Which one of the following is an ex a(mf/ so eb aklrp+dome1oy/p3412,j ample of a vector quantity?

  Which of the following operations will not cha 3qffb c sht(vr7;n x701ss3adfz 1kt.nge a vector?

  Which of the followingqk:xtg0oi 4l uxk0 r47gh+v+j is an accurate statement?

  The resultant of two vectors is the smallest when the angle between thes5q8fyea+ yn (hzkq 1a/ow1x 3m is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Whehm*gro l:1sb;6 hs,fu n 1fsbu os 6: hrhlm,*g;these two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which on tmrif4x 5p+uk576id xe of the following is a possu64x5krftiip 75m xd+ible answer for the magnitude of the resultant?

  Three forces, each havinx as2a 9ckof(n+,2-zvfd4p trg a magnitude of 30 N, pull on an object in directions that are2- ao fa2 pnks 9d+rfcxtvz(,4 $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown .314wd4v)xm :jffyq swongl:, the unknown vector is

  Ignoring air resistance, the horizontal component of / sw6nms6v:qjh/d6dr a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at antiaojt 0 8m1+p.jglkl,/c 7wt 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 acceleratio1-;oh9y + rflp1uduaqna9uu 1+d1fp -yol;hrq

  A soccer ball is kicked with a velocity jf/l 8k0qci 9oof 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 p3cznr of ,7w:is directed anti-parallel to the velocit woncf 7,:pr3zy vector,

  If the acceleration of an object is always directed perpendicular to its velika ;9 e;c3h.h )pfmb8ukamx)ocity)a c8u9 kbhk ;3me;xiamp.f )h,

  At what angle should a water-gun be guu 3r ukp6v)dhl.ba )nu1f.bv,:g-yaimed in order for the water to land with the v kl1)uuvg.b d.rn-:y,6fh p3ab )uuggreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles aboveiw2 wiqc d2/*i.r/k9o rym(j q the horizontal,m(j /2k irw2qd* i iw9y/qocr. each with the 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 second time. If the ball leaveshyz 2u w/9vcd3 your hand with t2vy3/ hczud9wwice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original bjhoeo89c 9/ )meerkmm(yu.tjr71c. l2 wmj+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 maximv z /lx27d 4 ;:3fkfiwmczzli1m0avn1um height, how does its speed compare to its initial s3 c:47zi0zz 2xlvw1ffm/;lnvm a ki 1dpeed?

  A stone is thrown horizontallyfb,lnf i:h67p vmw5 )r from the top of a tower at the same instant a bal wirf 6,v5m)fbhpnl 7:l is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant 2d-0qzikf)xk x3 2zdca second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall oqzfxcz 3) x-0d22kdikf the two bullets.

  A plane flying horizontally at a ke cd3ksvd;n1q 9 w)/)x*zvvkspeed of 67.4 m/s and at an elevation of 185 m drops a package. 6.5 seconds ladv;3w/ k9 q ncx *)dv)kszevk1ter it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is w+w(o 3+z8ibnhxb j; f ,lz:2m zg+tvhdropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling l,m+ohbgjw 2( +z 8z: iwb3vhxfnt;z+packages will

  A pilot drops a bomb from a plane flying horizontally at aynoujl b +lyj :2ftsk5 --:sf4 constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location ofls- lbjk:4-tfno5s2uy+jy f: the plane will

  The acceleration of gravity on the Moon is o+y f nx-)wk(, 15vw pip6hltcmnly one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed an5h)+vxpktp 1w n( ifw,ym-l c6d angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in theg;ecua p+,61wd:iw xw +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the;ww wepicax:1+gd 6,u other car is

  You are trying to cross a river that flows due southtxtv,3;e )c bkkqa m,q8o9(bohq87d j 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 tb) vkx37 ;o9 oq8qaqck (8,d,mhjet bshould head your motorboat

  Your motorboat can move at 30 km/h in still water. How much tiwyjsc9 o*b5d (,isrl-me will it take you to move 12 km downstream, in a river flc rsd(,yjw*l9i so-b 5owing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle o8 1l gipzcrd:me(c -pr)i-z2k: f3p vdf 30 degrees below the +x axis. The y component of A iscev:: dlp-zi8 -dr1)r kmg 2ipz(p fc3

  If a ball is thrown withwb5mkf*gi58lla2d : k a velocity of 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 in a directio hj0 bb+dzvp(c7 e2yr8 nzc.r3n north of east and you end up 2.0 km north and +3z7ndv hc ry20bze c(8 bjr.pseveral 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 iyqf) 7 d5gtf0kqwwi3)ts velocity is 8.00 m/s) f g0 i)f3tq5yd7qkww. 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. At whatmf qx :sns- 7y6u4c*/b:ebcf c angleb7mf6:eycnc* x /bfs-qu cs4: is the Sun elevated above the horizon?

  Two vectors A and B have comp*7s-jcvhr3l5p gphh ;onents (0, 1) and (-1, 3), respectively. What are the components o *7 hps3 vh-jp5hlcr;gf the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively3vkq8 mqn k n+p0b.v9n. What is magnitude of the9nv + qqnpmvk38bnk0. sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). V7wdlixgnwz3x(fx +43 *b pjm7 ector C = A + B . What is the magnitude of (ip*zlxx 7gmb34njxw7d 3w + fC ?

  A car travels 20 km West, then 20 km South. What is the magnitudeei3kvj4;vooa8o ll3)b *;f on of its displacevia *v)338n;;loo j f4l oekobment?

  Three vectors, expressed in Cartesian coordinates,px8qt31+zqbav+ q2vq 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 coordinatewyd w 2a)8rje)s, 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 thev11 bkg e,pdmge 69qa7 magnitude of vector C = A - ,11m9ve g6aq dk7gbp eB ?

  A runner runs halfway around a circular path of radius 10 m. What isb r 8(.+bzrzuku e*jh4 the displaceme8*zbr k(h.4zu +rbjuent of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the f*2 rbgypkmm5 ei9 .*u;1xbuymagnitude of the re xmy *b1e*ug9 .imp5kr;yubf2 sultant force?

  Two forces are acting on ah5*( fw:0o )-nydu ki nd9viven object as shown in Fig. below. What is the direction of the resultant foew5uo)d 9i* v (ih-kv:nny f0drce?

  Vector A is 5.0 cm long and points alonq45i85 d9pg409dli- yu qyrfpdm bz w7g the positive x axis. Vector B is 7.2 cm long and points atm5up8i 5 pg fyqzd4r9d4wyq0l7 d -ib9 $+51^{\circ}$ 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 53 cm long and poiwe 5(iaf5oy 7snts at $30^{\circ}$ above the positive x axis. Vector B is 28 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 23 m/s from the edgezlr8i.bhou c :yhv1jd 8k7(j, of a cliff. A stop watch measures the stone's trr:z1 lbihj8dy,v( oc j8h7. kuajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizlbd mnkujq rcuo(8o /,ze )zzn :+5/7montally, with a velocity of 11 m/s, from a bridge. It falls 14 m to the water below. How far does the rock travelr+ zo,u8zkdjb/l:5e c m/7(zq oumn)n horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above the ground, spjwc e knao, 1 a1n8xax0;g6)atrikes the ground after traveling horizontally a distance of 14 m. wpn6x0x )jka18 e o;1ag,aanc With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/+ 7oowf )u2 a;m(4chthyx2idss at an angle o)ifht7hyc d(4o x 2au+;s2mowf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump g9smzm*q9zp9, j6z a2u dn/k b.bnp8esoes into the jump with a speed of 14 m/s at an angle opz 9njmb b6/, sna9d9 .uz2qzpek8* smf $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 39.6 m 1s.7, th8hos/mtc exx v*6zur/s at an angle of $29.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launche9la/ib uxehe9 2pl)7bd with an initial velocity of 55.9 m/s at an angle of $19.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang:tg9o7v ic ywh9mwg*k(e3g-5g:g t mcle 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 a+0z i 1j blg-lyh7 uv(x9di/iht 18.8 $m/s$ from the roof of a building 49.4 $m$ 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 56.7 m x(blq4bbw5i/ /s at an bl/bx(i4qb5w angle of $45.8^{\circ}$ 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 qa6)uojl w8u5piq- 0t1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day whu0ijp-8aqtl o)w q5u6en 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 20 0zg ,krgp xswwi9 6u)zen9,x80 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the gr,098rngupse )zwx6 x9iz,kwg ound is

  A plane is flying duegyydenilt( 7/u.br(llam8 6 + South ($270^{\circ}$) 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 hea c8aj7dq 3mx5bded $30.0^{\circ}$ 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 with spe5eu 3hf ja5jdb p1mu+:ed 50.0 m/s ie+fpjm djuu 5 3:ha1b5n a forward 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 is4t8q1/ kvfh z.dc id:b 8.0 m/s, is directed across a river with a current of 6.0 tqdi/b4h1:8 k zd.cfvm/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 11 m/s in stilys+50c51x zj9cz ek*:olnnvv l water wishes to travel directly aczseo1k c5 nylc0n:9v+5 vz*jxross a river 1.9 km wide in which the current flows at 5.8 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 wi.bs18rt/r i o4xr azwbq(p1uqnl( 5)gshes to travel directly across a narrow strait in which the current flows at.asgr4(prq8 bo b( i)qlru 5 n11xwt/z 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide ktpdg5 3 *7rtxp: k7 q-avly*sreaches the opposite bank in *s 5ar d-kt:lvyxqg737*kp pt6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppos0 dp6 nq *(aaegc4o4,gw+avzb ite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of twb,z6(cnq pg*0 doa ev44ga+a he current?

  A boat, whose speed in stipw*hz)bq - 3uyi m y;u +jnd*wm.7ref8ll water is 1.24 m/s, must aim upstream at an angle of*) 7y+mj .u;pdw *ezm nwf83uy-rihqb $30.9^{\circ}$ (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)  $m/s$