Which one of the fol2m epvc(38a rwl (.ppprj2n;nlowing is an example of a vector quantity?

  Which of the following operations will not 2r0pw ;c/7cxnxo xkdbsq eyt,6c 942jchange a vector?

  Which of the following is an accurate statementll;l:/*qedrsa 2h k 0 ts:6uop2pkd +e?

  The resultant of two vectors is the smallest when th9;a1o)yva f-m3(4 kw st mcdsbe angle between them is

  Two displacement vectors hav4kup;yn y:7whe magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnip; y n4uk7yw:htude of the sum

  Two vectors, of magnitudes 20 and 50, are rw+oh c;rg:r; ruc:wi 9uxt)1added. Which one of the following is a possible answer for the magnitude of the res wc 1irrhc)gro:xt;rwuu;9:+ ultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dir)3 rnsn 2bhxj5jhd7ea6xsf 67ections th3bshhfr7xn 6 ej7 n2d6aj )x5sat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecta(v sz.n76 ue3 f1c)b-kh8c rowmro n6or is

  Ignoring air resistance, the halfa1+ izr/g (orizontal component of a projectile's velocity

  A ball is thrown with a velocico )ysi(og y8at/ *;axty 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 projectile's acceler 915(-bdb)zobeerst4 f5hnx) )ara dkation az5b t )dx(rkh)-e5oed f1rbn)9s4ab

  A soccer ball is kicked wfx5/x5fmp/zs ith a velocity 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 object is directed anti-parallel to the velkg /lh)mvfo a1ezp/+ s:u4r *gocity vector, ku l g+oag:/)*/rpz1 hv4msfe

  If the acceleration of an object y wwv 8 fjg,8(lz vg)nf-//elk ezzy95is always directed perpendicular to its velocit8 l85wn,9lefg(k-)fzzg vy jzv//eywy,

  At what angle should a water-gun be aimed in order for the wa teh3 h.+rst,lter to land with the greatest horizons et,hh3.rt+ ltal range?

  An Olympic athlete throws a javelin at four different angles above the hor)f*9 is-w iqzgpa 7ds,9fzqsvb6 y1j3izontal, each with thez1p*w 6 asqyvb- 7j9i,qd3ff)ssgz9i 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 forko*c :ad n ,5q+ixczf+ the second time. If the ball leaves your hand with twice the velocity it had on your fi5qc,ck a :*i f+zdn+oxrst throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an ori).aulclqxr sw8;o1b9b kb dhlc 6 545pginal 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 ftlac3n9 jl+ ubr -a jcj.jx4,2qj27xbield goal attempt reaches its maximum height, how does its speed compare to its initial snjrx btj a2cjj qxb+7al-.c9342,jlupeed?

  A stone is thrown horizontally from the top of 5.hkvypt f w/1wwo4o( a tower at the same instant a ball is dropped vertically. Which object is traveling fastow. tvop (w5 4ywfh1/ker when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is drur:f40i,ujf r4gv4ob n4 r,j dopped from the same height. Ignore air resistance. Compare the times of fall of thei4 4r,f v:dfro,4ujng0j4bru two bullets.

  A plane flying horizontally at a speed of 54.7;okn fsf 4x;x2-ex1xq m/s and at an elevation of 154 m drops a package. 6.9 seconds later it drops a second package. How far apart will thenx 2f;1;xx fsoeq -xk4 two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pa 2*.hgt yikm3l4d7 hcgckage is dropped. Neglecting air resistance, the distance between the fggl2yth 7hck .34*imdalling packages will

  A pilot drops a bomb fro:/o ,dpgqgo 5mb 7ah,lm a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal l7 m,hagg:5 dbqoolp/,ocation of the plane will

  The acceleration of gra)m)sfk u n9)zcvity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earn)mkcs 9f)z u)th, the ball would land

  You are traveling at 55 mi/h in the9 etze rb(ggr l50q +r+5yyf;+1 apvny +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The 95n0ge(fab5 g;q+lzt+1 rvr+ pyyeyrrelative velocity of your car to the other car is

  You are trying to cross a river that i,6(8 mh6 yvwt(mumxiflows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly westm(xyhvmu (ii866m, wt from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still wateurm-/eppx l qf0i.f +)r. How much time will it take you to move 12 km downstrim px+p)l.e/-rq fuf 0eam, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an ang,+hg-.km* ryh pf*qv gle of 30 degrees below the +x axis. The y g+vr- fy. ph,hqm*k *gcomponent of A is

  If a ball is thrown with a velocity of 25 m/s at 01c+yu/xgu-*k:ibeui g ny*r 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 directivxv m-/c8y40d l/ojv /i.0ckiiel x3 hon north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east 4i/mcy0eil-.l c dhxo83v ji0kvv//x have you walked?

  A butterfly moves with afj8ao3k2rwv- speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The 2j3vawkor-f8 angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow s0 cvrwq,+i:1 q0xag;/m deyaover a level ground. At what angle is the Sun elevated above the horwaqva,+m /yrx :;c1 qigs0d e0izon?

  Two vectors A and B have components 2c2v3e1jt ( tht/ymou(0, 1) and (-1, 3), respectively. What are tht23m2 vt1jhe /cuyt(oe components of the sum of these two vectors?

  Two vectors A and B have components g)d+/fuw4iyr *7 b-;dxybusayy0 s0j(0, 1) and (-1, 3), respectively. What is magnitude ofuy)ys0+y0- dg/ubris bx7dw4j* a fy; the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A +9-yn i)j/c kmw B . What is the magnitude o/mwj k i9cy-)nf C ?

  A car travels 20 km West, then 20 km South. What is the magnitude -gcrm4gxi3 )yycvc:( p)hj e yk.3 jx )jlvn19of its displacvy jygi):9yc(ec)h1 xv.xpk3 n-l4m3 jgjc)rement?

  Three vectors, expressed in Cartesian coordinate :s*7+ewiv dn 6l+km my3ruqa-s, 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 Car1( o-wiwmzcwfc+ 0 l-ntesian 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 vect-vyw5(yrf4m f ur7 h7vor B = (+3.0, -8.0), what is the magnitude of vectorf5y7m-4 vurw(hy vr f7 C = A - B ?

  A runner runs halfway around a circuorfc,:jtq x*j sp8ow(07 m:g glar path of radius 10 m. What is the displacement of the jogg jf:rg sqm(7oo:8 *p, jgxcwt0er?

  Two forces are acting on an object as shown in u3lq3fk 27as, pp2r wef8cx7lFig. below. What is the magnitude of tl2l r3 pp3f8ca x,kqwsf2eu77he resultant force?

  Two forces are acting on an object as shown in Fig.rm5w00dynh zw cfh78e h(cb;8 below. What is the direction of c8(wdhhnh by cf8wrz050 ;me7the resultant force?

  Vector A is 4.5 cm long and points along the positive x axis. Vector kkg09 qjtc)z* B is 5.4 cm long and pj *0ktg )c9zqkoints at $+27^{\circ}$ 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 73 cm long48 7top*gby.l6v r atmf;e6k h 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 32 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 29 m/s;jay*vbt qg- 8t+8fw m from the edge of a cliff. A stop watch measures the stone's trajector8f8tagm j-yq *t w+b;vy time from the top of the cliff to the bottom to be 3.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 1dz/x4 a+ cg0nch:74jhg -esny 9 m/s, from a bridge. It d/c ah7+ cyg40nsz: gn-4ejx hfalls 29 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, strikqppi 8-4k k5oam d)bu6aee)v/ es the ground after traveling horizontally a distance of 1p a k54/6)-pa) 8kibqoeume vd8 m. With what speed was it thrown?

  A jumper in the long-jump goes d +,k,plsvs d460b hyninto the jump with a speed of 12 m/s at an angle of hssvd p+b kn 04l,yd,6$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes ak2 wf0hs1jef7 3 nt*,cn)pyhgyf,g1into the jump with a speed of 9 m/s at an angle o n ah)ykc3 ,pw1tfs*efn70j,12 gfgyhf $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launcx6x,d wst*8i+uz+e xk hed with an initial velocity of 55.7 m/s at an angle of $41.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 43.8 m/s ;x+ya4)bnx wq at an angle of $32.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an4 nujh+,wfc4byu1-2,b*y m lwkc lck :gle 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 22/i vpxl:lwha +:3pr 0(6jtkbh.2 $m/s$ from the roof of a building 35.1 $m$ 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 40.6 m/s at an m28yvhtw- t*awh v3+uah3vtvw -y+*8mh2u wtangle of $41.0^{\circ}$ 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 at a velocity of 4.0 m/s. If93 ekchq,g9node ,tb0 you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, th q behk93e,d,0 cto9nge time it would take you to finish would be

  A plane has an air speed of 200 m c2i-cja)nz -m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relativec2zmi- nca -j) to the ground is

  A plane is flying due Soat0/4c x,syid f2qpz5uth ($270^{\circ}$) 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 headed wence4+ a*uz)h.a pzk*r 0 ay1x,kdd7i0dmd ($30.0^{\circ}$ 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 projectile with sp/*gjpqub uolu 76:q)peed 50.0 m/s in a forward dire b6/ pulu uqj)p*o:q7gction $30.0^{\circ}$ 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 across a river with a qlk+;ln19owu my ou(cb;wo(+ current of 6.0 m/s. What is the speed of the boato ( mll; +w(now+bcyk9;uqu1o as it crosses the river?

  The driver of a motorboat that can move at 1 0ldfm4k.rhx9em *+x /hh9 7c yu1lisy5 m/s in still water wishes to travel directly across a river 1.5 km wide in which the current flows at 7.1 m/s. How long wmllx 9dck1h 0 smf/u7y.*e4r9i+xhh y ill it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to , dk5vt qku61.nou,7+dwreo ytravel directly across a narro t k+y,.k6wv dq1uo,o7e5unr dw 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 oppoh0 h6c l5r+rgx5 w7supsite bank in 6 min 40 s. She is swept doh g5xs6+uc70 rl5 rwphwnstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the op1 qzro;c 1lx:mposite bank in 6 min 40 s. She 1rlxq;c:1 moz is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.0hvuxgo2 01x/jeec8 o;a;hp .t t d1-lw4 m/s, must aim upstream at an angle of- egtp w118tv;o;le c.0d2ojaxx/ huh $25.5^{\circ}$ (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)  $m/s$