Which one of the following is an example of a vector quanc *eoib wx )/1ey58rowtity?

  Which of the following operat)o87ijm r2fovilnq .a e3d1 -vions will not change a vector?

  Which of the following is anmbe0 ,4*h n.bhu w(gtg accurate statement?

  The resultant of two ve pcak7( *- rb/-ovpvagctors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 mk .pj: m:ek ;*gglwl8j, respectively. When these two vectors are adk:j8e.jpmglkg:lw;* ded, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the foups4.4*l u+dxtt , epellowing is a posts+ d.*4uuptexp4, elsible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull oaeonp,5h /pt)o+;av; ba, 1noky5io qp) 4pogn an object in directions t n o opo45pqa1np5,vp)i;o t /ak e,)baghy;o+hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectorzx/+s j v8 v9b* zxog1cgibe.. is

  Ignoring air resistance, the horizontal component of a projectikk2g .l)* zrdp;p akw)le's velocity

  A ball is thrown with a velocity of 20 m/s at an 7 mal 1m5 a m)aaj 32ufq0r. )yi4ef+e2ihubrnangle 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+9 ,ppyizi3 tc component of a projectile's accelerationyzp3iic t9+p,

  A soccer ball is kiczg8t8yflg+/iy n 1)l jked with 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 pjt rm 7a:xgq2;y72pj+g6yszof an object is directed anti-parallel to the velocitgrp27jz27tgs;6:m+ jy yx ap qy vector,

  If the acceleration of an object is always directed perpendicular to itso4f 6etxg./k0 iz6w jdtwr63t velocityir w306 d . 6ext4zg/6wtotkfj,

  At what angle should a wa,qgl- f u mn,452jgmedter-gun be aimed in order for the water to land with the greates5je ndfguql,4m2,m -gt horizontal range?

  An Olympic athlete throws a javelin at four diffe4phgbtn+ 0t c5*j*/or zdcm6 yrent angles above the horizontal, each with the same spc4zd/6n 5t*pg t0m *c+oy jrbheed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball f-m-e4iqy5+nlw5 qi h5 z m(dotor the second time. If the ball leaves your hand with twice the velocity it had on your first throe4whit d 5q-5(m-nylz+iq5 mow, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8 eid t k9wg3 kcyj0/w1x5/jdu(.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 goapor,v3 /lezv)jkddw4+ l0 9ah l attempt reaches its maximum height, how does its speh,d 3d+j z4lp 09)elrkvo/w aved compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instav1 qtbpjbv+ +)e5 )aolnt a ball is dropped vertically. Which object is traveling flaq 1 evj+ob+b) t)5pvaster when it hits the level ground below?

  A bullet is fired horizonu e7goi( rnhu rwu 0s61mg,b.,tally, and at the same instant a second bullet is dropped from the sair.g(,b1m h6nuws,7e0oug ru me height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 58.8 m/s and at an elevation of 12qt p11gvx yb(8u6kgz 49 m d pux vt8gz6 yq2gb1(1krops a package. 4.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pacjkyog5m j./r2c-y )jw2 9fzajkage is dropped. Neglecting air resistance, the distance between .fj jyy9-o 2jgrzw 5m 2jk)c/athe falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speedhdf: )g .unoc5. Neglecting air resistance, when the bomb hhfu)nd.o5: cg its the ground the horizontal location of the plane will

  The acceleration of gravity on iz/6 r1ipa2k3 zu0lts the Moon is only one-sixth of that on Earth. If you hiuz 02ta z1l3/kispr6it 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 straight( )9kvxg d 91;xouaohb, level road and pass a car traveling at 45 mi/h. 9k9 oxhuv gdo1)x;(abThe relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong curr s3y lq i.3h1hp7uff 0*wtp8waent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should het3iq 08h13h7wpy*ufwpl.fs aad your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take y* d:u xerpbug+0u vl4v,9 q1swou to move 12 km dogpw,r: u + sluxv*vqud94 1b0ewnstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8. d;4qkvphm,7rav e*be **xj0o0 m at an angle of 30 degrees below the +x axis. The y componenv7r h*ae4 dpb,j;0vkxqo*me* t of A is

  If a ball is thrown with a velocity o2 b4;ckk6xt*kya- mu5yn4 uwu f 25 m/s at 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 inr7, m yt vuolen2e01b( a direction north of east and you end up 2.0 (onu7y,m2e l rt vb1e0km 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. The x component of its velocitka*x6mh02,:.itp8leyxk / ( a1ujcydnjah b*y is 8.00 m/s. The angle between the direction of its motion and the x axis m(*0dh2 hk/up k6nacyabej8jlixm xy a1. ,*:tust be

  A 400-m tall tower cln7d vp0e58 4ngfe( hnasts a 600-m long shadow over a level ground. At what angle is the Sun elevated above thehg l74nnf8d (pnev50e horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whlsyh.0sz5z) o at are the components of the o5zhzs s0 .y)lsum of these two vectors?

  Two vectors A and B have components (0, 1) and cq2grzev34qsn 0s67yfj ck; *m( ,kwq(-1, 3), respectively. What is magnitude of the sum of th v7gcs0e 3(rsq qj46y k;nmfkq,wcz2*ese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B .aher h 64an-kdc)5c+esk. t1g What is the magnitud-ht )a+c5 rhec1a4.6dgk ekn se of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disply1vy 8b2+qtc h(a3ej na8jnq(1hyt y e2 +bc3vacement?

  Three vectors, expressed in Cartesian coordinates, ar /d8v:f jtxy+ybz :-qae
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 coordinath9ne j1o3d(3ue.(wqi 7 tp nhxli3r; hes, 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, -8.0), what is tj+3ab 5t7os;stqlo b 0he magnitude of vector C = A - B ?bboja+ sl5 q70so t3t;

  A runner runs halfway kje,4 h* m1don8szlt/around a circular path of radius 10 m. What is the displacement of the jogge48/hms 1zjtk dleo*n ,r?

  Two forces are acting on an object as shown in Fig. below. What is the magnitmo x )ae- wou, bn:+1cmcn*(fkude oo* 1:b-+nmxcna, fow)m( uckef the resultant force?

  Two forces are acting on anutssf ;yo wn6pu3298w;8 jpxj object as shown in Fig. below. What is the directionon9tu y ;2x8w pjpf3s86;suwj of the resultant force?

  Vector A is 4.7 cm long and points along the positive x axis.b inoa+pc.63w Vector B is 9.9 cm long and points atw6p3 acbo.i +n $+43^{\circ}$ 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 70 cm long and points at 8ubk onb(* c1ss9kt2e e4*rds$30^{\circ}$ above the positive x axis. Vector B is 15 cm long
and points along the negative x axis. Vector C is 28 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 28 ebzl/y)8 aiwow+.hzeek aft;zy(2e( 8;y.tu 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.b 2.ak+ z .e;ztef zuy)i8yl/w otywe(a 8eh(;3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity q6l ini7 v:8aey fkcn*pwod913 )vg(eof 16 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizp eq)n8ki(:df6o1 ne * w yva7l93vcigontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, strikesvszc0o1 fra ow (yjct3p1ht02b 51(nq the ground after traveling horizontally t0h2o sa(qz ctry 0 n11(1vo3wfj5c pba distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 c+6wite19ryb*;:w ytk8cc c f m/s at an angle r8:;ce6yk fwy1+ icbt9wc tc*of $20^{\circ}$ 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 14 m/s at an angle lhgzq)7l 5 /;lej8swfog5z);j 8 esllhfw7l/qf $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 25.3 m/s atll+5f wx twlo 2cz4o/w;a, an9v ,u9fm2ap y;h an angle of $15.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 34; obtxi g1j4ru; u ::tts7mbi;.3 m/s at an angle of $21.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of d20ntzp fz 7y3$30^{\circ}$ 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 237asuo8-o; nfj.7 $m/s$ from the roof of a building 40.9 $m$ 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 le oxxw7zqhvr mp52/l:4vel with an initial speed of 39.6 m/s at an 7pm4 hqvxz /5 l:2xorwangle of $45.7^{\circ}$ 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. If-sgu9:v-q x;vd jf:;e j8uouhlh7i.e 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 would take you to finish wou9g 8i:xdj-q;us;h-: v jehuf7u.e lvold be

  A plane has an air speed of 200 m/s due North, and is in a winvmzl 576cbgh2 d of 50.0 m/s to the West. Thgcm2 l5zv 76bhe plane's speed relative to the ground is

  A plane is flying due So8e6 3w17dpp:psazl1mw, a g v fkqu1(quth ($270^{\circ}$) 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 kj9 mv77nii.lim/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 wbpb nq.r;n9x 5s7 wmq9ith speed 50.0 m/s in a forward dirw5s nqmq nb9;7 bx.9rpection $30.0^{\circ}$ 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 :wi *f49ku vsh gf6sd-water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the river?wk g9 vsf f-4ds:hui6*

  The driver of a motorboat that can move at 8 m/s in still water wishes to tr ,c/ldgu./ 4eai;hk6srkbbkll*q;x7 avel directly across a rllqi6 ul4.bsx; /kbag*kd e7cr h,k/; iver 1.7 km wide in which the current flows at 3.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still wab,r4krp4-jge1 w :lapter wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream rw,kr jb p:4 e1a-lgp4should the driver head the boat?

  A swimmer heading directly across a river 20c4x3;gpqn a0g 0 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in s xcgan4p 30q;gtill water?

  A swimmer heading directly across a river 20 6n/xi :zacwv40 m wide reaches the opposite bank in 6 min:n a v6xi4cwz/ 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.92 m/s, must aim upstream at an angle o0y.sp-7h vtp8d:yyhi f dhi-spy8 7yt0h:.y vp$17.5^{\circ}$ (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)  $m/s$