Which one of the following is att s75t:xn1ssz .- zson example of a vector quantity?

  Which of the following operations will 4 sym*dln, ygjt h0*j25ktx ,so+ywr5not change a vector?

  Which of the following vu 64; tlj29tp*6sztkcv+z zkis an accurate statement?

  The resultant of two vectors is the smallest when the xo:pzip0 b*k,angle between them is

  Two displacement vectors have magnitudes s. sfzr )dmkqo)r- - syh(w7(oof 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of s r)ds7z mhf(ywo )qokr(-.-s the sum

  Two vectors, of magnitudes 20 and .9no plhxt9j* 50, are added. Which one of the following is a possible answer for the magnitude of the resultant ox.l9*jpthn9 ?

  Three forces, each having a magnia9z51++g cq4a5 nlgrz8wsc dstude of 30 N, pull on an object in directions that are 5+4 szr81+5agcg azn wsl dc9q$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the9 2qxrei;o +u i(g2 rjbc0hx4w unknown vector is

  Ignoring air resistana y/b (79owjsxce, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle o3f 7.vx1 zeito- :e 5zqsp9cehf $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, tf5j+ t3w8to+t i-0 kff9mi,wkhng0ls;c l ju7he horizontal component of a projectile's acceleration sn+;ff gc3,l7thut9+jil-o 8w0j k5ikft m0w

  A soccer ball is kicked with a vg7qz/n:v col 1b qc:i4elocity 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 of an 8)o* 3vb-s9flzicy l+8thb hnpj:ib.object is directed anti-parallel to the velocity vect 8) l:* bhhb+3pn9tfzsjylc i-vib8o.or,

  If the acceleration of an object is always directed per0a/rgli9j t7c 21s lampendicular to its velocitl acj 1slmt2 ra/9ig07y,

  At what angle should a water-gun be aimed in ordelqs/4jot *1mvr for the water to land with thjl/ tm4 o1v*sqe greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizontjm(n+ +n.+)kate lkmsn;xu b ;al, each with the same speed: +xe k;snj;tkm(l aun.b+m n+)$30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 ha2 rnx0g:yn8zhnd with twice the velocity ngzxh:0r28 ny it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an or002j lgme -gvriginal 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 f(0lpf5 aq oy* sz,5/kjkaf vi5ield goal attempt reaches its maximum height, how does its speed compare5p(vol5s y0a/zfkj , kai*5qf to its initial speed?

  A stone is thrown horizontally from the top of a to+dl. (7qxys.z d0twggwer at the same instant a ball is dropped vertically. Which object is traveling faster wh 0qxyd7sgz.l(d+w.tgen it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second buu wych-3 5o( zmi7- 0 xx4rey,ae2jdhsllet is dropped from the same height. Ignore air resistance. Compare the times of fall ohx xzsd5 4cew02 3o y,j7 iume--(haryf the two bullets.

  A plane flying horizontally at a speed of 61.8 m/s and at an elevation ; h9bpt:h :yyjof 234 m drops a package. 5.9 seconds later it drops a second package. How fa :bh;jyp :hty9r apart will the two packages land on the ground?

  A package of supplies is droppe xyfa 9en hnte-.5ye:9d from a plane, and one second later a second package is dropped. Neglecting ane- 95ehen :fay .9tyxir resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at g76./hwl(b 3dm l,f dy2bve pn s9)toha constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wsodlevtb 9 6n(hw,)7/l .y2 3bdfphgm ill

  The acceleration of gravity on the Moon is only one-sixt1o kx ip;w(l*fu:k ,cj.hae6 uh of that on Earth. If you hit a baseball on the Moon with tfk aux.ch6i;*jk1w u,:e( lpohe 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, leveldz 5t;7n6lnqmra u:2e road and pe62zrqdl;5 tnau:n 7 mass a 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 soua hoc lhy9810:obzt 4ya8deq)th with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from you4 y)hq:ca ooe18l b tdh9zya08r starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it tag axjme a8kuc6 e+01qzxlv+kl*f0 ;p2ke you to move 12 km downstream,8g aq je16zvx0a c*+2klu+lme;k xfp0 in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below t+fjn1x( srryn ls* +p4he +x axis. The y component of A inn +p lj1rsxyrs(f4 *+s

  If a ball is thrown with a velocity oep m-ti)g*)j 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 end um-6oz9f,x,n de av;xwp 2.0 km north and several kilometers east. 9zvwxof m-ae xn6,,d;How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 ykdf33v lpjr( lfx m(g f/,1/s,ukqw5m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of (fy1q/k5r/wf( l gj3k,fms ud,lp vx3its motion and the x axis must be

  A 400-m tall tower casts ak 1h21qdm1 ozy 600-m long shadow over a level ground. At what angle is 1 mdky1zh21qo the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1hozbx6 1lza y5xm;*b7.t cj d3, 3), respectively. What are the components of the sum of these c. l;by 1xzo7t6ja5dzm* h3bxtwo vectors?

  Two vectors A and B have components (0, 1) and (-1,6xku.,7d:3jicz ap bpx1o8xz 3), respectively. What is magnitude of the ppb7xox,:.a163 u8c i jdxkzzsum of these two vectors?

  Vector A = (1, 3). Vectopq; h, yt 8oetdm,5cfqel(+g )r B = (3, 0). Vector C = A + B . What is the magnitudeqt8;goemch ), 5fpel,d +(qty of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude o;1pv lwnj7 czsei::uvgdk+.a) o 9+wz f its displacementug iv++n17 a: 9;.:vzwclp sewdo zkj)?

  Three vectors, expressed in fk gfx 0,j249tp xuo1oCartesian 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 Cx- r 91j9hcx2z5r gt1j0m-ktrsb(ytwartesian 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 thejui53n 75ztc0pxs8wwwd 0 0b 3as h7sk magnitude of vector C = A - B ?z 0p 35h 8 uxbitanjw0ws750s7swkc3 d

  A runner runs halfway around a circular path of radius 10 m. What :dif-:z06v /,psiykpmyx.q)k( s k feis the displacement of the,k zq ppk:yid- k).6sf0e s f(y/xm:iv jogger?

  Two forces are acting on an obj35teaxb h(-akect as shown in Fig. below. What is the magnitude o5 (abxht3 ae-kf the resultant force?

  Two forces are acting on an object as shown in Fig. below /)b clif-ram ;w)puilo67yp0 . What is the direction of the resulfura0) 6/)cii-pwmoyblp 7;ltant force?

  Vector A is 3.7 cm longq0 lmh rai w ijy3o6l-5ge5b** wr(.uz and points along the positive x axis. Vector B is 9.3 cm long and po5 -*05b z.i3(awejw6iymllr o g*rquhints at $+54^{\circ}$ 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 57 cm long and points at 3 pabaux bdn*ede1446 $30^{\circ}$ above the positive x axis. Vector B is 18 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 initiw/tfp3kpo ut /uh:( ,kal speed of 23 m/s from the edge of a cliff. A stop watch measures the stou/o3f /:hpktk(p wu,tne's trajectory time from the top of the cliff to the bottom to be 4.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a bridge. yw,3k3pre )*up am,har w2 e*f It falls 23 m to the water below. How far does the rock travel horizoeerf,a23)rh 3ww*up,mak* yp ntally before striking the water?

  A ball thrown horizontally,,ys gt yycrr1e .n8n+ from a point 27 m above the ground, strikes the ground after travelinygr t1cy8rn, ny+es.,g horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump wi8zguz4,h.gqeoz * lb .th a speed of 12 m/s at an angle of .g 4,z.*gqbloz8zue h $20^{\circ}$ 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 speed of 1-3 g8jl4 bk duywqj/x)0 m/s at an angle 48 x)b/g kq3wjy-d julof $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 58.1 m/s at an angle of (,9ma ctevqq4t+ s6hp$18.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloci ogf2(mr+ p)b.g1a dphty of 40.3 m/s at an angle of $28.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fib) y:o;a1z k.dcvg 03iynzvkp-y7) bered 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 horizontally r7lu*nhg*o+ ro a/)dcat 27.1 $m/s$ from the roof of a building 58.3 $m$ 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 u l:-/gld()uhm te rap-v17th from ground level with an initial speed of 67.8 m/s at an anguh1l 7lp-t gaert-(vh):mu /dle of $43.6^{\circ}$ 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:f tlsmym 5uc9s) )t9e0cy yj;), 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 sloj ; lyeucc0sm:9tt)s yy95mf)ws your 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 North, and is in a wind of 50.0 vimn**e a 5ml6m/s to the West. The plane's speed relative to the ground i*ei n6a*mm5vl s

  A plane is flying due South (f i+o,,l c9u8w)rep2j:vx0c yu yt-ji$270^{\circ}$) 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 speyva8 9+m rio+8htp 9gfed 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 +pjk/ 3d00oxbbp9t: u b7uss53 dtkgh0 m/s horizontally fires a projectile with speed 50.0 m/s in a forward directt3gpbsdhj9+o 5 p: 0b/bukxdt0uk3 s7 ion $30.0^{\circ}$ 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(ab*vf m* 8 ,1qdbt*8; ae hjad p4hzxla;8qly across a river with a current of 6.0 m/s. What is the speed of the boat as it cy 14, bjzxq8fab8*vp; d8d*la mth*aeal; q(hrosses the river?

  The driver of a motorboat that can move at 13 m/s in still water wishecjm .8sq 8,/amd5)(etgx udah s to travel directly across a river 1.9 km wide in which the current flows at 3.6 m/s. Ho().gxdcaq8e ut8,mjsa5 h m d/w long will it take to cross the river?

  The driver of a motorboat thabba5 kny(-nlo 9f xo75t 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 drivln7b-xo k 5 95bfao(nyer head the boat?

  A swimmer heading directly across a river 2005ibm :hp l-g20e upq o,3p1.qh,azpxm m wide reaches the opposite bank in 6 min 40 s. She is swept d ,: q2p m0ioqzhh3pp,b5g.pm 1uea- xlownstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 2:n w)xxm 1dgt;z zf3p 30h7vii00 m wide reaches the opposite bank in 6 miv;7mwp0)i3g1 n:xt 3zxfd zihn 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed ,ydj v4fw2nr1,pol 7e(c b2i kin still water is 1.47 m/s, must aim upstream at an angle of4fl rd okc1jnwb2,72(e,vpy i $26.0^{\circ}$ (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)  $m/s$