Which one of the follh qe4lf8 2er *8yyuqt6owing is an example of a vector quantity?

  Which of the following operations will 0n+y +a0mpem,f jdp 0vnot change a vector?

  Which of the following is wg-,5o d7w9 j-aowm 2i,jcokuan accurate statement?

  The resultant of two vectors is the smallest when the angle betwe jtaf-q*(,l kren them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, resk.jsv fyab 02+pectively. When these two vectors are abfa2+j. ksv y0dded, the magnitude of the sum

  Two vectors, of magnitudes 20 andc;vpe3gq;acjv 5 :nffvxemz-74j *.w 50, are added. Which one of the following is a possible answer fox.7efce p5am c:w;j3-fvjgqv;zv 4 n *r the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in di4 j y:ydb)j db 696gf8np;imxirections that are 6 n4 jpb yx;:i8jf6d)mi9bg yd$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknos3-o20ky8 aogri z4p jwn vector is

  Ignoring air resistance, the horizontal component of a projectile's velocil/-d3gvjziw zi 0nl* 0ty

  A ball is thrown with a velocity ee(0wv.l (wg2gdr*xy.e 0aitf--xzn 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, the horizontal component of a projectilezc, 2 . hve.b1c,;t2e/g0ngmr fwzkz n's accelerationhrn zncwf.ez,vge; m1z 2.bk0 2,ctg/

  A soccer ball is kicked with a velocity of 25 m/s at hro vwqf2/nr2,i7(ls 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 anti-parallel to the velocb2t4hz (kt/ ytity v4(tt/ hzk2b ytector,

  If the acceleration of an object is always directed perpendicu.5s. z/qgynp qlar to its velocityp/. 5gnqyzqs .,

  At what angle should a water-gun be aimed in order for th (. c2ftbye/jqe water to land with the greate/2qfe. c b(tjyst horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizont6r lei cq6)x9j.2ys xlal, each with the sa xllsy x9ecrj.iq)26 6me 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 balljo:i- hx72bfcl u7i nih-43:1kfhhr i for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to hi23bnh-1x4lii:kfih:7f rj uch-7o your first serve) would be

  A ball is thrown at an origingkw5p2p3fljv41 d- jlal 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 maximum height, ho **t a8lnrr1dpw does its speed compare to its initial*d1rln t pra*8 speed?

  A stone is thrown horizont fgm* nq)vln pyax1)bfvwj/o. 5ptv(hf ) y89+ally from the top of a tower at the same instant a ball is drfo(qy)5 lmv h8)y1 p9 tpvg/+fa*.nnx) bwvjfopped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizvp m:zao5zl 3tsulk2ki3k*,8 +vwke3ontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times olm k *sovte u3p3kakkv5 l32z8 +:,iwzf fall of the two bullets.

  A plane flying horizontalln f+x+ns/ to(dy at a speed of 94.4 m/s and at an elevation of 143 m drops a package. 2.3 seconds later itx+ nn s+d/(oft 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 lat-k 12iwd3 a8colulox;er a second package is dropped. Neglecting air resistance, the distance between the falling packages willdil;lw -ouk 32oa8c 1x

  A pilot drops a bomb from a plane flying horizontally at a const d me* kvewd, ,ra+;a1ardk(o/iym;-cant speed. Neglecting air resi,a,+v-1 k*rddmaw;d ce;a (ek/mory istance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of grqh+e08e mxaiouw1-b)f22nd mavity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, th+f 8dxnamo )2wih2qu1e -0 mebe ball would land

  You are traveling at 55 mi/h in the +x axis relative to a sth+wxeqa p1c u 2yn;w*)raight, level road and pass a car traveling aq) uc+waypew; nhx1*2 t 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a rhfe w8w(pad*pv q:7)river that flows due south with a strong current. You start out in your motorboat on the rd*87 (pwavqf): ephw east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in st)aazy a*og(( qill water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/o( ag ()z*yaaqh?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the 576k.g dry hhb+x axis. The y crh67kydgh5.b omponent of A is

  If a ball is thrown with a velmw4qj 3mx4 dki z(7nj/ocity 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 m v,f+u yej75d6f;vgd line in a direction north of east and you end up 2 uyed;vv ,j6g+5 d7fmf.0 km 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 comg c:lco7s)(s,4g zmkfponent of its velocity is 8.00 m)7, z4o l:(gmgf cckss/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m lo, s 9 89agnaj61tzgpccddt3-tng shadow over a level ground. At what angle is the Sun elevated above ta gdad g3z-6tct 1,9p8ts ncj9he horizon?

  Two vectors A and B have components (0, 1) and /;jw+ uib sh;lr8uj6,m3 ismp(-1, 3), respectively. What are the components o b s;l/8s+,6uimp3rjwhui;mj f the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, rt z-; fvi9e3lku,hn03), respectively. What is magnitude o9k ;hn3ifz0 tre-,l uvf the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0).,*2ntjm-0wm epq )dxc Vector C = A + B . What is the magnitude of C ?-td mjw *p)20mxq,e cn

  A car travels 20 km West, then 20 km South. What is the magnitudes b -kqegl2x,6 of its displacement?ksx 2b- ql6ge,

  Three vectors, expressed in Cartz u f()bk090peem8gomesian 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, expreji2gadn:s s)djtl a9w ;)u96wssed in Cartesian 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) and vector B = (+3.0, -8.0), what eno8*) o4rnax0la u here8r 55is the magnitude of vector lr8an eore4) nhex50 oua8r 5*C = A - B ?

  A runner runs halfway around a circular path of radius 1xq; 7ft. iphf9 ( /tiurbee j/;o(tgy-0 m. What is the displacement o9.hf;/-bytjo( xri/(eg t ; fqpuet 7if the jogger?

  Two forces are acting on an object as shown in Fig. below. What is tmxo5 b5wbcx6b y46k0wztz a6 3he magnitude of the resultant f3x5t40x kz6z5 w6ycow 6abbmborce?

  Two forces are acting on an object as sho7icw3j48 z 6(uxv ogyewn in Fig. below. What is the direction of the resultant force?7z(e cj6o 4wiv38gxyu

  Vector A is 3.1 cm long/v t 5;af:qdux and points along the positive x axis. Vector B is 6.8 cm long and points u5v df;/:a xtqat $+27^{\circ}$ 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 59 cm long and pointlu-b ip (t4q*g7a:lc4om+mu1d 2p ae us at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 41 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 horizont80r3ksaki- 7vcz gcfj+xt3j4 ally with an initial speed of 24 m/s from the edge of a cliff. A stop watch s07v gxc+tfa3i k-438jk jrz cmeasures the stone's trajectory time from the top of the cliff to the bottom to be 2.6 s. What is the height of the cliff?

  A girl throws a rock horizontally, wk2 -vhnz: t* k/(h;r0l rgdxqnith a velocity of 12 m/s, from a bridge. It falls 25 m to the water below. Ho hn -kqn 0t*2k rvxgzh(lrd;/:w far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the 7sr srg1bayh(( 3;zkfou.qjemg 4nu 8x+lz/0ground, strikes the ground after travel+ .4(uq 0nbr k7 x a/r8jhz3emfsougl(y1sg; zing horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jumf. s cll2kzv-eck-+3k p with a speed of 12 m/s at an angle of v kc2 klslke3c-z.+-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 into the jump with a snhuvav bup) * r3s5yvof(, 4p2peed of 10 m/s at an angle rbu (o *4)ppfnv2svay53hvu,of $40^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initir8bo* r pv((uxal velocity of 59.6 m/s at an angle of $14.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 22.7 m/s at an angd/npmk(cj24 z le of $10.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglehy2nd5.r 4dg h 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.rj6or7a(n y8 q5 $m/s$ from the roof of a building 53.1 $m$ 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 iniu gxg+br2a e+a;qdb:: tial speed of 43.0 m/s at an angle ogr :+ebxa d q+g2ba;u:f $42.5^{\circ}$ 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), youtikcr,5) kzy96x/aqw5/c pf wic:q9y can run a 1500-m race at a velocity of 4.0 m/s. If you ran the s5c/c w6y kyrx5w/k)z: i f t9qcpaqi9,ame 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 would be

  A plane has an air speed of 200 m/s due North, and is i o hym4 s n*ucbisp08z f:k .5*3g(iexb:xqcw9n a wind of 50.0 m/s to the West. Tsbc:iy ux0**m8o (fxeh qwns :43c5b .k pi9gzhe plane's speed relative to the ground is

  A plane is flying due Sods f) h998cudg+ohs-outh ($270^{\circ}$) 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 dd6 lt-j9s1ane q v+p0r5xul)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 with speeddx f,f/b4i7dg 50.0 m/s , b/df d4gf7xiin 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 wate 2b1trr; o+c2qru tq9wf b:t/eh3wi.vr 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 rivvto/bwi:2 cq32 +b weqru1 r.h;t9rfter?

  The driver of a motorboat cik umr72eo6-that can move at 12 m/s in still water wishes to travel directly across a river 1.8 km wide in which the current flows at 6.7 m/s. How long will it take to cross the river?7eo6 m-2rikcu

  The driver of a motorboat that can move at 10 m/s in still.eqix2 y:z q ebww(;,p water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream shop:wbe2 w;, ei.zq yq(xuld the driver head the boat?

  A swimmer heading directly across a river 200 m wi0cnl kqx 7zy(9jmb+l0 de reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she s9z+0jy(lq 7xm cb kn0lwim in still water?

  A swimmer heading directly across a river 200 m wide reaches cf tpd s(9a8f 9d.muf+the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the spee+9tapfm.9f dc(s fdu8d of the current?

  A boat, whose speed in still water is 1.96 m/s, must aim upstream at,wn 5 tl5o frxc64o+br:l 25si 1vqlgs an angle of26:5iwxr+1g455qlsnbo lvclf so ,r t $18.5^{\circ}$ (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)  $m/s$