Which one of the following is an exo v8 t8d*qf3xhcufj,2 ample of a vector quantity?

  Which of the following operations will not changxuordx. (8*cm* wxe gi6p.ak.e a vector?

  Which of the following ixx 4tm,fo vj+vvka5- rr6)ei1s an accurate statement?

  The resultant of two 9qmw(kl0tyiv 6(1q/bzi 8 scnd )wp1lvectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 i:9 e,w77wbx2fdul ufm and 7.0 m, respectively. When these two vectors are added, the m, d77 2fiuu elw9fbxw:agnitude of the sum

  Two vectors, of magnitudl-t q9ime2 uwjl3 o:xlpd-u5 ct-z+k;es 20 and 50, are added. Which one of the following is a possible answer fdlt2lxme wukj +tl3i- :5u p;q9cz- -oor the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an obja46 uslke .ulpu)vegtx+qmy3 9,q52m ect in directions that al lut xk epav,q.s+mg)9y3q6em2uu 4 5re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, th3* 5i9rouydbi e unknown vector is

  Ignoring air resistance, the horizontal comg1cj*a, e49wc l60xbqg 4wguy ponent of a projectile's velocity

  A ball is thrown with a24g nmgo*lh,nj c ii6 t9r7;isp+qnqhu89.kl velocity 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 resistanc cnqa9nx0/v6k e, the horizontal component of a projectile's accelerationnc/vx0an9 k6q

  A soccer ball is kicked with a velo+ 1vwmjq9pmg( r(5j-yfj ltm 8city 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-paralu,98qvs ll0dp4din .mlel to the velocity vectorml ,vn i.u8s40ddp9lq,

  If the acceleration of an obvikpo3 7 +nhx*ject is always directed perpendicular to its velocityhx+pn 73 k*iov,

  At what angle should a water-gun be aimed in order for the water to landk; pl1 q1f9qpf with the greatest horizon9 q1lp;pqff1k tal range?

  An Olympic athlete throws a 7i atdn xc7l29z c3;jcjavelin at four different angles above the horizontal, each with the sczil9xca3n7;2d j7ct ame 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 ballg inqa)e,di 4t;5z 1gp leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to yo4 1epz q atn,g5);idigur first serve) would be

  A ball is thrown at an original speed ofk+ o9 soh+hzpzx mvm 6q18o4,k 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 if 3xhr-i2omo)dzf. i2v6 2kg* lx8wl qts maximum height, how does its speed compare to its initoixgv)3ri l6.m*zh 2x-2wqkl f8fo2dial speed?

  A stone is thrown horizontally from the top of a tower at the same instt/uy6djsl8so*)9 k v zrj2/i zant a ball is dropped vertically. Whlzuiv/* kj yrto8 d/s69j)s2zich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the8pr69y h5x:1zod7rj5 gieclm same instant a second bullet is dropped from the same height. Ignore air resistance. Comparro6jxg c5578:lpyrzi1h md e9 e the times of fall of the two bullets.

  A plane flying horizontally at a spq,ge c*: tfl-keed of 51.2 m/s and at an elevation of 187 m drops a package. 3.8 seconds later it drops a second package. How far apart,lcf eg* :tkq- will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one st5*.xc mhv*,osqr(zf ywfqy 8. ooo)jrsh313econd later a second package is dropped. Neglecting air resistanc5 yos)t qxrjf8 c.o3w(o, z*q v1hrmysfo. 3*he, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally ako+7v qnmg3or,**/kvdhr ka2t a constant speed. Neglecting air resistance, when the bomb hits the og2qnkkk mdar*o 3rv+*v7/ ,h ground the horizontal location of the plane will

  The acceleration of gravity(r l5-qe o*t2yusx-j q on the Moon is only one-sixth of that on Earth. If you hit a baseball on ye2(s*-q-5rujqol xt 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 straight, l8p7y7t(z xdjbu/;g+ 7dk pgl vevel road and pass a car traveling at 45 mi/h. The relative vel jt(y;d/lkv gg+7x8p b7u7dz pocity of your car to the other car is

  You are trying to cross a river that flows due south with aopl+yuj-(fxzo 6z kt ;s1lp -7 strong current. You start out in your motorboat on the east bank dez7-6 ool - p;uxykzs(+p j1lftsiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stil.6* q:.o( v h3jeqjzquak0olhk x(+ie l water. How much time will it take you to move 12 km downstream, in a river flowh iqv +q0:ee6zjojk.3a(x lquo. (hk*ing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. Thkx va;-qv5(4 ijg r8yre y component of avvj(4ri ygx;qr 5k 8-A is

  If a ball is thrown with a velocity of 25 m/s at a0 ve.p g1ztslrax)*+a6(aw sln 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 7)m ncw1mm -7n neka5gup 2.0nwenn c5km)7-mam1 7g km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. 4fiz x5u.mbroe69-b 1n0-q6nhdsp tfysld: *The x component of its velocity is 8.00 m/s. The 6m.-0e9 pd f64-:nshi5q ub rztny*x1 ofbsldangle between the direction of its motion and the x axis must be

  A 400-m tall tower ca o7 8w1ilfbp5kt )(1hptrqds6sts a 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizon?ksdl 8t (oq1 6hfipt b)p7r5w1

  Two vectors A and B have components (0, 1) a;o, x.*d4pgm fxhbuq1nd (-1, 3), respectively. What are the components of the sum of these twom*u ,pfq.xb1hdg 4o x; vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiv( m8 ln+b+qp )xmuypb(ely. What is magnitude 8b(x( nlpy bp)++mmq uof the sum of these two vectors?

  Vector A = (1, 3). Vector B =z o8yrm49qs dlex 9r1. (3, 0). Vector C = A + B . What is the magnitudys. r99ox zdm18l 4erqe of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude o 8a6mqwl77e gaiqs;w( f its displace6(7s;amqe7qw al i8wgment?

  Three vectors, expressed in Cartesian coordinates, 5q6 4tc,gysnfq9 g qi5e9+bbfare
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, expresdtemnq:j:( m)sed in Cartesian 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,)r-g1 i)g*cziojsv-g -4.0) and vector B = (+3.0, -8.0), what is the magnitude of vector ) sgv)g 1ogri*i-z-jcC = A - B ?

  A runner runs halfway around a circular path of radius 10 m. Wh*/2tu3 gk zi ihnax49tat is the displacement of the joggertixikh / 93nga*u2tz4?

  Two forces are acting on an object as shown in Fig. below. What is the magni :uon0v//a m5jxi r1m,)grxj atude of the resultant force/15 )axvmm0/joa rg xjrni:, u?

  Two forces are acting on an object 3 i))q*ge8b 0rbkqzi6 ouhi6+nqq5n ias shown in Fig. below. What is the direction of the resqg0h 56 qqbinrq zo* i86b)3n)+k ieuiultant force?

  Vector A is 5.1 cm long and points 4gqx; 6ofi3t12qlkpv along the positive x axis. Vector B is 9.8 cqp3v1;xtio 6 flkg2 q4m long and points at $+45^{\circ}$ 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 80 cm long and pxc5ze y/(72 azv/6of u tsrsr6au(6zeoints at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 35 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 withkioe3xb r 9 :*15kxle u9f5cheddk :w. an initial speed of 10 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 3.5 s. What is the height of the 9ux kfe 55xkeoc91w. bk: d3h*:iderlcliff?

  A girl throws a rock horizontally, with a velocity of 9 mq f*/ :vw2o6z,tevck h6,fm dh/s, from a bridge. It falls 21 m to the water below. How far does the rock travel horizontally before striking t2 6mfdv:6h z khtwe*/qof,v c,he water?

  A ball thrown horizontally k:dn 4bg8 wqxiw07fg2from a point 21 m above the ground, strikes the ground after traveling horizontally a distance of 13 x8:db 4wi 2g7fgwkq0nm. With what speed was it thrown?

  A jumper in the long-jump goes into the jump withl4 jxnf0*j8f 3 :xlanr a speed of 12 m/s at an angle of 3:4*x jf8nxrnflaj0l $20^{\circ}$ 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 jumil*)5r wzdyizdh0 /i9p with a speed of 13 m/s at an angle of)0 wi y/hir zdzli9*d5 $37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 42.2 m/r2z- l*zry(wt s at an angle of $15.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 38.7 m/s at an angle oznx rj,dtnm 1z8,/k:r f $49.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fip0kgo 7xs)ylu:vq- 4ared 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 holg+h ar*)2q x/y9oox,cev o )mrizontally at 23.2 $m/s$ from the roof of a building 34.1 $m$ 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 65.0 m/s akk o. ey15q gova.n/3it an angle ongy31. e aq.5vko/oik f $43.0^{\circ}$ 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 a 1500-m race at a velocity of 4.0 mj 2;qdgpq4p6): j p;nscxr *ixml(5db/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the time it wp rj;qpq6cxi*x;p) smd njl4 : d2(b5gould take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of kh; e 5,ghhv;p50.0 m/s to the West. The plane's speed relap,k;;egv 5h hhtive to the ground is

  A plane is flying due Soux *i/sx+r)+ r ms ushc4j;eyef9cj +n3th ($270^{\circ}$) 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 ihiw,xx1r,r anlk3k znlh4.1w067gn120 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 projectile7 -eeow8; edg77pdr ht with speed 50.0 m/s in a forward die7wep 8 do-ht7r;7e gdrection $30.0^{\circ}$ 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/1xk 9 4tllhhx9ms4e.as, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosse 94t9sl.l4h1 k mhaxxes the river?

  The driver of a motorboat that can move at 17 m/s in still water witnvo2ak77 5eci 1+e tg9*pykvshes to travel directly across a river 0.7 km wide in which the current flows at 7.2 m/s. How long will it take to crg tv5 *7yk e9p7 e2oi+cna1tkvoss the river?

  The driver of a motorboat that can move at 10 m/s in still ug-;zigfrf vxo 6,i2/q7qzc7water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should therz ;/zoxfv-q2i7c6,i fqgg u7 driver head the boat?

  A swimmer heading directly acb., vvk cp y0ux7k55/8uophkm cm/ r*pross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How pv/uvhk*rp m /,y5 7kcm0p ubxk8.5ocfast can she swim in still water?

  A swimmer heading directly across a river 200 m6 ;7u r4tpndvm wide reaches the opposite bank in 6 min 40 s. vt64;mnu7 rpd She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water ijpstysimtk e2b +99b*)6+q4y u i ip2ws 0.84 m/s, must aim upstream at an angle of 6+i+umk9tjyyb *iwqs2ps 4pbit9) 2e$28.6^{\circ}$ (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)  $m/s$