Which one of the fols)e8 pn u7 ak,5ufvo+ax lgrz+83ioy(lowing is an example of a vector quantity?

  Which of the following operations will not change a vecto6p m k j3ubowrl0+r9f.w, w4lyr?

  Which of the following is an accurate syss cn75mc7j9 t yv:0atatement?

  The resultant of two vectors is the smallest when the angle between them ie1a )hotv vc 2kp.:*rmbol/zuys-b6 .mm( -ovs

  Two displacement vectors have map,e 4mk /7kp2 m0jkhccgnitudes of 5.0 m and 7.0 m, respectively. When these tmk 0m7k, / kepchcj24pwo vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are adde,/ gozhn. xm wu6kj:v(u8k6qbd. Which one of the following is a zq:bkmh 6ugk o w86,./jux(vnpossible answer for the magnitude of the resultant?

  Three forces, each ha x/.dq :v1rc93n+lyif ;a 6d zf2icbdpving a magnitude of 30 N, pull on an object in directions tha c zx b.fd;+26 3:q paddcf/ylvinr19it are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector isup3a,oex+bb)9csg .cwfzn: fl+z (7 h

  Ignoring air resistance, the hg,05 ma+4u9n2 n1lj qf7 kkhi -bxgyruorizontal component of a projectile's velocity

  A ball is thrown with a v603)o;*sr 9 i+rnkk umrfdlo((w yerielocity 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 projectile's accelerjm4u1d f;m8 vnm2y ,geationj;dv1m 4f 8n2mmyg,ue

  A soccer ball is kicked with a velocity of 25 m/s tos,); 7exqi4v6kc we 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 objecta ponz4o20z .d is directed anti-parallel to the velocity veczao.0znd4p o2tor,

  If the acceleration of an object is always directed perpendiq)4u9 lmc+vc)t nz r(vcular to its velocity,z+c)u4 nlcm(q)tv 9 rv

  At what angle should a water-gun be aimed in order for the water to d(hf5a(wk32 gxjmfw 9nz8bzu* +f wq9land with the greatest horizontalhf fxaz8gb9z+knq5w9 d f *(3j(wuw2m range?

  An Olympic athlete throws a javelino6 ll s0oatv24d 0(iqo at four different angles above the horizonta lvo0i4 q(d06oaso 2ltl, 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 fovv-0weqbe 6 y1r the second time. If the ball leaves your hand with twice the velocity it had on your firvv-1 ew0e b6qyst throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speek7p0it gau9ec .pj6m c;e 24jsd 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 fix a+ gpo6ja0:jeld goal attempt reaches its maximum height, how does its speed compare to ita xjog+p0 a6j:s initial speed?

  A stone is thrown horizontally 3*r0l rjbtxd;de pw*yg :5dc 1from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster whenp0r*1e rlgxy3dcdb;tj5* w:d it hits the level ground below?

  A bullet is fired hodzctzh p9.8s xn+ ;.xx ayq6m-rizontally, and at the same instant a second bullet is dropped from the samexhcpq96 sdxn 8zm.yx-;+ .atz height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizgg7dtp xb g vjb ,o2(c,a;pb83ontally at a speed of 78.2 m/s and at an elevation of 143 m drops a package. 6.2 seconds later it drops a second package. How far apart will the two packages land on the ground? oxbdpbb,g p jtcag;3v7,(28g

  A package of supplies is dropped from a plane, and on4hr/ g1+ hv:vpx /xbybe second later a second package is dropped. Neglecting air resistance, t xpx4g yhh/b1:+/r vvbhe distance between the falling packages will

  A pilot drops a bomb frokg7(x0q0a cxc m a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal loca(0g7 qx0ccxk ation of the plane will

  The acceleration of gravity on the Moon isq-5*:.t 6cn ucu x:lwk nkm:js only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and l:c.tkmk u::wsq*xn j5-6 u ncat the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +xtq;b kdw(un(y8 x:)o8mo+k 7vsumu(p axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocim8vn(k (q u7su b+8(yxo m:uk)d ow;ptty of your car to the other car is

  You are trying to cross a river that flows due south with a strong current(n3wo(oazla1g d o7s) . You start 1n(7 zsawg oa()3o odlout in your motorboat on the 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 still water. k23otb au4, 0utrse-qHow much time will it take you to move 12 km downstream, in a river flowing at 6 qk- re3tou 0sbua,24t.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below tm+o*x( gtm upmir+0h6he +x axis. The y componenm6(*i hx +t omug+mp0rt of A is

  If a ball is thrown with a velocity of+dx byk-9m sh0 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 direction iake-kl5 6cana1d 9; knms qzu*cc+- 6north of east and you end up 2.0 km north and several kilometers east. How many dq +-k 1i5a slccndk6 zmeaknu9 ;-c*a6egrees north of east have you walked?

  A butterfly moves with a speed ) zmzwd (8ukya*ocg :*of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle b u*y: akz)m*g (8cowzdetween the direction of its motion and the x axis must be

  A 400-m tall tower castyx8 u+ 2c 9-)pafddcaq kikubq1tsifp;80u73s a 600-m long shadow over a level ground. At what angle is the Sun elevated above the h k p;27t8dcp uif)ubq dkx-qi saa9y +f0318ucorizon?

  Two vectors A and B sj 15)o8 e(ddmy q8nt-hfm+ku have components (0, 1) and (-1, 3), respectively. What are the components of the sum of these twoeu+fmk)(qyd 8jn8 o-mdt 1s5h vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), res n/)iz94s ge k gbi7cpqd.v:q7pectively. What is magnitude of gzsvqikd / g4i e)9pnbc.:q 77the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mpebam99a((*nz 2 qrbs agnitude oza a* bs9 rqb9p2n(me(f C ?

  A car travels 20 km West, then 20 km South. What iu9eeel ;j ya05s the magnitude of its displacemenley9j;aeeu 05 t?

  Three vectors, expressed in Cartesian coordirur s :5uom)2inates, 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, expressedir zxp9+vd i-5 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 is bg5 4 u8u2jfamthe magnitude of vector C =b82uaj4m u5g f A - B ?

  A runner runs halfway around a circular path of ra7 94wz)6/mgyvgtoor y gf ;o/odius 10 m. What is the displacemengofomzow/g g)4yy/or9v ; t67 t of the jogger?

  Two forces are acting on an object as shown fq *+9 -mckcybin Fig. below. What is the magnitude of the cy9ckqf b+-*mresultant force?

  Two forces are acting on an object as shown in Fig. bl apicv- 6)ywgp4giu;9:yr :welow. What is the direction of twycpilwu6r 9gy- i4)a gv;: p:he resultant force?

  Vector A is 3.3 cm long and points along the posrk:w3u6g;ur0lj:gn b itive x axis. Vector B is 5.1 c;r3lk:gnujrw 0bg6u:m long and points at $+47^{\circ}$ 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 55 cm long and poia,1tqe .f kj1af8cq7ents at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 27 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 11-9 ckdzl5j1 r n63eand m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2cj n6dn5d 9 lazr3k1e-.2 s. What is the height of the cliff?

  A girl throws a rock horizontally,thi 4kftp3e (. with a velocity of 10 m/s, from a bridge. It falls 15 m to the water below. How far does the rock travel ho4 tih3tp(kf.e rizontally before striking the water?

  A ball thrown horizontally from a point 21 m j.vs(h m i0m.pscz 3y5above the ground, strikes the ground after traveling horizontally a z5h.s ymij0s3 .(cv mpdistance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump withcgyu/ t-ix3*b a speed of 12 m/s at an angle b-xyg i/u*c 3tof $20^{\circ}$ 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 wi;x.ezl,ht-;tdm (e ialrp./f th a speed of 13 m/s at an angle fx- z,htli detmr/a .;el(p.;of $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launchedw5 ju x;hml9f4 with an initial velocity of 42.9 m/s at an angle of $39.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initi/yzyuov dye0re;+ vw z-j7s3 5al velocity of 31.4 m/s at an angle of $16.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at anf )6u xx7wkmh,0m)evh angle 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 9znk :wjn,b3d at 24.3 $m/s$ from the roof of a building 44.5 $m$ 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 level with an initial sp(ll (ntq:xh p8,c xp9leed of 56.8 m/s at an angle of c(:(htllx q8ppn l,x9$45.3^{\circ}$ 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 9l sah7f-ak9o1zd.xz sbja;. :gg s+bcan run a 1500-m race at a velocity 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, ts9zx1a g9k.aa 7s-o.l bb+z d: sjf;hghe time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is 64 bjx;f hqdnrpv,djuk( :.i0 in a wind of 50.0 m/s to the West. The plane's speed relative to the gbd(;xk0v.hdnf6pi4 j q: , ujrround is

  A plane is flying due Sou(rg/24s 8wnq9q bxhv jth ($270^{\circ}$) 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 mp+urx(; 8-na3nhoby6(rcqo of 120 km/h 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 speed 50.0 mtes9wwl y nn7xkurpd/ *:f0n92 j;pp (/s in a forward directiop 9u;lwn rp7 s:tfd0jy*wk/(n9x2epnn $30.0^{\circ}$ 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 is 8.0 m/s, is directed across a river with aw-ks+usw ub-b cu, -t0e ok0)-8auaqj current of 6.0 m/s. What is the speed of the boat as it crosses the rive ba -u-kwcuuu -be+ss0 w08,t )a-jkoqr?

  The driver of a motorboat that can move at 9 m/s in stillc .p t2jz.um:a water wishes to travel directly across a river 1.9 km wide in which the current flows at 3.5 m/s. How long:at 2u..pmcz j will it take to cross the river?

  The driver of a motorboat that32 kgd/j6cwqxmt4 ba+smye+s09g c6 p can 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 sc6emp +a6j9/ mxqb+ wscys 4ggtd320khould the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bankube:cwo ds .-. (ougq bxn4pl: xs6i75 in 6 min 40 s. She is swept downstreaux.b:5b(npcoso.slix4 q7:- u de w6 gm 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 mul-ghp9x):; w kkj cpxfrt( 21 wide reaches the opposite bank in 6 min 40 s. She is swept do)gkpxrpju9;h(2: -ktw 1x fclwnstream 480 m. What is the speed of the current?

  A boat, whose speed in k go tt540/eocstill water is 1.22 m/s, must aim upstream at an angle ofo4c/g k0 5tote $24.7^{\circ}$ (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)  $m/s$