Which one of the following is an example of a veci()dncqow,i a4r3g.a r f5)rotor quantity?

  Which of the following operations will not change a vectoriw( 66o pqb(4sbi3wkc ?

  Which of the following is an u(s*qbd3rcsw xoi rht dl8e0+ p2,d 1;accurate statement?

  The resultant of two vectors is the smallest when the angle between they ax: r +iheyx7t a98hy579lisf ce5+vm is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectjkf4p 06qtyy 7ively. When these two v fqk6y7ty40pj ectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, +781mk 9jherchoq3r x are added. Which one of the following is a possible answer for the magnitude of the rx1oc 7mhhe 9r8jkq+r 3esultant?

  Three forces, each having a magnitude of tm2bvz9si ags*/ l)6p30 N, pull on an object in directions tha b6*/zmgst)i l2svp9at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thag 6jzz).k t-4rcocs1e unknown vector is

  Ignoring air resistance, the horizontal c;a f; w1h/k4ax33tcwb (hpvptomponent of a projectile's velocity

  A ball is thrown with auyyfql;:,(d o 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, the horizontal component of a prdxdymv5l*rhy a.e-5+nd + 1ymojectile's accelerationd 5.+a*- r5y+1mmhnxyvdldye

  A soccer ball is kicked with a velocity of 25 m/s kzn*;ro.q *glat 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 veig:9ank a5h/: pp1oht ctor of an object is directed anti-parallel to the velocity k9:p/h g tnip: oa1h5avector,

  If the acceleration of an object is always directed perpendicular to it7u tls.ye 1 ydn)vcuu* an;n)1s velocity,.)1yvsn nld1)*u ut;cn 7 yeau

  At what angle should a water-gun be aimed in order for the water eh,(tkfb9 ky 4to land with the greatest horizontal rangy(k t4b9kf eh,e?

  An Olympic athlete throws a gv9wif3 8v 3z)6 n 3iiiroqxi(javelin at four different angles above the horizontal, each with the saro g9 i(wfn3q6x83z ii iv)v3ime 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 leaves your hand with sk/y:f1oh.sh twice th:h. fsoy1k/she 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 speed of 8.0 ipko6y00y/osdsmi2*ajpb hc/ ,9ua, 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 fobl) t0vb2). 1oabvau :p ioy+ield goal attempt reaches its maximum height, how does its yoolib 2t)+u): bpavb oa.01v speed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instantwhpaorp9 7 x :o9htst q/(+h0s a ball is dropped vertically. Which object is traveling faster when it hits qr7h sxo ph9 0t(:9whpot/s a+the level ground below?

  A bullet is fired horizontally, and at the same instzj/ /:voriht t)fm.x/ant a second bullet is dropped from the .mxjtzf/ r : ohtv)i//same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed ovdd85qk9 b7 kof 66.1 m/s and at an elevation of 200 m dropdob 8kv9kq5 7ds a package. 6.6 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from 6xvds f 1wi6 2*+etn4zx fkq+ya plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages wi fex+ n2+4 1v6xyk i6szdw*qtfll

  A pilot drops a bomb from a plane flying horizontally at a c : tvj/0yjrk,u/vo8qd onstant speed. Neglecting air resistance, when the bomb hits the g:yj 8d,0 vutqr/vo/j kround the horizontal location of the plane will

  The acceleration of gravity wq* nibl,h mkq;ry ;30on 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 w 0lw3mhqq* y;,b;kin rould on Earth, the ball would land

  You are traveling at 55 mi/h in the +xyl8 o+p2 czz*y axis relative to a straight, level road and pass a car traveling at 45 m2* zyoplc8+ zyi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a strong cua b9c 4k)urfz66 njqx8rrent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point.azrc9) 8qxf4 ukj6b6 n You should head your motorboat

  Your motorboat can move at 3 q*; tec/u- 8vxw)aicw0 km/h in still water. How much time will it take you to move 12 cexu*tww 8acq/;v- )ikm downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis/ xqydg5z( 1ql. The y comz(1/l yd5gqx qponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of fjd/1sn a9wnn9 j6+mt $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a dir1fcxk 2 o*)cb6,)r*x3a nh0aodkhojw ection north of east and you end up 2.0 km north and several kilometers east. How many degrees c1 * do2konaa30wj*r6ox)xhhkcf) , bnorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x co16 ;wbwl.- gkga .jdcgmponent of its velocity is 8.00 m/s. The db ;.gg.gwcaw-k1j6 langle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long sh-p r7 ia,k+w3cb8 fy akl/jqx-3 pax0pfd20mmadow over a level ground. At what angle is the Sun elevat ppm0+ 0fw3r l7p-,8qx kfiy -a/a3jbd2k cmaxed above the horizon?

  Two vectors A and B have components (0, 1) and m+h1/h*l : s;5qibxgiyrfmf8(-1, 3), respectively. What are the:*h rm 1m qfii5+8 l/hyfxs;gb components of the sum of these two vectors?

  Two vectors A and B have components (0, 10 jmygxl i czm.l9x(:2-8 flyn) and (-1, 3), respectively. What is magnitude of the sum of these two ve0 gn- ml8x9fj.l yyxi2mc( lz:ctors?

  Vector A = (1, 3). Vector B = w; 4luqysccz.xa 35f)(3, 0). Vector C = A + B . What is the magnitude o)3lw z.f4c;s caqxy5 uf C ?

  A car travels 20 km West, then 20 km South. Wb,tq w1st 0*jfhat is the magnitude of its displacemqtw,s*0bjf t 1ent?

  Three vectors, expressed in Cartesian coordinates, an1yrc lf3,wdcb) l5zt*o 70 hnre
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 coordinates, are /h 0nk;me0:t,bq baxy
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 the mxoj*8gw 0mfrb 0 hbk0-agnitude of vector 0xog0b-b *j8 0rwmhfk C = A - B ?

  A runner runs halfway around a circular path of radius k -jqwyq1p /j610 m. What is the displacement of the joggej-1/j qkpw6qyr?

  Two forces are acting on an object as shown (oeduwb el7x -3it-(x in Fig. below. What is the magnitude of the resx (iuo -ew-(bt3d7elxultant force?

  Two forces are acting on an object as shown in Fig.rto .zkh v1 *g.mi- vfvo5-9sr below. What is the direction of the resultant for1s-.vkgrt5 o-hv*i z9om rv .fce?

  Vector A is 4.5 cm long and points along the positive x axis. Vectorfz.:4 5mx j n061edwnl xzy7zs B is 7.0 cm long and points aew x 7z ym4d:lj0fzx 6z.15nnst $+28^{\circ}$ 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 73 cm long and points m:s b5k6kvzd5m;q) toat $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 23 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 26 m/s from the edge of fz( b:a4hn/l8mk wx6ea c:kbwlm4/8 hn e fa(xz6liff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, fro6 )6df tpxaipx -5f1dkl1kl- rm a bridge. It falls 28 m to the water below. How far does the rock travel horizonta6 6tdk-raf1 dk5-p 1llxxi) pflly before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes the grthlo,hon 8) w:rcio ;7ound after traveling horizontally a distance of 16 m. With what s)tcr ,hoh8 :niolw; 7opeed was it thrown?

  A jumper in the long-jump goes into the jump with a speee8xbdb.7va :u 1tv8)hv/fwmud of 12 m/s at an angle ofm8tb .8: 7 uv1afbx d)h/vuwve $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes inth( sf 2.5 dquhql*su:)sy f2bio the jump with a speed of 8 m/s at an angle off.bu) isq2sly2 fd(:s5*uhqh $23^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launcher0qeuv 1 /ey1 prs-mog6w;9hud with an initial velocity of 53.8 m/s at an angle of $48.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 57e8l:y qi jtt(k5 udu kj. cb6z(w(du,9.4 m/s at an angle of $15.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle o eq-; kh7hmwv;f $30^{\circ}$ 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 ml. 5aaq5r f8bhorizontally at 24.9 $m/s$ from the roof of a building 62.0 $m$ 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 wi fco :orm9)5ct*. 6xny wc3xnt); e ahel3h:sqth an initial speed of 65.6 m/s at an angley) 3:e 9 .qnt ;xhfaxrs3n*6)otomce5h wclc: of $47.2^{\circ}$ 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 velocity offnef 9qfaq)m8c. v/ d3ui.z; d 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slowsmcq d.za f q;8ef3 )vfun9.i/d 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 in a wind of 50.0 m/s torvn+ nmh;1;pa the +r;p mn;vna1hWest. The plane's speed relative to the ground is

  A plane is flying due Sout8q1t9g)vn5elihba/a o lc24:aptr 3g 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/h4m .uodm.uqa , 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 prdlb 6 pn*59i ohvyp9w8ojectile with speed 50.0 m/s in a forward direction 8pyv 59dolp 6b*ih9wn $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stilr/(w3.x)b ojr - rxbrrl water 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 -jrrobx.3r )r(x/w rb river?

  The driver of a motorboat that u.5loj 5ne )xunk9o:qcan move at 11 m/s in still water wishes to travel directly across a river 2.0 km wide in whiuo9n.ko :)n euj lqx55ch the current flows at 7.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s ilj*b ). i.fmoln still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver headfij lmbo.).l* the boat?

  A swimmer heading directly across a rlh 4vv+7ijmz4 9xs5, sc d lzxzb0qj;0iver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreb;cl,45 0vxi zdm4 7x09 zzs+s vjqhljam 480 m. How fast can she swim in still water?

  A swimmer heading dire dy*3kl0 m)1 s+budjxbctly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the s s0 y)1mb*lkxduj+3dbpeed of the current?

  A boat, whose speed in still water is 1.69 m/s, must aim upstream at ayxx*xgfg 2g,g b)-a qgys(u,mc;:o d1n angle ofqm;2 x*gfx1-aybg gy ,s, x:co ggd()u $18.2^{\circ}$ (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)  $m/s$