Which one of the following is an c zm5e *yfc*0oxx- n ;/1f rrgk2gxir9example of a vector quantity?

  Which of the following oper arm3s6p a4hezr7 x5o-ations will not change a vector?

  Which of the following is an accura1ogxd,p -lvly6x h-3p te statement?

  The resultant of two vectors i9jgped; xa;d).s5z ei s the smallest when the angle between them is

  Two displacement vecto54gtrw-ij*; in5bhr hrs have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, h554jin; tbrhgir-*w the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, arem;eckiy0e *foc-po q1 h q((cub)ly(/ fnv /r+ added. Which one of the following is a possible answer for the magnitude of the resultant?+;(1efu cf(h(/ccopq iy0 */r-e)novkqlmby

  Three forces, each having a ;g68eg,*eywe3lhb.q 0af. f crbgb b:magnitude of 30 N, pull on an object in directions that arbe06w*bbgyfgqb3f l.: h;,rgc.8e ea e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkmzm dx:y./ v-lnown vector is

  Ignoring air resistance, the horizontal component of a projectile's veloxuc*9 v7e)b*ep;u(zhh g ox/ ocity

  A ball is thrown with a velocity of 20 m/s at an angle zbecyyx)+, :q 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 accelerati1 (as1hpl5ha 1j bjhz8on1shaa1hjbjlzph(5 8 1

  A soccer ball is kicked with a velocity of 25 m/s at an angdayxr wkgt .5x785jor3,whw,le 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 directedivmkq,1hhx 2,l.1oah, hvo :w anti-parallel to the velocity ve2oh,xo 1:k 1w., mhh iva,hqlvctor,

  If the acceleration of an object is always directed pwpf 4 u w-rfj+:m6aclxsz6f- (erpendicular to its velocitp fwarfc:l6(w6u4f-x+m -s zjy,

  At what angle should a water-gun be aimed in order for the wa0adcziw3m;* yter to land with thecd zm0a3yiw ;* greatest horizontal range?

  An Olympic athlete throws a javero qi*h2 ,3x1yxzbw1dlin at four different angles above the horizontal, each ,o1wi*xqz3x 2 hb ry1dwith 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 leaves your hand xuctrj /v/n-: with twice the velocity it had on your first throw, its horizontv-nt/ur: xj/cal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at ancc:o0wj* 9oxi9x3-2ejkso yx,a i(fm 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 maximum heiek4j +: 1dbbwwght, how does its sj1+wbk 4 :ewbdpeed compare to its initial speed?

  A stone is thrown horizontally from the top of xrod+w*i 5.*m ic+jmaa tower at the same instant a ball is drw x*ica*m.rjo+m5 +diopped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same in :g*fh kh;d1itstant a second bullet is dropped from tkitg;h 1d *h:fhe same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally 1 mk2q yw fjei6cn/p-opa8.bhz ::t+dat a speed of 113.2 m/s and at an elevation of 226 m drops a package. 5.7 seconds later it drops a sk2aifhw yno mqz-::61jcp./+ bdp8etecond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, af rri + o4w6nmacu3g39nd one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages wr69ac+3 uomfn 3wig4r ill

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Negdv wa:oza9y;n9/ qar )o: n00bxi o.kmlect00 a;q.ar:imyb vo):xaw9kozndo9 n /ing air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of 7329k 9nbebo3mp. c dcckn-spzf(/usthat on Earth. If you hit a basec(ok9unc3sse 7 k.b 9n- b3mpdzpfc2/ball 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 cvysfa +,1chf68hc b4mi/h in the +x axis relative to a straight, level road and pass a car travelinv1a6y4 fbh+,h fc cc8sg 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 with a strong current. Youe)cy d ld;qq.2 start out)ed;2 y. qcqdl in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can mov wj5fo6xpw)pb-lbxw/q7)c a.e at 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/h /x) 6b75pq- wapbwfo jlx).wc?

  Vector A has magnitude 8.0 m at an anglxgv+g:sh87 bt e of 30 degrees below the +x axis. The y componentv7 sbxhg:+ g8t of A is

  If a ball is thrown with a velocity of 25 m/s at an tyu7:pn(tm) s52pf az ,a/b8)squue w 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 9ty* olcz3ge ckk;nl /i3ow1-up 2.0 km north and several kilometers east. How many l;knw/*yg1tzokc -o cile393degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x;yz5 :7mcdkcr component of its velocity is 8.00 m/s. The angle bcr;k57 md:z cyetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a levelj2h-eb:sb ex70 bz xd2 ground. At what angle is the Sun 2x:b72hxej0ebz s -dbelevated above the horizon?

  Two vectors A and B have components (0, 1) and (h/xvi korzy...1kha1xk4;uq-1, 3), respectively. What are the components of the sum of the/;kkh.x .a.ivuho 11y4xqrkzse two vectors?

  Two vectors A and B have comuq,z ,,g xyhiwkx: -,mponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum xg:,u,wm yi hxq-z,k, of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). bd(9(wpcqwo + Vector C = A + B . What is the magnitude (owwdp(9 cq+bof C ?

  A car travels 20 km West, then 20 +q;estrcora rd847t( km South. What is the magnitude of its displacemendct;r(4oa +q rt sre87t?

  Three vectors, expressed in Cartesiansf7z((b0cy 4 s cj7e7puf vjs; 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 Cartesia 95: o;aggs0 uyxxccdu1 ax)q6n 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, -4wmi rllm,gni q68u1pkbw89v1w0:u qp2*2k pf.0) and vector B = (+3.0, -8.0), what is the magnitude of vector81ug8mwkluw212 0pf:lq ,m bp9*qn r viwpk6i C = A - B ?

  A runner runs halfway around a circular path of radius 10 (+lehyh5 * g43q.qt bqod0wxsmj *ml3m. What is the displa 3jmmoxwl5hblqq 4de(sty* h*q+.0 g3 cement of the jogger?

  Two forces are acting on an object as shown in Fig.s3 f-o-hsg /x3h,/f ww5e4zds pormn9 below. What is the magnitude of the resultant force3zxd,4ns/sph9w o fh-/w5 osfgre m3- ?

  Two forces are actinq 7c3wh*. f x)ofp,vl0d,kev bg on an object as shown in Fig. below. What is the direction of the resultanf0v*.p,lfdb e3c,wv o7h )q kxt force?

  Vector A is 4.5 cm long and points along the positive x ax* .p2g pu4acpe:c )uaqis. Vector B is 5.7 cm l cpe2a)gap*:u.c4u p qong and points at $+35^{\circ}$ 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 52 cm long and points a9gi1rjhbvvv*vp w)xt): /- tw t $30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 33 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 horizout( 7fe agdpr3/* *nexntally with an initial speed of 19 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.8 s. What is td7 atf/pn(eg**3e urxhe height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, fre* zhf4bhqfvrt -a++ym+c n3vc),wp 8 om a bridge. It falls 20 m to the water below. Howw ,v3bc * 4m apfh-vr8zqtf+y)e++hcn far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 19 m abom58sl9fkau2 gyzk(p2 ,cf 9iy ve the ground, strikes the ground after traveling horizontally a distance of 15 m. With what spa( 8cklm s9 fyy2 p9,kig52uzfeed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 , x du-ira n/-qkfs69vf je2r4m/s at an angle 4r/2,dirjve -6qnf ks a9-xu fof $20^{\circ}$ 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 15 m/s ax/x ij ts:2+wbt an angle of x xi+sj:wb/t 2$31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an in9f9fr ,rkw-17hzh f jwav 6u8citial velocity of 22.7 m/s at an angle of $33.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial v:p dx.9pqsm)oli *az9 elocity of 43.2 m/s at an angle of $27.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofl c xp3p*3dx3t $30^{\circ}$ 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 horizoi3n)e+;zfkx i ntally at 27.3 $m/s$ from the roof of a building 42.1 $m$ 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 grounk)lz v/k 2p kds(sc3b:d level with an initial speed of 48.8 m/s at an ang p/dkz kl:c3k( vssb2)le of $43.0^{\circ}$ 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 winddjtug 3p8,bd 7), you can run a 1500-m race at a velocity of 4.0 m/s. If you ran the db p3dgu8j,7t 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 be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s to /i k;3n7ipkgj+ a4snuthe West. n 7 jgaup4/k sikni3+; The plane's speed relative to the ground is

  A plane is flying due South 0lt-g (ynlb ;c($270^{\circ}$) 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 i4 :uw v:(m s+bznhzh;d w,8dx120 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 200 m/s horizontally fires9n, 2q 7wrcbsa a projectile with speed 50.0 m/swabqs7 , n9c2r in 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 directed across a riveqhafg q eop-gr25k1e1 2f+oi1r with a current of 6.0 m/s. What is the speed of the boat i1fpf qaq51kr o 1+g2he2g-eoas it crosses the river?

  The driver of a motorboat that can move at 15 xv 7p3nzxtdz 57t6d x1m/s in still water wishes to travel directly across a river 0.9 km wide in whic tvx71x6 5xzztdd3p7nh the current flows at 5.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can mob7 fm7s/ .oaqlh;6d dmve at 10 m/s in still water wishes to travel directly across a narrow strait in which the curren 7d;bf dh6qm7ao.l ms/t flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acda gwp3k3c2g j-gn;b. y;p) jzross a river 200 m wide reaches the opposite bank in 6 min 40 s. Sk3.-y3pj j;ggbn 2 apw)z dgc;he is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a ri.k a.l.nl/jze ver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m.nlze. . jl/a.k What is the speed of the current?

  A boat, whose speed in still water is 1.31 m/s, must aim upstream r-.0tvg3 gpat at an angle of0rtvg- pg .at3 $21.5^{\circ}$ (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)  $m/s$