Which one of the followitq*(k(.lp nw-seaz7fa0vx4yt zue :8ng is an example of a vector quantity?

  Which of the following operations will not change a vectorzh2 y ju)h3j+ du6q1rw?

  Which of the following nn3 m cvi4k,:dis an accurate statement?

  The resultant of two vectors is t5jvbo* +k eywn z8j6.hq7 pn7phe smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.057nkxwt v+nhnofx05 w/:b 2;cfit0nz m and 7.0 m, respectively. When thcb5 5nt tx :o/h7iwxf2vn;fn k0n+wz0 ese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 i sgr40ax4y;r and 50, are added. Which one of the following is a possible answr 0;g4x4 rsiayer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull n7a,yqi+,/bg0j d kukon an object in directions thatq+u/kd7kg i,a ,0 yjnb are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown c cz h/mmfr2wq8od9f66s4u+dvector is

  Ignoring air resistance, the horizontal component of a projectiled+ hb6i j8 +df9k/fst.oekr- j's velocity

  A ball is thrown with a velocity of 20 m/s at an anc1pniga lu/z0 zgix7y;g47a1gle of $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistan7ih 1zs,gt8kwce, the horizontal component of a projectile's acceleration7iswzhk8 ,gt1

  A soccer ball is kicked withy3q158r /dz o 8egvz a1hju1dt 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 bomu+ 3rk53sevg qo-. of an object is directed anti-parallel to the velocitysq+.ovb e 3-o u3rm5gk vector,

  If the acceleration of an object is always directed perpendicular to is*znnm* x0bpq34iby/p 5n *f . adfw4zts velocitysz n*p3p z4dfm b/y5 f*a.xqnwn*4i b0,

  At what angle should a water-gun be aimed in order for thr9 mxaeo4 xkgq)m-d: 7e water to land with the greatest horizontamq 4g:)o9 7ear-xm kdxl range?

  An Olympic athlete thzs. 2deho8k* zrows a javelin at four different angles above the horizontal, eac82shzoz* d.keh 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 the ball)q w-x lnn l8wmwb*ov*n;g1 .h leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) nng)obwml8;- hvwn*xl.w1* q would be

  A ball is thrown at an original speed of 8.0 m/s at an angle ol4,/ceff5rjx1 n wb8 m4hq/qk8l2zjy f $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a (jcu/*(pm wtjfield goal attempt reaches its maximum height, how does its speed comparepm(j u*jt(w/c to its initial speed?

  A stone is thrown horizontally from the top ofmp,4el9or50r ya,0dw -h ( e5pyh nxyx a tower at the same instant a ball is dropped vertically. Which object is trav , eho(5nepapm0,xy4xhl9 ryd wyr0-5eling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same insoml8wxr ::/9u.s mxlitant a second bullet is dropped from the same height. Ignore air resistance. Com:sr9x/ ilw.8ou mx:lmpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 84.0 m/s and at an elevation of v)vh5+2 zl6 + fvvcjwm204 m drops a package. 4.5 seconds fv c52vmlzw )h6v+ +vjlater it 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 vaztkfe167mj(5a 8f3h 0b rrhsecond package af jke8farhrvzhb 0t5( 76 m13is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a co liq *lf)(:aqznstant speed. Neglecting air zf ilqq:()al*resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gphn ,2viex7curp 6.n; ravity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball v.nrpn,hu7ei 2p x 6;cwould land

  You are traveling at 55 mi/h in the +x axis relative to a straight, lev6(2b7puhw t tpel road and pass a car traveling at 45 m(6pp b wt27uthi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flow;-qaia q/isd*s due south with a strong current. You start out in your motod;-/qsaai*q i rboat on the east bank desiring to reach the 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 it take n:ab9/ k.zjzx.tb2iz you 9 za.n.kz:2/zbib txjto move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m iny lf+y6)33os et,qc at an angle of 30 degrees below the +x axis. The y cqsyf36n+ leotyc3, i)omponent of A is

  If a ball is thrown with ai*-semfvd; /c 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 straight line in a direction north of east and you e70ca5gd 3)syi:w4o bdnl 9kqcnd up 2.0 km north and several kilometers east.7 dw0:ci4sa )q9 lyk c3bdnog5 How many degrees north of east have you walked?

  A butterfly moves with a speed of 1ore23tem6f67igfygo :c,c9 u 2.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion yc76ut6ei f g e :of2mgo39,crand the x axis must be

  A 400-m tall tower casts a q/yrgp brpsz2s2 xs -4e4k;,u600-m long shadow over a level ground. At what angle is qrex2rg; ysk,pb zp4-u/ 2s s4the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respece3.sk,y4q n:i-n vyn5ih ce*ftively. What are the components of the sum oc.yn 34n,yhf*ev- in:qi 5sekf these two vectors?

  Two vectors A and B have components (0, 1) and (-1, y3 (l4ky x0du4vsi h+ gxlwf8z)y ;d(c3), respectively. What is magnitude of the 4zydfhu +xvd ((;slcywi 3x4 )8lk0gysum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnidoah ca9 *6pr.tude of C ?9.*6coapdrha

  A car travels 20 km West, then 20 km South. What f 28fqo)vncb) is the magnitude of its displacementc2)nff )qovb8 ?

  Three vectors, expresse3iwlt:cntae7z v +h-w;bcj o9e4 1th-d 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 Cartesian7/ ptl(wvzzt97.ms jx 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) and vector B = (+3.0, irvmb awcmx2j(y43gy( z -e* 3-8.0), what is the magnitude of vector C = A - B 4z r* (m 3cwebyy2i3m gx(vaj-?

  A runner runs halfway around a circular path of radius 10 m. What is t rcetk4w4d7 +ehe displacem4r7+tw ee4kc dent of the jogger?

  Two forces are acting onuyf5jyn9-hx:swj .3cztmb4+ an object as shown in Fig. below. What is the magnitude of the resultant force? 4twx.-yj ufs59hc3bzj+ymn:

  Two forces are acting on an object asl7:l +w;eorqj shown in Fig. below. What is the direction of the; r lo:+ej7lqw resultant force?

  Vector A is 4.8 cm long and points along the positive x axis. :r1)ca0hcsmpl /2hto Vector B is 7.5 cm l h)1mp lc02o/ra csht:ong and points at $+32^{\circ}$ 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 58 cm long and points at +iu d-7+gg q2xmj jh+l$30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 39 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 speed of 15 m/s from the m2dip wca-6,b edge of a cliff. A stop watch measure-ap,bw2imd c 6s the stone's trajectory time from the top of the cliff to the bottom to be 4.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a vxge( vhma ,2 t.1n9wyzelocity of 15 m/s, from a bridge. It falls 17 m to the water below. How far does the rock travel horizontally befora mw.1t vy(2z9nxhg,e e striking the water?

  A ball thrown horizontally from a point 23 m above the ground, sty mzq w.mx3,y/khad 2*rikes the ground after travelingm,my3wy *q2/kx.zhd a horizontally a distance of 17 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 angql: -x5fxx 3adl;sn6p le 35x xx-:;6lalnqdf spof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes p2 0*;qchtszo)f037t ayq 4lbt xcx8xinto the jump with a speed of 8 m/s at an angle of 8bcyax;h*pt) 4x0co 03qtz2s qfl7xt$18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitygtyol z r.rn2g 3vb26o7qb9d6 of 23.6 m/s at an angle of $20.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launq rmx5 *e4oi3 -htyu/bched with an initial velocity of 56.0 m/s at an angle of $12.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fir xix:1n g/m(fled 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 hot.lwe z) sgf(,rizontally at 27.4 $m/s$ from the roof of a building 54.1 $m$ 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 53.0 m/s at a 4 nikd 4r.qb3w4oqu8rn angle of wnq44o.drbk uqi r34 8$37.2^{\circ}$ 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), you can run a 1500-m race at a velocity ofe.4b0 m7l80urgenthuehe vq + s ;s.o- 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speh.0-s4.ntlsrg7u+u;0 h evm oeq8eb eed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in atn d det2noqn/)3.1c/; 0 lnxa/qsems wind of 50.0 m/s to the West. The ce)3n le2nts /xtnas0q o;1dqm/ .d/ nplane's speed relative to the ground is

  A plane is flying due S 1xxd(u9oa l cflxds+/svvc,g z1/7h0outh ($270^{\circ}$) 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 speedp)q d spk;(;iw 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 20 glok .be8eeyh; jwi-tt)4-ozu/y 9e60 m/s horizontally fires a projectile with speed 50.0 m/s in a forward directio)ukj ;ebe. h4ge ttezyo w/698l- i-oyn $30.0^{\circ}$ 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, crl t4( zt 8yddx xe:,fe-k(c,is directed across a river with a current of 6.0 m/s. What is the speed of the bfx:-4 ce(r k dye, (xctlt8dz,oat as it crosses the river?

  The driver of a motorboat that can move at 18 m/ 6kj/p ,x dga-g5ffl 8(ayeyy:s in still water wishes to travel directly across a river 1.(6ffagkdlayjy8 gy , p- ex:5/7 km wide in which the current flows at 4.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still watehshna+9f+qme zsu. 87)u dlc /j 7yl+xr wishes to travel directly across a narrow strait in which the current flows z+. hf7+ulqmd+79a8 /sch yx e)u jnslat 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide r8baoiwyn8t . 5eaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can sh8i8y.toban w5 e swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the ** 0t9 m*5hz3x ,wtq:1jbpy yse;agdx3d prwnopposite bank in 6 min 40 s. She is swept downstream 480 m. Wehwt jwd9ban ,p33dqy*t :zy0sr*px xm 1;g *5hat is the speed of the current?

  A boat, whose speed in still wkq6m0r+b ;hwxtd :h 94z mrb6jtq9 ps2ater is 1.97 m/s, must aim upstream at an angle of mb4rzh w mqs h9t0pj2:;dkrb9 +tx66 q$19.6^{\circ}$ (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)  $m/s$