Which one of the following is an example of a vector quantz6b 39 ,ftev k/fz hz-hutyb7*ity?

  Which of the following operations will not c;u-3) ovdlkuphange a vector?

  Which of the following is an accurate st:q /fcpvr69p8ta)q tc 8k(ae jatement?

  The resultant of two d8g(xvvez+ro1s69nb vqr -h*vectors is the smallest when the angle between them is

  Two displacement vectors haod39 z6jt y(hhmk/bf :/m0nv sve magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of tds vb0fo9k(:n//zjt m3myh 6h he sum

  Two vectors, of magnitudes 20 and 50, are added. Which one o ;jqxe0u7 2jqdf the following is a possible answer for the magnqxu7 0j qj2;editude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions t-gt us tp gncfe.pb8;h4 /x9/that g -hs/;tg4pctb.t8n xf9up /eare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vx9g la5 zoatu9s4x 7br(x dj;1ector is

  Ignoring air resistance, the horizontal component of 7m2;xgnrk:svk i 64d 4 yqr+ -w*pmgnta projectile's velocity

  A ball is thrown with a velocity of 20 mcjv5-: dyib*:t-q bnn/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, the horizontal component of a projectile's accelmsmi6 acq7)3 /fpj 8nkj0yk(deration6siamc k7d /j 3qj(kfm8yp) 0n

  A soccer ball is kicked with0trsmkdc+z/i)ry:w) 0 l9eoyu 3vu7 o 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 of an object is+ zu4w+dphcy6 directed anti-parallel to the velocity vec+y hw6+u pzd4ctor,

  If the acceleration of a04z3v j)jw up75lmwih41hx xon object is always directed perpendicular to its velocityxj 537)vhxpumw4o0zl4 i hwj1,

  At what angle should a water-gun be aimed in or pf9d( a6z rm/vxr.5bider for the water to land with the greatest horizonbz65m 9 v/(ar.fixpdrtal range?

  An Olympic athlete throws a javelin at four different a v n8usygya(ka7pnwb*4s+ (6 j;ios: gngles above the horizontalb(kup;n:+ oy(s6w4ai7v gaysn g*8sj , 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 tqqa/ni (f.j/j ime. If the ball leaves your hand with twice the velocity it had on your first throw, its horiz iaq//jf q(.njontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at gb0n/z(xr 4w+aid )qpan 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 aw,kdf -1g7ga fttempt reaches its maximum height, how does its ,-gf f7 dgwk1aspeed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at *o 6cu4. ahe ih4wq53u s1eqrzthe same instant a ball is dropped vertically. Which object is traveling faster when it hits the level groundq4iq aou u4he ewh.c3z1r s*65 below?

  A bullet is fired horizontally, and at the same instant a l d0a6f1sx-- her /ifasecond bullet is dropped from the same height. Igf- sx-6 hdafra0 eil/1nore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 70.0 m/s and at an elevation of 169 m8m5st 9cv 1hlv7xb-vd++tn9fjz ;ywu drops a package. 4.4 secon xmt7;1f5vv tc9 9j8uv+zwnlsyhdb +- ds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dri j 6am(mb9thp u5-qe2opped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fallinheujiqp 9m-m6a(5tb 2 g packages will

  A pilot drops a bomb from a plane flying horizontally atsinlxu83wxco l 70g1h9d;q2p a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the pl8lxi l 2dsgw 7xo3pu19n;q0hcane will

  The acceleration of gravity on the,wnwy+d /ra 2)gx3ur p Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (andur/x rdn ,yw2pag+3)w at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi+ +(bnzts +2 uk ;jvkz29bu4mhv ibrf(/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relati+m sifubrvuzz (+bh(; +9v2ktn 4jbk 2ve velocity of your car to the other car is

  You are trying to cross a river that flows g,/ sum1(oes;w* cfys due 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. euf,my*/s1;sw s( cog You should head your motorboat

  Your motorboat can move at 30 km/h in stih1f.c,j b vcv*ll water. How much time will it take you to move 12 km downstream, in a river fv fbvc.c*j1 h,lowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at afov 1l+y ;3r6-kl+ugauf - jwin angle of 30 degrees below the +x axis. The y cvi;k fa ju+lg13uy -olr+w6-f omponent of A is

  If a ball is thrown with a ;zy gx3) l.*n k6p z/kiqnl hwhs/k.0fvelocity 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 diruocwc 4i2d 2 ab.mvl+7ection north of east and you end up 2.0 km north and several kilometers emv. +ucb 24walic7d2o ast. How many degrees north of east have you walked?

  A butterfly moves with a spee/uu*. crsz v(cd of 12.0 m/s. The x component of its velocity is 8.0r zs(ucv* u./c0 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 ground. At whc(78 6wd9kf;qj obyg;u v x(xz+m iu3cat angle is thv mx6 ix8z7gyu c(;f+ub ;dj9qco3w (ke Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivelyut4o8ev59r(ujegos0gc /t,+xv 9aon . What are the componutv59, +t on9ao o4x/8s0jruveecg(g ents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whaw4d,b :6 ijccmt is magnitude of the sum of these two vm :6ib4,jcwcdectors?

  Vector A = (1, 3). Ve oi;dzk2 i0-l:kyjvzfzt ) ,uc3m-av*ctor B = (3, 0). Vector C = A + B . What is the magnitudk,ucmj fv al*2vz3: yt0iz )z ki--o;de of C ?

  A car travels 20 km West, tw0el:m.qyu b s1p (d*5l5r.(n t(m os b.tsuafhen 20 km South. What is the magnitude of its displactw. bu5qs.ml *u( (1 rlsyaodn5 eb(fpst:0m.ement?

  Three vectors, expressed in Cartes 2c0qhak6o:r/1sev ilian 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 Cartesian coordinatesgi. y; 4zfhtc v fwrq7/ao4w8x7p5m0w , 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( iht9x8xtie+7+e x2fbefijt*5 m /jg the magnitude of vecteh+ 58xte(jf9tte7 im if2jgxbx/i * +or C = A - B ?

  A runner runs halfway around a circular path/ foaq5m/p :tw of radius 10 m. What is the displacement of the jogger?/: otmaw 5p/fq

  Two forces are acting on ; impooh* 3hr9an object as shown in Fig. below. What is the magnitude of the rp3ohh i ;*9ormesultant force?

  Two forces are acting on an object as shown in Fig. below. What is the di .svtr 8+n,i.8zr ywlm+ywpa* rection of the rst*apn i8.yv8,wryz+lw . m+resultant force?

  Vector A is 5.6 cm l 5/ 5/rz;nzbrk8i y5/)zfd(kojvwecdong and points along the positive x axis. Vector B is 5.3 cdv8o )5 zk ezk/wnf(55yb/crd/irjz;m long and points at $+44^{\circ}$ 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 86 cm long and poiraz1lme beib 2v42f3p 7nfn +*nts at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 50 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 12 m/s from the edge:zg6 x5w pquh9 of a cliff. A st6ux59 :p gzhwqop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity p86reis1 xfn3ol/ou 6j her14 of 17 m/s, from a bridge. It falls 18 m to the water bj1/1 o3spr64enxe6h rli8ou f elow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, strikes th6 eh up4mq9 zlk0yii.+75rd eze ground after traveling horip 9q .iiz6dmerl7z y5h e+ku04zontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of19m aj6jkx:7 v3 l0xd6jf ubfh 12 m/s at an angle of6fm6xjd9: 3 ukfb0 v7lj1xjah $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long -qiihr( qj+7i-jump goes into the jump with a speed of 13 m/s at an angle of hi-j ri(+qq 7i$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initialrw96,ojhiv tyn*-e/vat-0 tw velocity of 22.5 m/s at an angle of $18.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloonr)p*0(varb m y n8*44jt dbwn 7y9rpcity of 30.0 m/s at an angle of $30.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ayi)vl la+/gin4c/c: n ngle 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(wdptj svmkr/-cd m -te.oozj6-7* w) 26.6 $m/s$ from the roof of a building 32.7 $m$ 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 lu;-:sprehcvrki3 q+d(w f)( with an initial speed of 61.5 m/s at an angle of q3wepk -h(fd+cr:r) su(i ;v l$41.7^{\circ}$ 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 vel,80yqsy8iq.qrf nzgds 9*es +ocity 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 wouq08gnz 8q.rqf sdeyi,9 y*+ssld take you to finish would be

  A plane has an air speed of 200 m/s due North, an d5 gc.5g3mhcbd is in a wind of 50.0 m/s to the West. The plane's bg 35mgdc5 h.cspeed relative to the ground is

  A plane is flying due Soxrii-qu( 0 1zjuth ($270^{\circ}$) 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 i4 ac9:dfpc:tw s 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 with spe gulk.:hw3 z5ckhn73jwfd(n -*v sqraj6-mk: ed 50.0 m/s in a forward digdm h* q: r3hwfjj6:a(snzw nk5vc-lku. 73-krection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in st9iuw0,dpw h+ d:wwn-nill water is 8.0 m/s, is directed across a river with a current of 6.0 mpw u: -ddnw,+9nw 0wih/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that 2svza1w ,z nt2can move at 20 m/s in still water wishes to travel directly across a river 1.6 km wide in which the current flows at 3.1 m/s. w 2tsz2vn,1z a How long will it take to cross the river?

  The driver of a motorboat that can move az,lp*o8x.qul * f1gynb:f. bot 10 m/s in still water wishes to travel directly across a naro. qbx:u1 fz*l,gb.olf* pyn8row strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading dirt;z n5bc4tcrt1,zph9 1l sky)q+we 9yectly across a river 200 m wide reaches the opposite bank i9t1 1 5tpk; yrwzh4ce,btqsl 9y zc)+nn 6 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 the0,jr ze*3g l vlmahc:( opposite bank in 6 min 40 s. She is swept downstream 480 m. What is thegcj3* z l:(vah m,r0le speed of the current?

  A boat, whose speed in stilb8k,1ty / gbyel water is 1.38 m/s, must aim upstream at an angle of b, gby 81teky/$14.2^{\circ}$ (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)  $m/s$