Which one of the following is an example of a vector quantri1y,d8 v6 zwqz:qd*f ity?

  Which of the following operations will not change aaf96 6uyg8dkb/i qg o- vector?

  Which of the followin ,j6gv wx45ns +v5cjpgg is an accurate statement?

  The resultant of two vectors is the smalletf(ef*v5qmv .t+c sb/ drc /6sst when the angle between them is

  Two displacement vectors .il 24vkurqn* have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, tu r2l.4v ink*qhe magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which tx*k+ wqnox u;e/h:st 9i/+mwlu1.b eone of the following is a possible answer for the magnitude of th ieb/ s+mxw/q*w. tx:t;k e1hul9u+noe resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in diei+l2u+gj k d iu-e m:(k gr)9zhmb/u0*k0ljqrections thatjml d90+ mrkzbj+lu-k / (g iqek0euh)i:*u2g are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,w-2 d :aunqcj( the unknown vector is

  Ignoring air resistance, the horizontal componenhfi kqeq-9e 9n.iwwn j(-m56xt of a projectile's velocity

  A ball is thrown with a vzws. s:1)hwbl8 lxr7dxj( m2velocity 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 accelera h catkr)98(idbu3*/vn lbmw, tion b8,*m dv/tuk9abi(lw3r h)n c

  A soccer ball is kicked with a velocity of 25 m/s at5vqi+-utm2 nz5w1q le 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 3m:ogi/klh3l+jbsnks r 3 0/t is directed anti-parallel to the velocity ve/lt3 0il njo:km b3hsg+ r3s/kctor,

  If the acceleration of an object is always directed perpendicular to its veloc ffzu 4mi(j89tit( f4tfzj8i9um y,

  At what angle should a water-gun be aimed in order for the jpa02xftokc i1,u+2zcd1jc, water to land with the1 t2pc,k,ax1d+ uzicjf0 cjo2 greatest horizontal range?

  An Olympic athlete throws a jave 5p.mjj)bso(plin at four different angles above the horizontal, each j.jp b(om)s5pwith 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 t w -ofn19p1mz8y f3uwtime. If the ball leaves your hand with twice the velocity it had on yo9pzf8uwy3 1 m-ft1nw our first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an origin mzsj)uq m1f5+al 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 attempti -u4*sgsiry 95mb;hq reaches its maximum height, how does its spe 5*4gmriquib;ss9y h -ed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at t55- vy8ey5ad n4owbmfhe same instant a ball is dropped vertically. Which object is traveling fasteraby d5mo8f4n 5e5yv-w when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bucfmrk 2+qy :(6;z2v:qv rrnx zllet is dropped from the same height. Ignore air re qx2 :qvkrn6:rrfc z;z+(2vy msistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speedajbx7xjeoqepk;5 c (/c hvs((j3/(v h of 40.7 m/s and at an elevation of 132 m drops a package. 2.2 seconds later it drops a second pac(7 ao(e j 3jxqs ;hk5 x(jev/bvc(/phckage. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second lat3h +uq* y,zkfcer a second package is dropped. Neglecting air resistance, the distance between the falling packages hyk,uz+*c3 qfwill

  A pilot drops a bomb from a plane flying horizontally at a constqxxj8:m ))y.rsa -g fi/ p4wouant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane s.8w ijg xpfxaqm/)o 4 -:y)urwill

  The acceleration of gravity on the Moon is only one-sixth of thahi-(pq;:56furd h 1uccw6h, ioc gb p6yl, ik5t on Earth. If you hit a baseball on the Moon with the same effo 6cdgu 6uii,i1ho yh h ;-cpkw,56(rqc: b5lpfrt (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 str(gab )h:8k pzmalb7 1taight, level road and pamat (7) g1azbhpl 8k:bss a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cre (fsv(9dcj nv bj* lw,6v-m4goss a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your startnjg4f -je,sm(69bl*(c vvwdving point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. H 27kim8cx2d 4h cvb*vkow much time will it take you to move 12 km downstream, in a river flowing at 6kvb2c78di *2kv m4x ch.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degree/3 1g7ipzibrs s below the +x axis. The y comppizgi 7/r1bs 3onent of A is

  If a ball is thrown with a velocity of 25 m/s at: je-dyypf u- dg6u;h( an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a syie 75xzt6l5-b*bntl traight line in a direction north of east and you end up 2.0 km north and several kilometers east. How t-t 6557zyl blni* xbemany degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 6z6 /dwsah:js4 y*f*xxn8co fm/s. The x component of its velocity is 8.00 m/s. The anj*xd*n6s:s 4z hycowx8f/ af6 gle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m lop9qx fci-dx. 4ng shadow over a level ground. At what angle is the Sun elevated afc-4x9d qixp.bove the horizon?

  Two vectors A and B have components (0, 1) andh(1 1n71jalfk so 4hgb (-1, 3), respectively. What are the componentbgh 1sh7( lj1k fon14as of the sum of these two vectors?

  Two vectors A and B have components (e c2d8/;td i)mprkm t.0, 1) and (-1, 3), respectively. What is magnituddmt e ;m /kci.8tp)2rde of the sum of these two vectors?

  Vector A = (1, 3). Vectc35g)5k vimw xor B = (3, 0). Vector C = A + B . What is the magnitude5xi5gc )m3vw k of C ?

  A car travels 20 km West, d3qhltp7wzm ((4:tvpa(qs t. then 20 km South. What is the magnitude of its displacementqvttw (:4ltds(qpp 7h(.za3 m?

  Three vectors, expressed in Cartesian / .izsar sry v 6.qefv,l/c4*tcoordinates, 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 Cartesian coordinabtni:s )b :w/s xhr*.ttes, 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, -8jm 1 ytxo/sx/5/poy* r.0), what is the magnitude of vector C = A - /5 1 yyrxt mjsop/o/*xB ?

  A runner runs halfway around a circ1x5j.ejp sd/ixo-q q:px 07ag,, fdtsular path of radius 10 m. What is the displacem :1,tsgdeiqxxp 7od ps q,j-a.xjf /50ent of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the 8-4pg *meep48pij izumagnitude of the resigu8epj4 -p8 ez*pi 4multant force?

  Two forces are acting on an object as shown in Fig.f ajp1h.*yzxlzki;; 5t o4v8r below. What is the directionalrox f*h y k18z54 zi;jt;v.p of the resultant force?

  Vector A is 5.5 cm londjtl9zf.6 9 weg and points along the positive x axis. Vector B is 9.8 cm long and pointsldz6e9 ft9jw. at $+34^{\circ}$ 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 82 cm lo*i,tp)j*f wu zng and points at $30^{\circ}$ above the positive x axis. Vector B is 19 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 wit im9.. 0u rrh((3(x9v ac(hbyq tdxcjhh an initial speed of 28 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 bottorxj(qvt drxh 0.(9h(3ay(bhcc9i. um m to be 4.0 s. What is the height of the cliff?

  A girl throws a rock hori(itsm 5x 6ay8tzontally, with a velocity of 19 m/s, from a bridge. It falls 11 m to the water below. How far does the rock travel horizontally before striking the ms86a it(ytx5water?

  A ball thrown horizontally from a point 30 m above the ground, sn -*s5x n tijvqkx+c8)trikes the ground after traveling horizontally a distance of 2ix)n8n *- k+j tsqcx5v4 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an an57*yfd1gt 58omtni /qppuhj 4x3zs+lcc-vx3gle ofiz dmpxl yqxcs74 5 t5cg/n*t 13fhujv-8+po3 $20^{\circ}$ 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 wi0z(*.iymtrn+5f j m0qi;qssxth a speed of 11 m/s at an angle of5* rszm n qijq0+(;txm .sfi0y $23^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launjck:9b 87ijpt-t 9b wtched with an initial velocity of 35.0 m/s at an angle of $31.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an ia43l c 7cy pczbm0fm0*nitial velocity of 32.2 m/s at an angle of $13.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle-kma i w0tjwv0y87 w(k 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 horizobaxn eo-2lcq ;+vu7 7jntally at 16.8 $m/s$ from the roof of a building 51.2 $m$ 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 inivc l8vf7fpo a2;0(o ifp .y9f(9vwhydtial speed of 43.2 m/s at an angle o(y2ip7 v9apdwo(0 l .9;fovcy hfvf8ff $43.0^{\circ}$ 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 wind), you can run w7vo;yz gijd1xp+-ufa )q6/ pa 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day v7xi gf6 ouy)-q pw1ad;+z jp/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 :qq:fbuqi9d5 x e)w 0c.mihar33s.kd in a wind of 50.0 m/s to the West. The plane's speed relative to the gro0if)q hds5e3icum.kxb:39:qawd. r qund is

  A plane is flying due Southk oeg/m*v;d2r ($270^{\circ}$) 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 ofr9ge2 j :zyys2 *mubd* 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 200 m/s horizontally fires a projectile with sxe, 3ioos,a n-e+w /* *lplrizpeed 50.0 m/ a +is oer3e*,wpz *lnxo-/,lis 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,lrr/((k7 wzo: 4m tr9 :yhhidq is directed across a river with a current of 6.0 m/s. What is the spek/q lri d9 4 :to(m:zyh(hwr7red of the boat as it crosses the river?

  The driver of a motorboat /o2:4 hml1wdbo qrx,lthat can move at 13 m/s in still water wishes to travel directly across a river 1.6 km wide in which the current flows at 7.4 m/s. How long wil4,dqmhx12r/w llob: ol it take to cross the river?

  The driver of a motorboat that ca768u d83w xtt k+qy3cs2jdzhq n 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. duds3cyw63h28tj +8 7qqtx kz At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank i(6g9 sgeniai)gi/evy;d ( fl9n 6 min 40 s. enf(iv) eyg6g i d;alsgi /9(9She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river rzqc*; q8to ek*ooi8 (200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed ooir*q8* ; ck8oq to(zef the current?

  A boat, whose speed in still water is 1.31 m/s, must aim upstream at an angle;cz; th/x;r iue( jwf9 of;;we h9xit(rz u/jc;f $19.1^{\circ}$ (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)  $m/s$