Which one of the followiu/mendaji1 kct;-d5qn2 pe ) ,ng is an example of a vector quantity?

  Which of the following op/t 3l9n27 ze;y. al5uxpztvkzerations will not change a vector?

  Which of the following is+8ak50 r nm)(lq qs3p fbbw-ke an accurate statement?

  The resultant of two vectors is the sman -pkb1:xpmiotm(k//j 90qzo 9r9zph llest when the angle between them is

  Two displacement vectors have magnitu.e(p u+lqgieg30y xlch 5js0 1des of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude ou e.l(0i hpl 01qgs xec5gy3+jf the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one yute* 6m ;3pqj e3k9lxof the following is a possible answer for the magnikp6eutl*emx jq3;9y3 tude of the resultant?

  Three forces, each having a magnitude of 30 N, pull6;k f vbr ;qx(fx -+m2(bhytfk on an object in directions that (f+ br2;v;y bkh6 (x-txmkffqare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownsn a ro/qm0jx u:gn,:;, the unknown vector is

  Ignoring air resistance, the horizontala)guwb0qa;7mzxoj df5 94(b2 cv lr9u component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an anfyx. *;uz)vustix5 h(7xsuw.p7fz-e gle 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 proki9z ip3cr d6 y))vgv;g vd q*+(3huncjectile's accelerationc6n3py)+(gvdrvgcd3qi *hi)uz 9 vk ;

  A soccer ball is kicked with a velocity--q cziaut,;y p:lh.f 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 )l cg buhuiq0+ aw4z4l v6.e2wan object is directed anti-parallel to the velocity vecto4l. lv40qwa b wuiz+62ecuh)g r,

  If the acceleration of an object is a48: lvime;jqr ns:)lhlways directed perpendicular to its velocity,lhnjl 4;vs:qi8rm :)e

  At what angle should 01b/4wru -x0-heoitrn.qd cd a water-gun be aimed in order for the water to land with the greatest horizontal .tn0c i-/0qob r-r1xwddeh4urange?

  An Olympic athlete throws a javelin at four different angles above the horizlf+ l v)rytzyt 9 bq6+0h3.9 /vlxf;yz(zhdqg ontatvqyq)dhll9gfb/frh3+ 9yvz ty;l0 z +6.x ( zl, 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 leaves your snzqg 08o937hy*eyel hand with twice the velocity it h79 *y0l8egsznye oh 3qad on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original sp,iw *(d;rpejlbkg 62 .e(jrlom6 nd,feed 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 attivdxjly .88zo+49u 3o3w tnazempt reaches its maximum height, how does its speed comparea3 8ixt z4v3.n8u+ ojoyz9lwd to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same insta rvl)/efvmrv: 6xzs :,lyc:c;ib 31lf nt a ball is dropped vertically. Which lylf x r),mz6s c1v il:cvr;v3:bfe/: object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the sam(soux (zct sg.4(i*vx qij:-ae instant a second bullet is dropped from the same height. Ignoi-g :*uzq4issx. (xcovj((at re air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 52.6 m/s a c429td hw5afrnd at an elevation of 182 m drops a package. 3.9 seconds later it drops a second package. How fa5d94ch atrf2wr apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one sd6+e ts ja)0j7jceld7-gd 0z xecond later a second package is dropped. Neglecting air resistance, the distance between the falling packages e std6j 0+xd 70jed)lga-cjz7will

  A pilot drops a bomb from a plane flying horizontally at a constant w;66nxfqxfx (, r4vv gspeed. Neglecting air resistance, when the bomb hits the ground the horizontal g 6q;nxvx(4 ffv6rwx,location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. Ifah 64c1lv6nff you hit a baseball on the Moon with the same effort (and at the speevn66h14 claf fd and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a strh-5hhczq.2 4mli ig/53aksud aight, level road and pass a car traveli q hs-/4 gm2 dzul.c5aihh3k5ing at 45 mi/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 curreqtkdete e7 pnyerq5 f (4-9nw2n3r .z;nt. You start out in your motorboat on the east bank desnwtqe ez e(fr.dn2nrtky-e3p5 794 q;iring 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 still water. How muchad pdk 5h4b1dn0trr73 time will it take you to move 12 km downstream, in a river flowin7 d0rkhda n1 4d5r3tpbg at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees bew 7 i16w: z,awyrbguj 6-i8uf sob7g7z65gn ptlow the +x axis. The y compon aw sw7if-867ot67bu rpg5ibugynjzw:z6,1 gent of A is

  If a ball is thrown with a velocity of 25-*pd 6 07 :uci),sm jlkwnbzlr:cvt: k 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 lin/ ctx stm/-c)l4 fc3cw lwmy/1e in a direction north of east and you end up 2.0 km north and sevec)l/w c/3wyx c c4f-1tm/tmslral 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 its velocity 6lh44wtg;tiyd0b/:pf rru gvis/ 51d x25qgr is 8.00 m/s. The angle between the direction 6:p dr i2r vtwlygiuq1ds4xr0b t;ghfg/5/5 4of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shse;y t q :3puv,wnx*)cadow over a level ground. At what angle is thw)ep;x:t*c 3yvnq s,ue Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-z;zd(2on6 bj.hx/1sma 7kex n 1, 3), respectively. What are the cn1k7xhs6./;a zo(dxn zb2e jm omponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3),a;1+tebh6- ,l 9yhe v qsmym5q respectively. What is magnitude of the sum of these t1+eme5-y ahqlmvq ,tsh b9y;6wo vectors?

  Vector A = (1, 3). Vector B = (3, 0).+ahb5wt5 vh x-, wrwf0 Vector C = A + B . What is the magnitude of C ?rb 0 f-htww5xwa5+,h v

  A car travels 20 km West, then 20 km Sarf5fsh4h *2 south. What is the magnitude of its displaceh h5saffr*2 s4ment?

  Three vectors, expressed in Cartes +hp7bh2uwq8b w/s6i qx8a zc(ian 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 coordinates, 1sx+x l3q5 7h a1ftwiuare
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) awakt.gfxb;8- nd vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?w-tgfab.; xk8

  A runner runs halfway around a circular path of radius 10 m. W*qumam p7b*gc.ulo 4rwq(w,;hat is the displacement of the jog(l quu cpo.a;ww47 qr*mgbm,*ger?

  Two forces are acting on an object as shown in Fig. below. hphh8gblcc m m9w4 ;09What is the magnitude of the wmhhg0bcmc;h84l9 p9resultant force?

  Two forces are acting on an object as s4atcoex z(6l.4q f-pbhown in Fig. below. What is the direction of the resultant force.-z a46e(l4c tqobxfp?

  Vector A is 5.5 cm long and6b,go j--p0:zrh: xzvnekz1 z points along the positive x axis. Vector B is 7.6 cm kgz zzor10 j -xv-:6ehpb ,nz:long and points at $+22^{\circ}$ 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 67 cm long and pi7msmcc,ope6;8+ yz 8v0 gwzeoints at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 46 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 s3zlc:egbu7z g./xi h4pf:uz /peed of 25 m/s from the edge of ./z34bu/: ggluzpi cef7 :hz xa cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 5 m/s, from a bridgeb1if85wknryp )03wkr( c 2.uskmi7z h. It falls 22 m to the water below. How far does the rock travel horizontally be0my5i. u3rrwk zk(1 w)pknc87hbf is2fore striking the water?

  A ball thrown horizontally from a point 20 m above thn,f g2zj1n6gde ground, strikes the ground afterj1g nz 6d2,fgn traveling horizontally a distance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 oj8(3aexflz1c* gz2 5 fxhwi f2s0;j;ykjr 8gm/s at an angle ow8j3jr2;1c 5( 2l0x hgxkfi;* fjzs oyefzg8af $20^{\circ}$ 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 w h ns76*4barfdx d:kg/ith a speed of 13 m/s at an angle of kf4 b 6:7d sgd/rx*anh$29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitwo7q7s )6m8jg4ipnjvn :nw- ry of 53.0 m/s at an angle of $16.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with -9ecf hy 0mx/;obq o9gan initial velocity of 42.6 m/s at an angle of $37.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an a hukrd ):h )jcb6jl+.qngle 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 horizontl/(8 tf / ck)(ibdt a5ki*assoally at 24.1 $m/s$ from the roof of a building 54.5 $m$ 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 levj 5g2ishuia, e8s 8w7/k :jnnqel with an initial speed of 40.2 m/s at an angl8 k 5sjii2e:nw,8a7h /sgjuqne of $38.7^{\circ}$ 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 velocity of 4.0 kn94iaj:l u9pmepofow 02 z;r-pq84g pt/ z/mm/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 8 om-p94apfi rq ;2:j/eznwm4 p9t gl0z uo/pkit would take you to finish would be

  A plane has an air speed of 200 m/s d4(usdp4jow dg1p -3fqk7 fe*4qmytvo-54 ytoue North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground 3yst t4(e4ooqj4 7p qfwmdpfuo-5 -yg1d4v k* is

  A plane is flying due Southb8j ziu)t f8h4n3.jsmly(yu;xxwen n+ ((hb9 ($270^{\circ}$) 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;d+h , fv+sd zmlxpgix . .k-d.(0zsmzded $30.0^{\circ}$ 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 j3p7e eh dx+cr0 .dxtbqc/-m8m/s horizontally fires a projectile with speed 50.0 m/s in a forwarx-t+bx0.deqhc 7cp/ 83 mdjr ed 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 inb(ls0 8i0 p9 mgienn)s still 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 cipi 8mbs0nls(n 9) eg0rosses the river?

  The driver of a motorboat that can move at 14:5cecu9gs en/ptx7 . k m/s in still water wishes to travel directly across a river 0.9 km wide in which the current f.7sntc:uxek9e c 5gp /lows at 3.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that ca,wx (v6p/t9an c +zc -nr uqzs3+yrh0xn move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream( -/v6z0wn+hczt,x u+rs9n3xq pyr ca should the driver head the boat?

  A swimmer heading directly across a river 200 m wide uqazh94 f(.e7ups fe4reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she4f(9ep hqf4aueuz7.s swim in still water?

  A swimmer heading directly across a rijyz5ckl7 j fuz 8(:mn0ver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the currelj 0 f7kc5nu(zzy8m:jnt?

  A boat, whose speed in still water is 1.72 m/s, m2ubm 16p.(t m d/rhjijc1 7dsaust aim upstream at an angle of121 j6(rjpc/isbm7hdau td .m $24.5^{\circ}$ (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)  $m/s$