Which one of the following is an example odgd(x( e +tk7kzuvt8. f a vector quantity?

  Which of the following operations will not c m1jhk-4 dz0zphange a vector?

  Which of the following is an accurate s.(3( zvfxbpfc tatement?

  The resultant of two vectors is the shvn3et 9lf55q 2qwu 5mmallest when the angle between them is

  Two displacement vectors have mag5jl 0eom r:9bioet,v: nitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the s lbom5e 9joi:t0,v re:um

  Two vectors, of magnitudes 20 and 50, are added. Which one of the fop2z* fp gr8w9bkf9iz )llowing is a possible answer for the magrf 2b)z fzw89*pkpi9gnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direjkv9z; pl- rst(oi :i9ctions that are : (-9i9rjs;oltkiz vp$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoc gtot/6w1g4 cwn vector is

  Ignoring air resistanv (-sl -n1tqsace, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20hcl(ql( m,u )qzib.n2 m/s 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, the horizontal component of a projectile's acceleragmp x44s2 odb-tion-4x 2o b4gsmdp

  A soccer ball is kicked with a velocity of 25 m/s at an angle of 5k 80nt.y 5huiw *o.4urgkoop$45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vecto*v7/ r)g y, ag,mk (6.z euw;+bfk ummvnarx9vr of an object is directed anti-parallel to the velocity vectm venyag;/urkmm()ka gufzv w+9 ,., v6rx7b*or,

  If the acceleration of anxj94c7 s bqgao-0n4ncw-/ddm object is always directed perpendicular to its velocityocb0 md9/dgqw 4- sn74xajc-n,

  At what angle should a water-gun be aimed in order for thj6o-d 4j:9 fzdikoaeo5)sdu b k3dp49e water to land with the gre5k9oos dfdz4a djib d)9epj:64k uo-3atest horizontal range?

  An Olympic athlete throws a javelin at fogt tf6dx2jyqdi1733ad2d m +z ur different angles above the horizontal, each with theqdfty7adx mz+6t231idg 3dj 2 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 leaves your hand with 1ecj,c.x9ffq twiccxfe,9q f.1jc e 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 origifvl .4oh 2(a nfn;xlu1,e g1opnal 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 rn2s8qxn sz a;6o*wd*t ;5vfdv eaches its maximum height, how does its speed compare to its initit8w;v;d s6**s2nfq5dnvxo z aal speed?

  A stone is thrown horizontally from the top of a tower at the sn6m 8sm81ty gname instant a ball is dropped vertically. Which object is traveling faster when it hits the level grounn1 8m8mn6tys gd below?

  A bullet is fired horizonu+q(jwhx4 n-wj6 u5qxtally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Coqjuw6h5x4j( +xqwn u-mpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 103.5 m/s and at an elevation of 157 m7 s csyuw;c1a: drop;c w1s :sau7ycs a package. 5.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from az 6n(vpg;e v+r plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fallingzn 6re;(gp +vv packages will

  A pilot drops a bomb*q,0e x29ouwrg b-x at from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locatiab t9q xur*,w-exog20on of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Eartmoglfl-r6coyp6 - j0( h. 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 would lan6opfc - mol6ygj0-(lrd

  You are traveling at 55 mi/hh)+ /x 3ptafvld yg+qho;1 i4s in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The h ;vp4t+h/)od+gxlqi 1 ay3sfrelative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong cur)e-d (el, dr: +afwac4x+2 teq8lwkaxrent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorborxdl e)++w 2 l4eawdt8(-:ef,x cqaakat

  Your motorboat can move at 30 km/h in still water. How much +rnu(q1lpwvy 6hy1j0.u +cl jtime will it take you to move 12 km downstream, in a river flowing ar0p+ql.y 6uwjh1 vu1nc(j y +lt 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of x0a (v64k( kbvdt-b wcke+r+ f30 degrees below the +x axis. The y compo( (cek4+ftv +kdkabr0xb-w6vnent of A is

  If a ball is thrown winuzx d99+bqrq:y: k +c:h+9 g;fj cjsjth 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 straight line in a direction nor droiye5wxizxf - o9,*x/ g;3dpm54 aby.gfi4 th of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have ybdxox5iz w5,49 .y4xfmpg*aio-f ig/3re; dy ou walked?

  A butterfly moves with a spe.in-1w2gj .4q mopxared of 12.0 m/s. The x component of its velocity is 8.00 m/s. n.qo.- m1xp2ra igjw 4 The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts z*kj qj) dx7cdarn:0w0 sc 9u+a 600-m long shadow over a level ground. At what angle is the Sun eledj79jr00x:a czn*)cwk qs +u dvated above the horizon?

  Two vectors A and B have componenw-f:/aveoap1m 9 5z blts (0, 1) and (-1, 3), respectively. What are the components of the sum oo5apwalm /e: zv1 f-9bf these two vectors?

  Two vectors A and B have components (0, 1) an vum:f :rn5ss;xpq(6od (-1, 3), respectively. What is magnitude of the 5 vs n:;mrufs(o q:6xpsum of these two vectors?

  Vector A = (1, 3). Vector B =tg9 ped4 mhb8: (3, 0). Vector C = A + B . What is the magnitude of :8 p ht4mdeb9gC ?

  A car travels 20 km Westm2ml2xcb;he5* xn6fs , then 20 km South. What is the magnitude of its displacemenmelmx26* hc5n2sb; fxt?

  Three vectors, expressed in Cartesiany +xdtgt v/;m)qhyag2.n9 0 fw 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 coordin )p00pzmfe()/ q8j exv4 z,yhc w/hqnjates, 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 magnitu c t+ec3blutk+v;4f6yqtlf0 +de of vector C = Au;0ftk+ev c+q6y ll3bc tf4 +t - B ?

  A runner runs halfway around a cfdn9t1,hd i6g2i nq0 dircular path of radius 10 m. What is the displacemen,gn f 12 n96i0idtdhdqt of the jogger?

  Two forces are acting 7- qz xn, laz+n+jj(h3w)ph wxg4iua:az88fxon an object as shown in Fig. below. What is the magnitude of8l+znj3wx)aq-zzx xf8 aniw:u 7 ga+ 4j,p(hh the resultant force?

  Two forces are acting on an object as shdk7 o v:p jalk*+/ aket(79cqorog, 7vown in Fig. below. What is the direction of the resultang 7d+oj7lo :ake avrt (*9k, /o7cvqpkt force?

  Vector A is 5.3 cm long and points along the positive x axis. Vector B is 6.pea0 - 8- 9e+0srv5upfxf5 o qdval5rf4 cm long and points at l 5vrp+quar 508oa59p0e- fve f-xdsf$+48^{\circ}$ 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 79 cm long and points :q f 70jt1ot*bkcrbg/at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 37 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 ilj,jfaie .u0w):y :n gnitial speed of 13 m/s from the edge of a cliff. A stop watch measures the stone's trajectory t jl uwj:0a, i)fgey:.nime from the top of the cliff to the bottom to be 4.0 s. What is the height of the cliff?

  A girl throws a rock horizontallf,tft,g f4sx gxh8(,rj p; g-.fq:jzyy, with a velocity of 15 m/s, from a bridge. It falltjf ,fxy rg tjfxp qg,;g-:h,8.z (4sfs 13 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 25 m above the ground, strikess)3n 8,g8 c,6wxtvjr,5t bt(l xvcjqi the ground after traveling horizontally a distance of 13 m. With what sr,sl xtc8gt8 6nj)wq3 vbi(5x ,c,jvtpeed was it thrown?

  A jumper in the long-jump gorek:ku (ivb.ol*-2 o pes into the jump with a speed of 12 m/s at an angle of oki (:l. ekvr pubo*-2$20^{\circ}$ 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 spip/mmr7d * 2qceed of 8 m/s at an angle o/qmidm 2rp* 7cf $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launc7 acz. .w(c.5ddp1mvi*fne8 jfx *ytfhed with an initial velocity of 24.2 m/s at an angle of $37.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched wi wo h9lnmxz j3-6tqi:1th an initial velocity of 21.3 m/s at an angle of $30.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired b yp +r3 jnaygj.-:cni8 xc-ln/;txaiy.t4q7at 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 horizo(bkco)po6q 4ili 9t9t* z)zmh ntally at 20.8 $m/s$ from the roof of a building 45.4 $m$ 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 fireddo 3mh kh8)/uz7vntv 5p.ge+m from ground level with an initial speed of 38.9 m/s at an zm. kn vghem +uhpo378t)5v/dangle of $40.1^{\circ}$ 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 uj) nu1e;h(u6cnwy 9oedfc;. 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 which slows you;y eudw) ;enuj6f c c(h19nuo.r speed 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 5c d2de*yel- sNorth, and is in a wind of 50.0 m/s to the West. The plane's spe*lddc25 seey- ed relative to the ground is

  A plane is flying due South /;z eop0z:z/ny-. hifwr eogap+*lx1($270^{\circ}$) 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 m4;vf0v bz y.dy 6nheb*d pc/,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 movinguc.2 gwo(6v xn 200 m/s horizontally fires a projectile with speed 50.0 m/s inwuoxn2cgv 6( . 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 deiqorh (;76jjirected across a river with a curr ; 6jh7rjioq(eent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat thd,. wt uig7hy3at can move at 12 m/s in still water wishes to travel directly across a river 0.5 km wide in which the current flows at 5.2 m/s. How long will it take to cwty 3dihu g.,7ross the river?

  The driver of a motorboat that can move at 10 hdhoe*gs15 b5 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 t 1dgb h5o5se*hhe driver head the boat?

  A swimmer heading directly across a river 200 m widqsg6v5ziioa51/tr 9 c e reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wat5gzt5i6 sicva1 r 9oq/er?

  A swimmer heading directly across a river 200 m wide reaches the opposite fbsbl s 4xsafa7 4c9+o9jyz5*bank in 6 misyaz f*c4 o459 xb9s+a bfsl7jn 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.17 m/sn+ttz7)vh 4 jq, must aim upstream at an angle of 4zq t)n +7htjv$24.9^{\circ}$ (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)  $m/s$