Which one of the following is an example of a vector quantin 0h0al f*ng/rty?

  Which of the following operations will -e 7sqo;s z3 (koxp0kgnot change a vector?

  Which of the following is an accurate statemencso 4v.snh fyj, 2u)tjnj-+u1t?

  The resultant of two vectors is the smallest whenvax3 5yq.k de 7dr jr4i;.m8em the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, x4pb0il* p )yerespectively. When these two vectors a0bp*) lyxeip4 re added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whichlppxyqsmu 9u.c;(:2f one of the following is a possible answer for the magnitude ou sc qfx( .2;9p:luympf the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directionsp.tp n qps)d 9,1pwj2r c*ake( thp )e2, (w.njk sadc*qrp ppt19at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the 84bjjbt )-og 45e p-fg ofu9hpunknown vector is

  Ignoring air resistance, the horizontal component of a 8jq1d j;wj/hn /we2ny projectile's velocity

  A ball is thrown with a velocity of 20 m/sehmd5/ sjc k(9 pfp1g2 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 a4 jw4ww*j p*s8qp9wzq ccelerationjw48zw*ws 4p9q wj *qp

  A soccer ball is kicked with a velocity of 25 m/s at an ovy2mz+ 0g r/rangle of $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vecqky2* bf;sh:bc3oa ;w tor of an object is directed anti-parallel to the velocity vecto kh23s;;b:oy *w bafcqr,

  If the acceleration of an r2cev+i. u5 uvellky9+ ij,c5 object is always directed perpendicular to its velocity, 5r+i e,yl2v5e+c juv.cuki9l

  At what angle should a water-gun be aimed in order for the water to landu psp+j*,o* a)gs htch1x:fp4 with tht :ox,hh*pspj*cg 1+p4)usf ae greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles abovd 8(f3pwg(gm n-jp-mve the horizontal, each withpmw-g8gn(d- jfvp3 m ( 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 leave*r,y(ul2hr6ce, fn 1erf so rs-( blhf6 ssy6+s your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serce hs* ff6yfrl(nr1h6ue(s+r 2bs6o, slr,-yve) would be

  A ball is thrown at an original speed of 8.0 m/s at ay+q8r,b/ z exwn 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 goaluffbx te/1) 8l attempt reaches its maximum height, how does its speed compare to its initial spe tlffu/x)b1 8eed?

  A stone is thrown horizont(:/aswq1 lweo0p:cil yqdv x5x49p v6ally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hiqdxey: qwp/9cl5wlo :i01( 6savx4 vpts the level ground below?

  A bullet is fired horizontally, and at the same instant a seconduiy;fd/3-w 5yclfw 0:1iimn/ n 0xqk v bullet is dropped from the same height. Ignore air resistance. Compare the times of fal-:lyfuv/i10dn;yn wf m3xck 5/0 qw iil of the two bullets.

  A plane flying horizontally at a ua)gru hfiv()(k.mlr pk0c 7 9i:i6sn speed of 89.5 m/s and at an elevation of 272 m drops a package. 3.3 seconds later it drops a second package. How far apart will the two packages land on the groundrm(6pcka9) rihi.ksil gu :vu)f0(n 7 ?

  A package of supplies is dropped from a plane, and one s* rx;ag.xsu1i a3mwk4k1;f i gecond later a second package is dropped. Neglecting air resistance, the distance between the falling packages wila;1;ig k .f1riasg4x*x wmk3 ul

  A pilot drops a bomb from a plane flying horizontally at3v1 8gidg(c) j s- kd(vp0huym a constant speed. Neglecting air resistance, when the bomb hits the ground thedc j ivgmkgp)v u3h0s-d y8((1 horizontal location of the plane will

  The acceleration of grak avfw- 3zbv;(vity on the Moon is only one-sixth of that on Earth. If you hit a base afvwz(-;v3k bball 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 r(v1xyvorao o(x* z 9*.tr9jlrs4:fy fj v*5duelative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocit9 (oaso:xvdvfl*ruj 1.x4zj yy(v **9of5 rtry of your car to the other car is

  You are trying to cross a r)o q8ha)/3*yd b gwvta,onoy *k: e1abiver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the3 w/o1,*o:qt n8)yoved*aghaay)bbk 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 ta)ed71 t j59xlx 1j; f,i.lirsrew0jqd ke you to move 12 km downstream, in a river flowing at05rxl jex qt1;delf1ii sjw97d. )jr, 6.0 km/h?

  Vector A has magnitude 8.0 m at an 5mml (t(puc mgqb-y,6 angle of 30 degrees below the +x axis. The y component (mp-m l 6cg5b,( ymqtuof A is

  If a ball is thrown with a velocity of 25 m/s at an anaqnc(9qb wwqtz3e7 i+k *a;7wjf/p) dgle 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 a1v ,jhos*gogj) 1a+rw direction north of east and you end up 2.0 km north and several kilometers east. How many degrjr)g1,g swoj 1*o+vahees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x c.k xv6)u.6 gvx*ji+if :yhh vmomponent of its velocity is 8.00 m/s. The a iu*.6hxkig hvm :).+y6vxj vfngle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At wha up agb:zu p. 4ms+7dhz(jhfie *n7.;et angle is the Sun elevated above the j(.+f.i*7zn;mpgeezu4 :b d 7u pah shhorizon?

  Two vectors A and B have components (0, 1) and (-1, r0uhvg906y ls 3), respectively. What are the components of the sum of these two vectorlh0u90 v yg6srs?

  Two vectors A and B have v-e6 uyqwi2e-components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of the--e wv 2iequ6yse two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . (h)rn9 -xyj cqzc06 hk What is the magnitude of C cjyrk cx)90 (zhqn-h6?

  A car travels 20 km West, then 20 km Sout: n usj5vr dg0:ykkoh5ww*-1bh. What is the magnitude of its displaceme o50*k-wkjnyv:hrs d15 g:bu wnt?

  Three vectors, expressed in Cartes (kv/p50hrdth ian 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, expres1j4q;r x kjf.2vb idf.x +vf4nsed 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), w m +65pqao+xadhat is the magnitude of vector C = A - Baqxo 56mad++p ?

  A runner runs halfway around a circuj 4c(/joqkr;s lar path of radius 10 m. What is the displacement jqj c /rks;(4oof the jogger?

  Two forces are acting r x.2oe s*n8u hbln8 cot;;dc6on an object as shown in Fig. below. What is the magnitude of the resultant forc8;donelcxnc* 6o; 2b8r h.uste?

  Two forces are acting on an obje* tfqi42em( 2zbmyplbdd + ;u:ct as shown in Fig. below. What is the direction of t2(qzlbu 2peby*;+m f m t4d:idhe resultant force?

  Vector A is 4.6 cm long and points along the pos ja v.iuelt,*3w *d3nsitive x axis. Vector B is 7.1 cm long and points i,.ts3aued*wnl 3v*jat $+28^{\circ}$ 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 65 cm long and q -vj*/crq+i+ 1ck a (b*vjazupoints at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 28 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 27 m/s from the edgemsh(arz 2oq ;swe-5ay0h o t3gp,l20f of a cliff. A sog0eh t 2p o,al( y;q-0zhs 2f53rsmwatop watch 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, wit)ca-qgnxw1h3uu un36 h a velocity of 20 m/s, from a bridge. It falls 17 m to the water belo6nq 3u3wu un-c gax)h1w. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally frome*8 dxb:l;wc6/t c(1ndqqdz;wq 7nz;bjik y9 a point 21 m above the ground, strikes the ground after traveling horizontally a distance of 13 m. With e*y;w8dx d6dcq/nq ;k(zjt:791wi b l;zbnq cwhat speed was it thrown?

  A jumper in the long-jump goes into the jump yi 64.4ccx acswith a speed of 12 m/s at an angle c 4sci.6cayx4of $20^{\circ}$ 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 ttk/w.:.s zjg jump with a speed of 14 m/s at an angle of gtk.w:sj ./tz$34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 54.3 v e*lvqd)+ewzr9 b5 5pm/s at an angle of $41.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initirl;6+2 wvj-dqnny a g*bag)* wal velocity of 35.2 m/s at an angle of $19.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fiv0gni/-54c2y;cajhx ifq2s jswre +7red 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 horizo my 1 3xu; z.ksq*mfnlx4s89oa6(ivffntally at 27.2 $m/s$ from the roof of a building 47.8 $m$ 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 4g l,:2)ib0ar4;ax pa a*w uabf1.9 m/s at an ;2xw)bfa ba,u0* rgl :paaia4angle of $37.4^{\circ}$ 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) av4u uu; z8 cbb;w1emma;/y1e, 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 which slows your speed by 2.0 m/s, the time it would take you to finish wo;by4ub8 vz ue;1/a; mum1 aewculd be

  A plane has an air speed of 200 m/s due North, aai fiix8-u 97snd is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground ifi79xa u8is-i s

  A plane is flying due South b:el+* qul 9/pln+ifq ($270^{\circ}$) 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+o,d uxqvhdf4k:lkl 3ejg 64g *0(le:ar pe7 v 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 horizon9vfos d/t /hlo8;:nga9 ohr q 07gps+qtally fires a projectile with speed 50.0 m/s in 7s8a t phsng+/90qoo/g;f9oqhvdrl: 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 dired: q de (oj 69)ornz/m9a4svpccted across a river with a cu rjs(m9 co/:a9z4 d)pd q6ovnerrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can movbjs; sw1rh1 yc3*r4p oe at 9 m/s in still water wishes to travel directly across a river 1.7 km wide in which the current flows at 3.3 m/s. How 1c;1hjrys *s w ob43rplong will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in ;u yj1ed,jw)5(p bdxvstill water wishes to travel directly across a narrow strait in which the current flows v yp5b;wu( d),x1d ejjat 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directlyof3*041fct gq98 6aph ylrlrt across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept01tq843*9loty frha prgl6 cf downstream 480 m. How fast can she swim in still water?

  A swimmer heading dizln:-n hn2h8r rectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the sn8rl:hn2hn z- peed of the current?

  A boat, whose speed in still water is 1.73 m/s, must aim upstream atufm(mkja4 hd3.vtb)u 4fm3p*4c k s 2l an angle of 4j ( mk23lf*.katvmc3puf4bhd um)s4$29.2^{\circ}$ (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)  $m/s$