one of the following is an e 8-vx7oe q(uxjxample of a vector quantity?

  Which of the following operations will not change a 8fu8 z5ux c:odvector?

  Which of the following is an accurate stav6jdp9r7ffy w+mk r +*,d zmt8tement?

  The resultant of two vectors is the smallest when the angl .retchp(:3pngr d1q8e between them is

  Two displacement vectors h z5/ea4lpi; 8p.fe yyxgbmh28fayl +8ave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the z/ 2bmfy884 gl +phf epiy;.y85 lxeaamagnitude of the sum

  Two vectors, of magnitudes 20 and 50, are ak9lb*m 3yenzbnlmju6672re7 ms j 7t -dded. Which one of the following is a possi usml-jnl3t7 6r2mn*ekz9 6jym 7beb7ble answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dilobkn7+5bdr 6al* n)brections that 75oarblknlb+ *)n6bd are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the upa7otd6 sg*6y4xde::md w. p dnknown vector is

  Ignoring air resistance, the horizontal v2ghs7 / dmg(gcomponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/sk5 jxxm9msjy f :g4h8bw*0wu : at 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, oell6x 3rk4/,v k qhl299ikbzthe horizontal component of a projectile's accelerationi6elv9 /,bk4kz k 3qhxll92ro

  A soccer ball is kicked wi/5llm8t(bt 2pmn *fuo th 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 objecvid8dx(sh 0: rvj o,1glbb7 *ct is directed anti-parallel to the velocity ved1 jv:v8 c os(bh,bg0*li r7dxctor,

  If the acceleration of an object is always diy(z)aft q5irx 88xys - ri/y+jrected perpendicular to its velocity,qy/8tix zf5r -s8j)yr+ (xiy a

  At what angle should a water-gun bfaj (j*k g8(rue aimed in order for the water to land with the grgj r *(fj(8kuaeatest horizontal range?

  An Olympic athlete throws a javelin at four d m swsel/fyw moa-w ey/59*/(rifferent angles above the horizontal, each wsy/wawmwo fy-9r l(e*e //ms5ith 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 tc,g1 pnz2kw*q yr:x9whe second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R *ncwk21 :rw 9,gx qypz(compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/t/g zc8cx.,ml rh8yz9s 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 reaches its maximum (p / i,jir6y xbx((t4i6r x;jrt:yraw3x6 xqqheight, how does its speed compare to its initqxrjwxx ;bix6y,6trti4/ yp( i(jxq3(:6rraial speed?

  A stone is thrown horizontally from1ygej l- 4iqb;odes/) 1mei0a the top of a tower at the same instant a ball is dropped vertical 0ym1aeq/js;d)lg4 1 ei-eb ioly. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant axt) 7*f1qn4z jj u 9zzdsujk(kj.(:h u second bullet is dropped from the same height. Ignore kujfu1j9( *uxzh :7jz.4 zns) djt(k qair resistance. Compare the times of fall of the two bullets.

  A plane flying horizont, */jlz6bp-5h lxril *mx t7ptally at a speed of 94.3 m/s and at an elevation of 230 m drops a package. 4.5 seconds later it x7l5,-z6ipm rxtljbth*p*l/ 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 se;c:m5 y kxrq m2x khe4f/,i0vscond package is dropped. Neglecting air resistance, the distance beteq5xf 24is ;k ,/xv: kryhc0mmween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Ne :6ms 8i9ru,ak-kuitl glecting air resistance, when the bomb hits the ground the horizontal locatiokta9m,u i6s- l:kui8rn of the plane will

  The acceleration of gravity on the Moon is only one-sk /kx8ck +qdpc5oen ;/ixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at theccok5dn p8qxkk+//;e 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 straight, level rf+l35f cprh-(ib flm+ vj*pf7;s pb/doad and pass a car traveling pp( c 5db; rh 3fbfipsm +fv7*-+/lfjlat 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strzjy( mav,s9 7vong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You s ,zamvv9y7s( jhould head your motorboat

  Your motorboat can move at 30 km/h in still water. How mum, nlp +w;+0 w49hhr 2gt;zasj/ea paech time will it take you to move 12 km down +0rt;mlph+ ea4,sh wgnj pe2 aaz;/9wstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at ag;pxd*ja6m , lf.re u)n angle of 30 degrees below the +x axis. The y componentf .urdg6a p*l) ,;mjex of A is

  If a ball is thrown - 5 v,c53:sunlo4 erznet(pqjwith a velocity 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 q qu,07+cchvs ,o o9kcstraight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many dec +,0uhcqo9o7qsc v, kgrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component ofl xxb-j n.)e-*u dekr)mh 6nq0/jpa/m its velocity is 8.00 m/s. The angle betweenreux)j//6l h0xp djb.ke*amq nn) --m the direction of its motion and the x axis must be

  A 400-m tall tower cashsupub4v-nv y-8i 1 8 mw38 bnv.be3sqts a 600-m long shadow over a level ground. At what angle is the Sunvvs buw -3up8by-inmvsq 4b 8e.83h1n elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. ; 0j3xzidoj 8m33t3 atgc/s qnWhat are the components of the sum of these two vi33qn 383o;g/ xj jdttczs0ma ectors?

  Two vectors A and B havej30mu;m7o5bnhj 2vv jy hz4tnhsk5 1( components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two v k jmhhbsn327; u yj1o5mn(zv 4jtv50hectors?

  Vector A = (1, 3). Vec f5()jr8kpwic tor B = (3, 0). Vector C = A + B . What is the magnitude o rf 5pjwc)ik(8f C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its d*ek2gz: )is;lpfct5 l 4a2fcmisplacemene k:4c2 5)*iasf zltp2lmfc g;t?

  Three vectors, express,q q .bwriv-wpm/a:n, ed 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 coordinz.vfua/, h 9+epba 01;aaamlnates, 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 vectoxjrou: kauyg ,.d*zt; 95)ywfr B = (+3.0, -8.0), what is the magnitude of vector C =juy5o)a9 z.*yx;gfd k rw :,ut A - B ?

  A runner runs halfway around a cir af61i -8iaruiyh 5me82 1halgcular path of radius 10 m. What is the displacement of the jogge8g a 1-8ihrf6 2lhaym uei5ai1r?

  Two forces are acting on an object as shown in Fig. below. What is the magn-q .pcyvzv :2kitude of the resultant fv zv-.:pqcy k2orce?

  Two forces are acting on an o.6y )mzq7 q :8hhdvstd1rj-ww bject as shown in Fig. below. What is the direction of the resultant qd hd8:mj 1r. hyt6qv-zws w)7force?

  Vector A is 3.1 cm long and points along the positive x axis. Vectorj52 )e2tdxzvm ox:+da B is 5.4 cm lonmaz:o t)xedd+v2 5j2xg and points at $+48^{\circ}$ 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 57 cm long aq*p h-;hlg:tc nd points at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 44 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 igzajbbz0* b21 nitial speed of 12 m/s from the edge of a cliff. A stop wbgz j bzb12a*0atch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of (za0j /s,jsfuziq (,pzx *1 pz19 m/s, from a bridge. It falls 15 m to the water below. How far does the rock travel hori0 ,zjjs(f,pszz i(1x aupz *q/zontally before striking the water?

  A ball thrown horizontally from a p6.lt yjqzfrd-m4j: *+1fgfpu q xew6,oint 28 m above the ground, strikes the ground after traveling horizontally a distance of 13 m. With what spee*6jt,+fp:fem qq xf1r-wy 4lg6. zdjud was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angls oc(e/6xq 4wde ofoqw4x dc/6(e s $20^{\circ}$ 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 1s 3nz r61+1dp.+btgd2 tzxire4 m/s at an angle ez t+n 2br1dpx1isd+rtg 6 3z.of $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 29.0 m/s at an angle of 8y k s3xyc19ixjur,7g$24.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 54.1 m/s at an angle58ht9v w:.lc pygel) y of $43.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fimt y/mon)/6zi z48s crred 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 horizontal5n2btt4 rlpkbuui+ )+ ly at 17.5 $m/s$ from the roof of a building 69.9 $m$ 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 59.2zgncm:)(0- ho+zu.8rksova/0tgh v:r 4 zhl z m/s at an a :hvh/gz8:0ot+z rmcz ohrv)-zu kg(0lans4.ngle of $37.2^{\circ}$ 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), +cua4n::d und d qbo08n -fxs,you can 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 whic, a 8cs0 dn4:n+uduobxfnd: q-h 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 n5vb 3 hehr05f flwr,1200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to thfrr505e,3 w bv hnfh1le ground is

  A plane is flying due n,xxe4 one101,tuiqkp :d:u u)xfp a9South ($270^{\circ}$) 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 is1rd3y f4ccm 9-eayhw : 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 horizon gyy;adu0h1r) x aks)1tally fires a projectile with speed 50.0 m/s in a forward directioy;a1xy g1aud))0krhsn $30.0^{\circ}$ 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 a/pr5hp* yg+bla;q 68 qmq4zgjbf 4ea-cross a river with a current of 6.0 m/q*m8zg4pl 6qgj/4ye5rb f+ aqp b;ha-s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 8 m/s in still water wishes to trav +iwnt(.pwh/fel directly across a river 1.8 km wide in wfh t/(pw+nwi.hich the current flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a motorboat 3 ft9rsn(p8 lnyfa6j5 that can move at 10 m/s in still water wishes to travel direc3tfnj5 p9f la6ry n8s(tly across a narrow 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 river 200 m wide reaches the oppoq34b8 ,ng5zgoo ma w(mkbgm40site bank in 6 min 40 s. She is swept downstream 480 m bogkm34 mag (q0,own4bz8m5g. How fast can she swim in still water?

  A swimmer heading directly acrosbg.as3tz1 t pg08 zprl:jr)- fs a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream rs01) a-jtgpp.t8f brzl3g :z480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.7 a1/o9:q7;40px yjndemlb fux3 m/s, must aim upstream at an angle ofulja pybmf q09: /de147;oxn x $16.7^{\circ}$ (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)  $m/s$