Which one of the following is an example of a vector quaw* v2yzsrf. hyg)p+- xntity?

  Which of the following operations will not change a vector2 bv0wxj n77eqq2ojp: ?

  Which of the following is an hu1n n-)zacg: accurate statement?

  The resultant of two vectors is the smallest when the angle 9f6i7cuz) w3nl:rcmg between them is

  Two displacement vectors have magnitugkcibm pk.aj+qd . ;92des of 5.0 m and 7.0 m, respectively. When these two vectorsjd.+ ipagb.kcm; q29k are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of thzp0l p,4z1 rxwe following is a possible answer for the magnitude of the resullpz x, r1zp0w4tant?

  Three forces, each having a magnitude of 30 N, pull on an objeca3u:ge6k6bl jt in directions th3:ua6jl6bk geat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowob+6*c kv uxevfsv.+ 9n vector is

  Ignoring air resistance, the horizontal component of a bgwliv-p s;:2jn tn / ;-)qxqyprojectile's velocity

  A ball is thrown with a eoty 7w4i 0uph 4sdm4nziq48q39q l6k 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 resistance, thn.f,)* lh 2f(qcl. jo mse*(/filikgxe horizontal component of a projectile's accelerationhlfkl f2(c)ji i*ml,.*ex/s.onf (gq

  A soccer ball is kicked with a vesl.hh+ (f 0nkhb0x(ns) r uxr-locity 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 s ggbv9nreu;) yp,2 r)anti-parallel to the velocity vgrn )pbrgyeu,s ) v2;9ector,

  If the acceleration of dxc7ms i dz;4wqocc8q6 x:wy2ae6+ b:an object is always directed perpendicular to its velocit4 bxzcww8 m;2yd6x ::si6oa qqec7d+cy,

  At what angle should a water-gun be aim hxb i63gi,8/lap t-jzed in order for the water to land with the greatest hori p bxig h3,jl8/a6it-zzontal range?

  An Olympic athlete throws a javelin at fouq8ehr hcde)6:rob7* k r different angles above the horizontal, each with trq 7hd: k *)6eceb8orhhe 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 secodb7ff *axwj 32nd time. If the ball leaves your hand with twice the velocity it had on your first throw, a3f2d b 7xwf*jits horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s 0 fs s;vq aauc*fz(zrfjtd(0s x4 1,v85hbd+lat 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 maximum heighw;2 xqod ufkg9f v-/or)s m62pt, how does its speed compare to its inis;vfumw 9gqrp2) -26 oxo fdk/tial speed?

  A stone is thrown horizontally from xi( m y91jkb)u .klq33vesav4the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster3k xs)b vq4a3y1jmilk ev.u9( when it hits the level ground below?

  A bullet is fired horizontally, andkegqm8(444yhbw +obm at the same instant a second bullet is dropped44h+mybqo (g4ekmwb8 from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 71.8 m/s and at an elevation of 248 m u6i ec/,e-tk3 78eens; usjvb drops a package. 2.2 seconds later it drops a second package. How far apart will the twn,;/iee 3e8-scb e s kut7uj6vo packages land on the ground?

  A package of supplies is dropped from a plane, an8 yz tk)6))7mi8dyjsbw(ayh r-t jhe. d one second later a second package is dropy mr7 z)b (dsyi).j)hh8wke6a -yt8tjped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizon9s. mjhfi b-bl: 3y5ndtally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the9-hfb n3l b.sy5i:mj d plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Exc 2xf n2dqj0.arth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball wou22xn.c 0jqfdxld land

  You are traveling at 55 mi/h in the +x axis relative to a s+ ibz+z 36zuavtraight, level road and pass a car traveling at 45 mi/h. The relativez63 ivb++zzua velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong current. Yo r)uyn0yx2rv (u start out in your motorboat on the east bank desiring to reach the west bank directly west from your starx 0rr uny2y)v(ting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still w 8h)t sjce/ej(ater. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/h/ e8e)jc(s jht?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belovnfkt-u(t 8ionpl 2p6 a/5 fi3w the +x axis. The y component pf(ap85i nk3u6 o/lvi-nftt 2 of A is

  If a ball is thrown with a velocity of 25 m/s at an avsc2r 2 +l(mdu836ezbuey,vmngle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a strauwu8l ,7qc09g zu olf(ight line in a direction north of east and you end up 2.0 km north and several kilometers c97( fzuulow,q8g 0lueast. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component od6 o4 f4md/g9gh2iigsf its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis42/gi9 osmgf6g 4ddhi must be

  A 400-m tall tower casts a 600-m long shadow ovhgvzjwp y )1)4a;sc,, vhq y:oer a level ground. At what angle is the Sun elevatp:;,wavz cq)s4 )o y y,jv1hhged above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectimx6 e0r v;wkk+vely. What are the components of the sum of these two vectmxe6r;w +v0kk ors?

  Two vectors A and B have components (0, 1) anyj (87dflq/fcd (-1, 3), respectively. What is magnitude of thdff c7l /(8jyqe sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + (d o.0)wj554 )flsr wuettwsbB . What is the magnitude o) l)rww(t5 j5d bu.esfs4o0t wf C ?

  A car travels 20 km West, then 20 km South. Whd*yd.mx;qrd+0 j3qof) mu*ai at is the magnitude of its displacemem+*q*ua xoq r0 3)fj;mid dd.ynt?

  Three vectors, exprem+ ewaf463f9zl;ujn ue;f m h5/jm6qwssed in Cartesian 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 Cartesi,/ z49;dhc3 sw ao8x9skqmgbban 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, -4.0) andettl8 2m eh.2.0d.kw0wqs ubh vector B = (+3.0, -8.0), what is the magnitude of vector C d.ktw8t .eq0 2e u.m2hh l0wbs= A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the disp.pa )5srbpdy;g 9ju. elacement of the jogdeus.; 9abj) pgp5 yr.ger?

  Two forces are acting on an object jm 0 7,biymy79gd o(cqas shown in Fig. below. What is the magnitude of the resultant force?bi9mqd07cg j(yoy7m ,

  Two forces are acting on an objer4t y-p1d *gctvl0on4a )wt5ect as shown in Fig. below. What is the direction of the resultant foglc1*)5 terdtapt v y0- 44onwrce?

  Vector A is 3.6 cm long and points along the positive x axis. m urd1s6sv9or;(. iqe Vector B is 7.7 csv6 umser;.o(r i 9dq1m long and points at $+49^{\circ}$ 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 72 cm long and points at; zio 9q,srj4x vhso99 $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 48 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 fro bubqq..idkyd 1z 75n6mdl7d4m the edge of a cliff. A stop watch measures the stone's trajectory t 6ddkydqbd174.imbzu7l.5q n ime from the top of the cliff to the bottom to be 4.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 8 m/ssonql1)s /6r1c ahc b3, from a bridge. It falls 24 m to the water below. How far does the h 1ocac)/rs3n 6sblq 1rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 27 m above the ground, strikes the grow: 8n4 qwya0ykund after traveling horizontally a distanceywa :y 4k0w8nq of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes e.cu;.urcz1c -h fdq g-c+bx7into the jump with a speed of 12 m/s at an angle of bu c+ -ucerdxc7h 1z-.cgq.;f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intv5 qg0h/bie sy0li/, xo the jump with a speed of 12 m/s at an angle oflxe y/s5b i/ gi,0q0vh $38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 43/e;+h utc3o;d8 fpcnm.7 m/s at an angle of $43.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with aw0d3 r/:5ifcc+iof v zn initial velocity of 28.2 m/s at an angle of $39.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglei jat6-rov3:fyz:tp f9 t u8u8 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 horizjsd) je:us -lda(t7r ) q56vcqontally at 26.0 $m/s$ from the roof of a building 55.6 $m$ 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 initia sr*p1h/way,b w-uq*g:uor+x 5 + mikul speed of 42.4 m/s at an angle of *wamh ,p5-s: o/r+ *gib+u1xyquukwr$46.1^{\circ}$ 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 ca qa(pb.86cd bq b.imn8n run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 .a8b bq.id(mcq bp6 8nm/s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s.knkit+ 1 /*tmfo1m fg due North, and is in a wind of 50.0 m/s to the Wesf1m1m/k.i kgf nott *+t. The plane's speed relative to the ground is

  A plane is flying due :r rk+hfgn 5g6c w44+ip;e qruSouth ($270^{\circ}$) 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 kmq4 jv*c6+1jjh u6a*gpzij -jf /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 2d* 6sd j)e rg0)vbmze(00 m/s horizontally fires a projectile with speed 50.0 m/s in a mdgr6*) e)z0 ved(jsbforward 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 river with kravl)yhag 5p11 4stz 4-bhu 2a current of 6. 2-rh)4 up1glsyka b h1a45tvz0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/s in still water wishes to t4el r82gi-xrc ravel direcl-2 r8gc4rexi tly across a river 0.7 km wide in which the current flows at 3.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m7ago5zp(, zh e/s in still water wishes to travel directly across a narrow strait in which the curr57zh,(age opzent flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acro)ikl8wqz 9dg9ss a river 200 m wide reaches the opposite bank in 6 min 40 s. wdi9klg q9z8) She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide revpvhy aeyl+1/p-ki + /aches the opposite bank in 6 min 40 s. She is swept downs vyhp+/ka-lp/y+vei1tream 480 m. What is the speed of the current?

  A boat, whose speed in still water is ch*8, c ,bpyt)wghq 3u1.75 m/s, must aim upstream at an angle of y,,gh8 hcqbtw)*pc 3u$22.2^{\circ}$ (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)  $m/s$