Which one of the following is an example of octz.4kw lak) - .)gafrjmx xcpi0lz1 5+ *ls(a vector quantity?

  Which of the following opey: )ho:5f jf;5h qakbr.koxuf4x a:z;rations will not change a vector?

  Which of the followingr scpka3vrajd ed36:g ) g43s- is an accurate statement?

  The resultant of two vectors is the smallest when h1o ,:u znu5flthe angle between them is

  Two displacement vectors have magnitudes of 5.0 m4*-vp6 (p*e7 i onxwukqetyc) and 7.0 m, respectively. When thesep *o*k xqwpeiye7 -v(4nt cu)6 two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addeodd8jrt:+1m-m t agdq7j u32wd. Which one of the following is a possible answ8twrd:ma1mug 7 tddo2+q3j -jer for the magnitude of the resultant?

  Three forces, each having a r0ls-4dtn,f 5tmi 8;lg k wo,hmagnitude of 30 N, pull on an object in directions that h5, kl in;mtt o40sl,fg8rdw-are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is)bn*vp,t1 qi 9g/z 4ffko lwx0

  Ignoring air resistance, the horizontal component of a projectile'sr6vmj -ssdkhn-a3 * ;e velocity

  A ball is thrown with a velocity of 20 m/s :o:v+lfha lj jw (q)y*rdh0;*fwwli; 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 cb r:n,i*g6 jrsc fv8+a projectile's accelerationn+r8 b:c vsr,i6j*fcg

  A soccer ball is kicked withhj- w6rw:cy7fm85y7m yk.g rm 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 y)gn)oee c8ih bmy;zdv9 99c-the velocity vecto9 mh;d cv bei)y9zy9c8e)g-no r,

  If the acceleration of an object is always directed pqkt:v2uf*m ls(3 . ljcerpendicular to its velocit*mt jfsck( 2llu:qv.3y,

  At what angle should a water-gun be aimed in order for the water to landmu.f*o-p ic q6ua.+ zy with th. u-z. q*fy6p uocai+me greatest horizontal range?

  An Olympic athlete throws a javelin at four differentc )0tqnmsagq:dr ncy2 +9(rj+ angles above the horizontal, each with the saq++jyndqsc t2:m9 acr (g)nr0 me 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 .h ,mi oi7o)zso d hr(qi8*xi4hand with twice the velocity it had on your first throw, its horizontal range R (compared to 4q *iix,i .r hzo)(dshoi8o7m your first serve) would be

  A ball is thrown at an otche0gx9ixq75 b 5)f lriginal 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 attempt reaches its yzua(fw0l+ al5 u)f +cmaximum height, how does its speed compa)ul fl5yazf(ac 0+uw+re to its initial speed?

  A stone is thrown horizontalctp* 4ay-5f(lla e u3ht5.b; p pj4pdlly from the top of a tower at the same instant a ball is dropped vertically. Which object iafp5t4lcpadujb5 e.py4; th -3lp(l *s traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is ds +1sntj73 it7f3jkx kropped from the same height. Ignore air resistance. Compare the times of fall of the two bulletk+3xfn7ti j7kjs3s 1 ts.

  A plane flying horizontally at a speed of 119.6 m/s and at an tg4g6 fxz-e3g elevation of 230 m drops a package. 6.0 seconds later it drops a second package. How far apart e 34gtxgz-g6fwill the two packages land on the ground?

  A package of supplies is droppn 38 rzqbq-:hued from a plane, and one second later a second package is dropped. Neglecting:38nqhb -qruz air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a consta ab igz0yk94r65cn-+u2c rlh unt speed. Neglec2964rzh -gl+ykc cb5urnaiu 0 ting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is6jz s(zjdw5h 1p,ld* q only one-sixth of that on Earth. If yo(j,15zw zhp s*d6ljqdu hit a baseball 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 relative to a st i+incw:e(ly y) oh.:draight, level road and pass a car traveling at 45 mi/wl:(cydh.o n + ):iyeih. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a gy8 1hy:wt nm 9 3rnx6txlic17strong current. You start out in your motorboat on the east bank de9yy tgh1 63ncnm7 wr:lxi1 x8tsiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can mo v jj qc9d-/nqtj6zjq likn923-y( so,f29beive at 30 km/h in still water. How much time will it take you t9(q js-j v 9 itnylebq,jki-o92 n6fc2jd3 z/qo move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axish5/*mn ,tn jsj. The y component o,/m*tn s5n jhjf A is

  If a ball is thrown with a velocity of 25 m/s at an angle of/ u68nvw4 ,q:ni)xm*tvkw vuz $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line b:33fnajd n.dulx+:5 /ukypr in a direction north of east and you end up 2.0 km north andbfdljd+ky 35/na pn3u:urx:. several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed ok-v .hc+mpiqzc.n h*j( (w +jlf 12.0 m/s. The x component of its velocity is 8.00 m/hiz. l*+mj .+(njvkcch - p(qws. The angle 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. 2(/dc urnk/ oy2vx.hp.t,oydAt what angle is the Sun elevated abr,c2 p vu/ (.notk/doh2dy.y xove the horizon?

  Two vectors A and B x;k 2i1c)xw zy6fsvb/ have components (0, 1) and (-1, 3), respectively. What are1is2kzwf6x/ x) ;vcy b the components of the sum of these two vectors?

  Two vectors A and B have ci9 ygie92 ;ebjomponents (0, 1) and (-1, 3), respectively. What is magnitude o ye99b2jiie;g f the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . xgni c,7pa 2:uWhat is the magnitude op:7 2,icagun xf C ?

  A car travels 20 km West, then 20 ;px3dx-f ek-ma wx w*0km South. What is the magnitude of its displace xx 3 x*p;-0e-dwfkwamment?

  Three vectors, expressed in Cartesian coordinfan(8 b 7x ajqe2ob62gates, 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 coordinad3ln31cojta fpdn1k ny) q:86 tes, 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 vec)e, ye(,vs-c b- ()tbspxqmt ltor B = (+3.0, -8.0), what is the magnitude of yem(bt- ,xq ) ,b-t)(ple vscsvector C = A - B ?

  A runner runs halfway around a circularukw 0;/+,ivtjs3zdu r path of radius 10 m. What is the displacement of,rtvzduju;0 wi k+s/ 3 the jogger?

  Two forces are acting on an object as shvskim kxpvr 12 (l6cv0w9 0l2xown in Fig. below. What is the magnitude of the resuli 6kvmxpc1 xkr29l0vs0wl2 v(tant force?

  Two forces are acting on an o*81xkt*ub.(.i fdy49csorpjec81m1u et og a bject as shown in Fig. below. What is the direction of the resultan 1uto*4t9 *jso1 .emed8fuckcya1. xipgr(8bt force?

  Vector A is 3.7 cm l 6:q1q ftq6jnhong and points along the positive x axis. Vector B is 7.6 cm long and points at h:jnqtfq6q61 $+41^{\circ}$ 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 51 cm long and poincmp jh9r o5z41ts at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 21 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 21 m/s cs vm 5x2o-h5ww( +mtvn2 *ayofrom the edge of a cliff. A stop watch vw m5vsx*5hmy +tn2awc(oo- 2measures the stone's trajectory time from the top of the cliff to the bottom to be 2.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 96.o0jm qvk:7ndmx , y ;1iatzw m/s, from a bridge. It falls 12 m to the water below. How far does the rock travel horow 1,a;vmidx.zkjq67 t 0:nymizontally before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes the groudxhkmo 5b 6yr6 +6 gwk46lu,ddnd after traveling horizontalwk6mhkoudg 6l drb45x y, 6+d6ly a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed y7k cdxsh0(6dof 12 m/s at an angle of xdc76(kdhs 0y$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into 4y5r.v +czew ethe jump with a speed of 13 m/s at an angle ofcez e+ywr5 .4v $25^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity ; o3 uc*sd73xaplcn4gof 50.0 m/s at an angle of $19.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an init 0lq3cg f/sy,8uhvu3p ial velocity of 26.3 m/s at an angle of $23.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of 2a af .oviq-+b$30^{\circ}$ 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 h;-e)e ga e*-lajlk, c16.1 $m/s$ from the roof of a building 40.7 $m$ 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 firedl mz3o+3*kwrgps(j4l from ground level with an initial speed of 39.5 m/s at an an or(+3zp4j llwm*3 sgkgle of $40.3^{\circ}$ 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), yot)w:xq5q4v 1vmcz l f)u can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on aq wlx5 m)fvvt1: cq)4z 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,q(4 ia8mghlx/l :0hrut rz:xmfx;n 46 and is in a wind of 50.0 m/s to the West. The plane's 6z/u grxx i q4 ( lfmnrm8hxah;:40lt:speed relative to the ground is

  A plane is flying due Southtq37xjx ,,: 5nhfrz nb ($270^{\circ}$) 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/ho4 p al,-nko.f 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 horizonta fr-lxji* l..ar-g,molly fires a projectile with speed 50.0 m/s in a forwarglmr-, raiolx *-j. .fd 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 intci-95gi *jj o still water is 8.0 m/s, is directed across a river with a current of 6.0 m59-ic to jig*j/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 15 m/s in sd44nqzvwp)0:1 ypfnqtill water wishes to travel directly across a river 0.7 km wide in which the current wypf4:v1np nz04) q qdflows at 4.4 m/s. How long will it take to cross the river?

  The driver of a motorboat that can mf(7-)g, qf1ou0bel cffk.ww iove 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 g -(0u,f7fi 1ql)wkw fcefo.bshould the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches tybw.a zepjcst.-;v/s);9k zphe opposite bank in 6 min wpptc)b;a-ej zs/9 . k;v syz.40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly t)g, izhg25rbz : lu ld+id8j3across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed)tz: gblzr,d+3 52igjlu8ihd of the current?

  A boat, whose speed in still water is 2.11 m/s, must aim upstr4hpm7dvf*u0mu6 rvz 6fq8 ng+eam at an angle of rq mz8gmnv0d+f u6p*vfh 764u$26.8^{\circ}$ (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)  $m/s$