Which one of the following is an example of a vect4u w9,)yf-f2; xjwi8n gey1ot rqt g(yor quantity?

  Which of the following operations will nd es.u8vfg(lavlg10 8a8 bo7z ot change a vector?

  Which of the following is an accurate statefi7m, 28mer p8hh- c/uuhpa28s-s7uko ik n g,ment?

  The resultant of two vectors is the smallest when the angle between them0uxvu/k,n ll0 is

  Two displacement vectors have magnitudes of ;oetn6 f0(aofqb/ as- 5.0 m and 7.0 m, respectively. When these two vectors are adde(qfaobtnf/s6 e -; 0oad, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which onp yttr-79(jd og*l3jqe of the following is a possible answer7lq3*pd-tro y(j9 j tg for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions v8 (dqs gi5;yctci8qdgy (;5sv hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowu,tiv;7nc* hdn vector is

  Ignoring air resistance, the horizontal componh f0dxqscw/0+r,cj l+ent of a projectile's velocity

  A ball is thrown with a veloc+y 5c6;j k1zs3zcziq uity of 20 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 pibw) f:7oqsfi3w8 ph7rojectile's acceleration8b3:piff 7hqw 7si)ow

  A soccer ball is kicked with a velocity of 25 m/s at an g jo+yos( e8i.:) ifwwm:yc*cangle 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 objel r.c (h0c(avolz l+f6ct is directed anti-parallel to the velocity vhccf( l.l zl0(o6va+r ector,

  If the acceleration of an object is alwa wd-9v5w u(rkan*pix; ys directed perpendicular to its velocity,w*nak-d9( r p;i5vwux

  At what angle should a water-gun be aimed in order fq4 hpsr) przndf3r)1+or the water to land with the greatest horizontal rangepq+sr) zdrfp43n hr )1?

  An Olympic athlete throws a jfl:84fc )o e(w lbpc.wb:ko:wdo.6 hdavelin at four different angles above the horizontal, each k:o)dbef.bowwcf6:dl l wo .c( hp4:8with 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 secondq )g4ns6fs- dk time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first sesfgs )6dqk4n -rve) would be

  A ball is thrown at agg c+n:n*wr; c)jlfv8n original 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 maxim u( r;pblez1w vlm9-e0um height, how does its speed compare to its initial speed?l0eu ;9- lpbr(mzw1 ev

  A stone is thrown horizontally from the top of e6;q(xv0 esfca tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the levev;csfex (6q0 el ground below?

  A bullet is fired horizontally, and at the same instant a secd bzb( m6rya9dpf79,iond bullet is dropped from the same height. Ignorzrd9b7a ,9(m y b6fpide air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed ofe+*o(yf)nm n1p o iao4 90.5 m/s and at an elevation of 240 m drops a package. 2.4 seconds later it drops a second package. How far apart will the two packagesni+f)em(y41o * opano land on the ground?

  A package of supplies is dropped from a plane, and one second later a seco3nw9hgj7o1b j l2.b*s7ll hfg nd package is dropped. Neglecting air resistance, the distance betweenogl3 h9s w j g.blnlj2b*17fh7 the falling packages will

  A pilot drops a bomb from a planab io0adur 2.6wjv;z yh 9m0q/e flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits 2ua h9yri 0v6zod 0/j.amw b;qthe ground the horizontal location of the plane will

  The acceleration of gr b23z(pm5oynmavity on the Moon is only one-sixth of that on Earth. If you hit a basebalz 2mpn3o5yb(ml 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 +70d8xsw n 835-ovrozxafyr8gx axis relative to a straight, level road and pass axrg nz58adro8f0 w8 s3yoxv7- car 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 wo+o ica, nzlc6qgr;puc09y: 7vl ;v8qith a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your staro alncgqlcvo6 cuyi; 0q;z79r p v8,+:ting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much ;:l+ab/w iv* fve:z96lh puugq/) bju time will it take you to move 12 a:lfewv9uu vh6b /b+:/;lipq)jzu* g km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degreoec17.cs9xaeu/ 5jjlh)7 nd f8n: ziees below the +x axis. The y compon7n)/elc5:897sua zho. i xefnje 1jdcent of A is

  If a ball is thrown wi)rdd/zzur3*yu-y rs c + k *w+v(xxin1th 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- + s8v3kl8dd gccla4a in a direction north of east and you end up 28vs+4kl l-g3a dad8cc.0 km north 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 of its velocity iswf2)t:3vj ukf2gd 4ra 8.00 m/s. The angle betwevdfa3g2uw) 4frj:t2k en the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shad zb9*kf, i3mivh9r+e()bezdz l z-. boow over a level ground. At what angle is zzi (bod rh)efl3e*z.v m9 9ib-zkb, +the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whaifq*e 5w wo3w5t are the components of the sum of these tw w5e5q*wfio w3o vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respecttwr t9rm lg+ +v-7g71jus d9q-wbu:arively. What is magnitude wvg rgs:7+t+uu 9mt--97wlrqrab1jd of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Wzukmyblj1 i0p( 01n1 xhat is the magnitude of Ckj 11yl0xp bn 0(zumi1 ?

  A car travels 20 km Westo+tumcqxrgd8* dm3 8 : zb*tm1, then 20 km South. What is the magnitude of its displacementmt* 1gm3 c+ 8*tb qdm8o:dxruz?

  Three vectors, expressed in Cartesian coordinates, aev 6j*gov,- vk.pwa*mre
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 -qn6qc,ylc za; v40 v znl:t1hcoordinates, 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 magnitude wkqty8, zj3k (i)zu/kof vecto,j8z z t kkqku()y3/wir C = A - B ?

  A runner runs halfway around a circulati:r:p8*nf+ jclxg2q cfo g 39r path of radius 10 m. What is the displacement of the joggnti8*pojc: qc:r f92fx +gg3ler?

  Two forces are acting on an object as shown in F4;t;isup ,n os7pn nb*ig. below. What is the magnitude of thi 4u bnn;;,*pnpsst7oe resultant force?

  Two forces are acting on az bxnf027e bnvu2adw-gsd gsl((173 pn object as shown in Fig. below. What is the direction of lpzs2a0(d 7d1xvu3-2nb (n gfe bs7 gwthe resultant force?

  Vector A is 3.0 cm long and points along the positive x axis. V:z3yhi- wgb c7ector B is 8.2 cm long awic7y-3zh :g bnd points at $+25^{\circ}$ 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 66 cm lonjzl-vxm+-raaowi6 t mc4e5 tc*ks4-) g and points at $30^{\circ}$ above the positive x axis. Vector B is 23 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 14 m/s from the edge ost;m y mo 6sug4*.af8tf7ryqk6 7cw- zf a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.2 s. What is the heot6.ucfrfqs7y-4t7z *86s wyk;m am gight of the cliff?

  A girl throws a rock horizontally, with a velocimku funkf0u 2/os; 4i5rqx c1)ty of 7 m/s, from a bridge. It falls 24 m to the wcu k4fx ;nkqu5 1/ 2riu0ofms)ater below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, strikes the grou.gk 6f 8 5etp.thm kj,d5o6bobnd after traveling horizontally a distance of 14 m. With what speed was iomt6bhk,e f5jg8btd k..56p ot thrown?

  A jumper in the long-jump goes into the jump with a speed+op ,,rukqykbb 5 6r7t of 12 m/s at an angle oo ,bqbu7yt rp6k ,5r+kf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goekrq;( hsla5 wl( 0ai,ls into the jump with a speed of 15 m/s at an angle 0l ,ih(rqa5 ;ws(klalof $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched 8-jfkgvibs +(with an initial velocity of 44.1 m/s at an angle of $38.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launch9,hi0+v(*mhu wxxj3ks9 px l j1x/qn ped with an initial velocity of 41.5 m/s at an angle of $17.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of wz/+c3nca-f 0 s y8dg7tkn/wi$30^{\circ}$ 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 2r zr pkh+ z mra.)yo*wa;2i5/ne:jh2h1.4 $m/s$ from the roof of a building 41.5 $m$ 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 ground2r7po- ppa xzo/hg n6/ level with an initial speed of 45.2 m/s at an ar xp-oghp/2oa z67np/ngle of $45.4^{\circ}$ 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 150osmr (:g.(hnv 0-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 your speed by 2.0 m/s, the time it would take you to finish would:( vsmrn(.ogh be

  A plane has an air speed of 2004nrq8 jshb4(.sy+ ewd m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to th(jybs q4r+e4 sdhnw8 .e ground is

  A plane is flying due Sout28+spf +c y4kfxafq2mh ($270^{\circ}$) 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 8 zs j1t(cfcc3z,n3iiis 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 horizontally fires a projue 0/hg:sz qv30 sb2: 0kbpetzectile with speed 50.0 m/s in a for:gq/0ts 0epz 3 :u0sbzvbekh2ward 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 a+c xokt*yu8 .ocross a river with a current of 6.0 m/s. What is the 8u ockoxt.+ *yspeed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in st,x1 9zxkzfp8 hill water wishes to travel directly across a river 1.5 km wide in which the p89hz 1kf z,xxcurrent flows at 7.2 m/s. How long will it take to cross the river?

  The driver of a motorboat thatcrl4qc1y-wi i ik1yf y6r)j8i7: ;tzw can move at 10 m/s in still water wishes to travel directlyykw)ctl r;qy4-8y7ji1iwf :czi i61r 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 oppfo:+ k9s l-d0 nl.jgprosite bank in 6 min 40 s. She is swef9odl:-kp rg.0njl s+pt downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches thw :,qf rh3m4bhe opposite bank in 6 min 40 s. She is swept downstream 480 m.,qhrw 3hfbm4: What is the speed of the current?

  A boat, whose speed in still pb cfrh(a g ph;8gxras1*( c08water is 1.66 m/s, must aim upstream at an angle of(*psg ;cgrhbpr 0a(xc8ah 8 1f $21.6^{\circ}$ (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)  $m/s$