Which one of the following is an example of a vector3jmhc8tj1p) f1/nx- d,kn cti quantity?

  Which of the following operatioy dwcd7:zd4x/(xvwr2/ k b u6)lmq:tons will not change a vector?

  Which of the following is 4at9f*lv 5yxr/1jh t9vflgdb y;(5h a0lw g h1an accurate statement?

  The resultant of two vectors is the smallest when twph sq/hq3*c(he angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Whyx0j3w)m6dz(d c gz .hen these two vectors are added, the magnitude of th)w(dc0zh.3 jmdxz6 gye sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following sd5+3f ouohvwg)dcrhr :t3w*c4c o9) is a po*)t4f)dchoc rdg53 uw:vw r3oh9so +c ssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object 4qjcsdq/b93.nzfo+dpz-4 lcin directions that are p9 d4+4b ol- .qn/czfcdz3jqs$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thq* n:j5n)tg:sb4tjgkc lx q;( e unknown vector is

  Ignoring air resistance,pb6vd/ r*o7tti 50h jh the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s u w1gfhj/*n04 pvji+:mrns9w +z+ y bxat 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 accelezlyt(g 1q bu)dyd.(o 1ration1z( dlyd(btqu.)ygo1

  A soccer ball is kicked with a velozar2 hgv1/i m,hgc 56bcity 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 vedg qe(6rhezdh5+s(7/sot *ywctor of an object is directed anti-parallel to the velocit(e(e6/5 y7 sd owtg hsz*h+rqdy vector,

  If the acceleration of an object is always direc3ud q5l d:d/h d(2uwzyg,yzmb /.w4hxted perpendicular to its velocityd,zuudqw3zw xm(gh.b yyh/d l 45 /:d2,

  At what angle should a water-gun be aimed in ordery4s .p i37b zch7g xqj;c10ncw for the water to land with the greates0jz3xp7qwn1c 4 ccsyg h;7i.bt horizontal range?

  An Olympic athlete throws a javelin at four di9r+lell hkams, 567safferent angles above the horizontal, each with the 6a7+ 9s l l5klsameh,rsame 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 vb0 u6q(b4ywth9nkhs(r ;y1dime. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compare(h(v6 4bdrs0kqhut ybn1 9yw;d to your first serve) would be

  A ball is thrown at an original speed ofn4mcw ,yoer7z36us( c8 uzzr1 :ar0nj 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 maximum height, how 2uqc+w4 n-/g id,iq xidoes its speed comparexn-4iq +u2cq idw g,i/ to its initial speed?

  A stone is thrown horizontally from the tddev6mb r97 y6op of a tower at the same instant a ball is dropped vertically. ddbmv7 9e6yr6 Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the sk .xifhgu*6(bame instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of .guxbi*h 6k(fthe two bullets.

  A plane flying horizontally at a speed of 85.3 m/s and at anp-af7w 0.qjrxf5 /yaw elevation of 164 m drops a package. 3.9 seconds latw/xyfa.q7p awrj0 5-fer it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a planr0s- .5qvdfd ks4;f wde, and one second later a second package i fs0kf;v qds54 w-d.rds dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying hor 1oume2 ad3k7jizontally at a constant speed. Neglecting air resistance, when the bomb hits the grouj odk3uea 7m12nd the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Eat92eq3j 4q ktrhu8w b1rth. 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 would lan9etth4qwbk32j 8ruq1 d

  You are traveling at 55 mi/h in the +x axmg dz lx)ngu* i(196xhis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of you xggh *xmu)iz9nd16(lr car to the other car is

  You are trying to cross a river that flows du+p u5qz1kyrjr j;:aa* e 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 starting point. You should head your*;pa+ja15 qr yzrjk:u motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take yb 5eau 75v3swq kq,a2n4ep6izn+eeq7l, r9e rou to move 12 km downstream, in a river flowpae75k7 z65 2ew e43vnue,bl qq,+reqsarin9ing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle ofbbn+. zo n8(wqm.2fv q 30 degrees below the +x axis. The y comp2qnfm8bnq .(.zv+ bowonent of A is

  If a ball is thrown with a velocity of 25 m/s at an avi4j.7vhhh8icqo v 4 :8r+ kxhs37mqungle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a strm+:0x qbc*m)y0h go)j llpq7aaight line in a direction north of east and you end up 2.0 klo: lpq7qgc *ab )h0j)0 +ymmxm 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. Thezkad.ewyu *u8jbg/,vmv /+ (k x component of its velocity is 8.00 ajuw(ed /y*./k mvgk,b+8zuv m/s. 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 grouh,m 6gwi aq7t*os2h4mnd. At what anglea6ho4 m7s2, hit m*qgw is the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) anyq1d8 qr 35vqkd (-1, 3), respectively. What are the components of the sum of th13 5qrdqyqv 8kese two vectors?

  Two vectors A and B have components1d4yxl-bm4 ol (0, 1) and (-1, 3), respectively. What is 44m -ydo1xbll magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Ve w(uhv/8d9p x dynts+:ctor C = A + B . What is the magnitude of C ?x :8dy(vhwpt9/ +un sd

  A car travels 20 km West, then 20 km South. What is the magnitude of itscon(gijuuqmu2 8,; m : displacemeuu2o n i(q;g:mc8j, umnt?

  Three vectors, expressed in Cartesian coordinqto bo)f a i: q;kp+1) e-dxc0tdfl.3pates, 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 co1xitn*-uz g/oa .b2y rordinates, 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, -4.0j)+kx70zc.fr up/ iel ) and vector B = (+3.0, -8.0), what is the magnitude of vectoe/zr7 fcpkix l+).uj0r C = A - B ?

  A runner runs halfway around -x moc1xtm1o4g);ouqa circular path of radius 10 m. What is the displacement o;uo1)gxxm m q4t1-coo f the jogger?

  Two forces are acting on an object as shown indie 3x13 y1uwd Fig. below. What is the magnitude of the resultant forc 3eyi xw11dd3ue?

  Two forces are acting on an obz,qi;iz-- g, cs0 ls4lyunbk.ject as shown in Fig. below. What is the direction of ; ,q-zbsslny,li-0gc4 u z.ik the resultant force?

  Vector A is 4.4 cm long and p-sf1k vc,lga c-9pc7toints along the positive x axis. Vector B is 8.5 cm long and points lctasgpv 79-c1f ,ck-at $+42^{\circ}$ 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 89 cm long mi- 1ydpk +y/q+ : wuhk8qfa6tand points at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 43 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 14 m/s pj co/10bh; m vebj(y,from the edge of a clp b;(1jcvb,/ mjoh 0eyiff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizonta,i hrh(q7x)u vlly, with a velocity of 9 m/s, from a bridge. It falls 18 m to the water below. How fqhu x,)(rh7iv ar does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 26 k1,c n b7cujp-. altc/m above the ground, strikes the ground after traveling horizontally a distance of 22 m. With wht1/7p c,cub al.kjnc-at speed was it thrown?

  A jumper in the long-jump goes into the jump with a 3vxfxdtphget. d6,8(speed of 12 m/s at an angle of,p gt3xd xt6dv8h(e. f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-ju hh7rb/d;l1 vwvn1tr;mp goes into the jump with a speed of 10 m/s at an angle ofl1;dh t 17n;vwr/hrvb $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloz30 azmj)kd5ecity of 42.9 m/s at an angle of $23.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of xl/ 0d2bpo/ew 59.2 m/s at an angle of $43.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedn x3jnq o*685zxgqmy3 et9u z6d:mf e5 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 horizontally at 24(0 cpp;vqgu u;.6 $m/s$ from the roof of a building 48.6 $m$ 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 grouxbf7d: t huxh;t8p (a9tl4m -wnd level with an initial speed of 57.6 m/s at an angle of :(t t-h f;tbd xhpula87wxm 94$41.2^{\circ}$ 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 velf(mvk+g sg5d 8ocity 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 m/s, the time it would take you tof8 sv+( 5mkggd finish would be

  A plane has an air speed of 200 m/s due North, and is is,y.06q wk e )hhhx3rtn a wind of 50.0 m/s to the West xye)hw.30k ,srh6hqt. The plane's speed relative to the ground is

  A plane is flying due Soutp2lxi hl t3+gcce9(:p f:2p /r3luhif h ($270^{\circ}$) 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/h is headed nm n,-(pslld3a8hpc 4$30.0^{\circ}$ 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 movini./ttg1a4 mp e(rz7nug 200 m/s horizontally fires a projectile with speed 50.0 m/s in a f/t(4ri ap 7zeu1gtm.n orward 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 acrcj1 x)2lfb o. w;5tgdwoss a river with a current of 2)xgcbw;f t 1 jw.o5ld6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 18 m/s in still water wishes to trave5kh ;jgpu ny)5l direc5hn g)k5up j;ytly across a river 1.5 km wide in which the current flows at 5.3 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 water wishes t:e;c/iuu)jhh0z0nkb br ra8.o travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upu 0hn a.e) r/zbbru;kc 0i:jh8stream should the driver head the boat?

  A swimmer heading directly across a river 200 m wideeurft1o7, c9x reaches the opposite bank in 6 min 40 s. She itf9uer 1c xo,7s swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m n73ac ba ;tyvg+yf,9 u/j4y;*mvge yxwide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of +9e cy;v3;yu*y v 4ja7b xgynm,ft/agthe current?

  A boat, whose speed in still water is tqz:e1lnkr0*zew ud5by2)h , 1.25 m/s, must aim upstream at an angle of 20 eu hwzyrlqz :1*k,te5b)dn $17.0^{\circ}$ (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)  $m/s$