Which one of the following is an example ofluztb 1i;d*6a a vector quantity?

  Which of the following operations will not change a vectori l+ 4bulg(-gg?

  Which of the following is an accurate statemef s 8rvs56v*qjnj/9pdeh7 p 3bnt?

  The resultant of two vectors is the smallest when the angle bet/eb238hd bg nhween them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. 9 fjel0dsr5n *w 1.x6;lsansdWhen these two vectors ar wfrsx 5sll0n;*j9 6s1d .anede added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which onfup.vs:v r vkpz)(: 0ye of the following is a possible ansy .sk pvuvv)prz0:f: (wer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direct1mwsqda1 bdi1* 9lj,g; lp4snd6 bzo;ions thas a olwgbqld4 1s9,dp*116mjnb; id;zt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknow.f;, 3qhhrgn iaf(rk9 n vector is

  Ignoring air resistance, the ho anny*+eg27f srizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angf 44ne qns v+bg-dtcb4*kx f/*le 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 horizontabi 361rimf4l60vk qf jy1uy oz./qzz,l component of a projectile's accelerationl6z1b qi/fzk. 3jz u4ym0v16, fyoqri

  A soccer ball is kicked with a velocity of 25 m/s at an anz58(yds :0 jepxdf x a/;ep/rv)lhvl/gle 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-paf: o*-msb. x(bsai4qdrallel to the velocity vds.soa4: (xbf-mb*iq ector,

  If the acceleration of an object is apm3+*s:d iwwv1 rfimsb 24 ru5lways directed perpendicular to its velocitp5rwv*d1ms4r+2m3wu i ifsb: y,

  At what angle should a water-gun be aim)fkhl c*f:ep 8ed in order for the water to land with the greatest * :ckl e)fpfh8horizontal range?

  An Olympic athlete throws a javelin at four different anglemdn sq0i l(4blg od ca67n4,zxhg2 -:is above the horizontal, each with the same spegx:am7n4cdzo0-blgi qn (6i4 h2sl ,ded: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 tha4p4bk z6ml4ew -sbn)e ball leaves your hand with twic k-44awbnmbpl)s 4 6zee the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an ob7)1vd rayor, vj y-5ss8ojn 3riginal 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 reaches its maximum xfh.4gq0 wk 8h8, wyothcvj3) height, how does its speed cgxhj4 .wcwhq3 hy 8,8) tf0kvoompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a ba gzf9ag*:tcueqhh98d iv5qz+ a.i( nrjz816fll is dropped vertically. Which objecuin6fcvg :jzqa+rtzd (*5fe8a.h8g9hi9z q 1t is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the sa-o3ft:wd s 4+u nro(uume instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fal+(n:t3 uof sd4wr-ou ul of the two bullets.

  A plane flying horizontally at a speed of 104.4 m/s anrb rz m d5sils0i+3*+et(8 cqtd at an elevation of 283 m drops a package. 2.0 seconds later it drops a second package. How far apart will the two pacms+ 3ds8*cr(q50ir tielt+bzkages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pa(* onhqq ;g/pockage is dropped. Neglecting air resistance, the distance between the falling paog; qn*q/ho(p ckages will

  A pilot drops a bomb from a plane flying horizontall1-b i kp8i5bphy at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of -h5b18k pbipi the plane will

  The acceleration of gravity on 8x v.7unc5fgt;t egps w).)( uqzxuy *the Moon is only one-sixth of that on Earth. If you hit a 5gu)s. c gevqx7 tnt p;u.zu8(yxw*)fbaseball 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 straight, levwzdo(0ur o*q6uh0 n.3my.qt cel road and pass a ca wm(on.qhuo t0u.d3y6rc *zq0r traveling at 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 strong current. You 1skzlv4;:ummp779cutcm ij8w *ysb9 start out in your motorboat on the east bank desiring to reach the west bank directly west f m7y:zbu t719v8sjk iwlc4sm*9m;upcrom 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 rwhzvgj)08d1rk7k g( you to move 12 km downstream, in a rzjdrg8w7kh g(1)rv0 kiver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below tchi4xn 0 gfi n*; 6u4ie5zpfq0he +x axis. The y componf upg0h nn*c6 5 40zxei4iq;ifent of A is

  If a ball is thrown with a velocity of 25 m/y0snns ;*gp 2ds 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 north5 q)gcmi2woxf8pl9 8 o of east and you end up 2.0 km north2lf 89oxoimp58g cw )q and several 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 (*23lwzss,f;dzd(41di dn kzqoczjs8 tfi ((of its velocity is 8.00 m/s. The angle between the direction of its motion andd tzc;n(zo8ds1 sd z(wzj kl,3*qfsi((fid 24 the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level gr ydz2/mfy r-8a6a/xh/jdw ot 6ound. At what angle is the Sun elevatza//-my w6t o2jdra f /hd68xyed above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What angqw 123p-vsl re the components of the sum of these twq21n vswp 3gl-o vectors?

  Two vectors A and B have co gp0cy nky+hsl -)oyc 1/jg,t(mponents (0, 1) and (-1, 3), respectively. What is magnitude of gj-p y1()sl y yc/c oht,n0+kgthe sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vf-a wmfti;3d8*d- cqxector C = A + B . What is the magnitud 8fatf--3d;cqd mwix*e of C ?

  A car travels 20 km West, then 20 km South. W,a8 r f y2kf7rxfc*qx,hat is the magnitude of its displacementr af7,q,f8x*ycx k2r f?

  Three vectors, expressed8d9mr.r+ 3b-f 6qeh-htct 0;yjqstx qq9mh( o 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 auzm* yxww5-hb7j o6.in Cartesian 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, -8.0), what is the mar i 9pl+t/*mesc lcp -t1gs+r:gnitude of vp1l it/+s-9merlsc c *r+:gtpector C = A - B ?

  A runner runs halfway around a circular path of radius 10 mezb0.98tg ioz. What is the displacement of the bg. 9zi8oz t0ejogger?

  Two forces are acting on an object 7vw upu+8pk3f as shown in Fig. below. What is the magnitude of the resultant7vku+ 3w 8ppuf force?

  Two forces are acting on an object as shown in Fh c;w,f-upgo .ig. below. What is the direction of the resultant foc-guw.p h,;force?

  Vector A is 5.1 cm long and points along the positive x axis. Vector B is x8n )m,clv9au0(5kmg osflum1* l3mh 9.2 cm long and pointl05gmscl)umo, u nmh(91mva8*x l 3fks at $+23^{\circ}$ 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 53 cm long sr e kadv6;z)*g6r+a yzl+gx:lvm;t 7 and points at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 40 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 16 m/s from afw04v2st9vz ;i/h juthe edge of a cliff. A stop watch measures the stosu0ai 9v2 thwfj/4vz;ne's trajectory time from the top of the cliff to the bottom to be 4.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velonce7do-ew, rvp 0so tj6pi)2fr*l-5 ycity of 7 m/s, from a bridge. It falls 25 m to the water below. How far does the rock travel horizontally bef -oi r7,e ds-prnoj y0v6*lpw)e2t5cf ore striking the water?

  A ball thrown horizontk 8 5-3abwwpsrypfg -s7vy1l(ally from a point 21 m above the ground, strikes the ground after traveling horizontally a distance of 21 m. With whaa-r fpw8(ys-3k b5 s1vpg7 wlyt speed was it thrown?

  A jumper in the long-jump goes into the jj2p gv r9u8,6rsg,7za* x udbeump with a speed of 12 m/s at an angle of ,jb*d2vxz 96ragg s eu ,8ur7p$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes i,8ior bu o38gbae0g8t nto the jump with a speed of 12 m/s at an angle of b08 8raugbotoi3e,g 8 $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 20.8 m/s at an angle o;,l+ ona 6tuvvn0 c4ivf $34.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 34.1 m/s at an anglu8dvgszb* j7-3pkd6v pme8n t1 w9k6ee of $46.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglel1wltz t*f) .v 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 22ed8 l5xugxip8d tg .+..7 $m/s$ from the roof of a building 66.2 $m$ 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 initin mzp3ri- zmx2f q)7z2al speed of 60.2 m/s at an anglx2p 72znr q z-3)mfimze of $37.5^{\circ}$ 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 a9,u a30d-yj oy hqgg3xt 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 9gh3yyda, oug j-0 3qxm/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 a wind of 50.0 m/s to ttt:5fs u06bxbq fwj (,he West. The p:xb q(tsfjfu,0 6w5tblane's speed relative to the ground is

  A plane is flying due Spo:lq) v.cyee3:i6 l*n cy t6houth ($270^{\circ}$) 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 headed6kle7qk 2t ea/ $30.0^{\circ}$ 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 horizonta c.vnzixp7oqc xks5mi 0o7,( 3lly fires a projectile with speed 50.0 m/s in a forward directiokxni,s77cqzo.o0xm5p ( v3i cn $30.0^{\circ}$ 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 mj n5k03)pqnl8-7,wd rma o vu8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosseu3 m08)q nw,nm va7d 5jl-orkps the river?

  The driver of a motorboat that can move at 14 m/s in still wate*); bs4sxsxj+aa b6bpr wishes to travel directly across a river 0.6 km wide in which the current flows at 3.3 m/s. How long will it take tbsjxa*a +6 4sx)bsbp;o cross the river?

  The driver of a motorboat ,yr+4gxd c1qai dew0 ;that can move 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 xage0+,;dcr1dyiw4qhead the boat?

  A swimmer heading direzdq +ssp4f;g 9ctly across a river 200 m wide reaches the opposite bank in 6 min 40 sq zs +f4;pdg9s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opasz9*yy-t 3tse7 x(mcposite bank in 6 min 40 s. She is swept downstream 480 m. What is the cym7 sate9 txyz(*s3-speed of the current?

  A boat, whose speed in still water is 1.18 m/s, must aim upstrean(6 snmzp,amizg+l: 8ll,:.zr dyg t2m at an angle of gs:t:2l(pmz nl d6 y nzazg8,r.im,+l $13.5^{\circ}$ (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)  $m/s$