Which one of the followxgazev85 v4r; ing is an example of a vector quantity?

  Which of the following operations will not change a vectau t5ej; br1.l2ixl1aor?

  Which of the following is an accurate 0lyi8m 2thl**uuxm;y lr,u+n statement?

  The resultant of two vectors is the smallest when the angle between theme: qx 5s:b0uvm is

  Two displacement vectors h6tj 5av -m8rvyave magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, a6vjt5 yr8m v-the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Wh n9qu ,zfnp.:xich one of the following is a possib n qnpu,9fx:z.le answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objel zec1 + h 8apq7-6skgq7)wwj- tqdwj)ct in directions that are1qjgz)7 w t - qh +7qw)6dpkjwsel8-ca $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector ic06*h.vx 3/ omeaj wufs

  Ignoring air resistance, t3e 0l:l*ggb qxhe horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angp 3z rreb q7n,ge1/jlt8 j)2ylle 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, th2h/l u .lms+uue horizontal component of a projectile's accelerationu.l /u+l2hmus

  A soccer ball is kicked with a velocity of 8u( ar (h,spt;m,dvxn 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 direk;ddxdi 1 kb- p8xgh84cted anti-parallel to the velocity vec8 dkk1g 4hd;b8xi-dpxtor,

  If the acceleration of an object is always directed peqy* idk lbo0el68b6u 2rpendicular to its velocitq2eb0l*6 o k6ldybi8u y,

  At what angle should a water-gun be aimed in order for the wa)h4zv*o h ;m )a3ovo6jlx6ok qter to land with the greatest horizon ;ao3ozm6h)ooh vxj 6q l*)4vktal range?

  An Olympic athlete thr*sse rxnk+ /r-ows a javelin at four different angles above the horizontal, each with the srse+nxsr k*- /ame 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 s oly3;1aer8t decond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compareyt1oa dl8; r3ed to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at )6t -j5 tkomcqan 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 heigc4ynx+ gfp lb--)w)/p+zy8bw zux0pj ht, how does its speed cgbp)lny4 8p w/--wuzb)xz+ 0j+pycfxompare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instan .ens4ellmi359r.sh.wo +x ymt a ball is dropped vertically. Which obe l+mln5.oss.xe3rym9. wi4hject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant atvk.1 y a,ftfay.ed 8,;q 1zkg second bullet is dropped from the same height. Ignore air resistaz.k,afgky a;dy1 v8qe,. ttf1nce. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 66.3 m/s and at an elevat7a8 m7xd ;vnxrion of 163 m drops a package. 6.3 seconds later it drops a second package. How far apar8v7rm7 dxa ;nxt will the two packages land on the ground?

  A package of supplies is dropcouspy-/6 ,g/bgsa ; tped from a plane, and one second later a second package is dropped. Neygt ;og /pcsb-s6/au ,glecting air resistance, the distance between the falling packages will

  A pilot drops a bomb+s fgg).+4j ,f v +fevbtyomhy+f.tz j b++:hr from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizohf,: yemfsbh vgb).joj+gf +vfr.y4++++tz t ntal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth 7+tl9xs9tt jhmqk7l2 of that on Earth. If you hit a baseball on the Moon with the same effort (and at the77qx9sthjt lm92lk t + speed 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 straight, level roi o/gg4n 3bq8kad and pass a car traveling at 45 mi/h. The relative velocity of your car to the other 4q gk go/3n8ibcar is

  You are trying to cross a river that flows due south with a strong curretdz9kr(wo; osk30.j4 t pr4 zpnt. You start out in your motorboat on the east bank desiring to;po zjrr koktp 3w(.4t4d0s9z 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 much time w*dhea v 1lob+)ill it take you to move 12 kmbae v+1hld o)* downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belsuhb 8l gb5-byp-,pjyu/.l 7wow the +x axis. The y comjb y-ll7u/bh bu8sygp p,.-w5ponent of A is

  If a ball is thrown with a velocitj w-ney, 99 iwy2 c8j9zkb+tkby 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 ded)yd-w.k 3zg irection north of east and you end up 2.0 km north and several kilometers east. .kwe d )y3-gzd 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 vep0pkeu /ko rh n,g/-d6locity is 8.00 m/s. The angle betwe n rokde-0g/u6p,/pk hen the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a f+leqj xyoku85 im,+,level ground. At what angle is the Sun elevated above ,i8u+o l mkjyexf+,5qthe horizon?

  Two vectors A and B have components (0, gs+eb7;d*o5b9al sts gc 7r)c 1) and (-1, 3), respectively. What are the components of thtb esbsd+la; cgo)7*795gsrce sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1,d3t/ / qojvgz,eud84k 3), respectively. What is magnit4t k3/d8o qjg/z,dev uude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = oy- ha.r+:m he420dqvqvoa.l (3, 0). Vector C = A + B . What is the magnitude qh 4 :mveaod .o+.aq 0vly-rh2of C ?

  A car travels 20 km West, then 20 km South. y6 uwibk+ 21ba What is the magnitude of its displacement?u6+ab k21wbiy

  Three vectors, expressed in 4:s/xsjma.l ofwv f). Cartesian 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, expresuxb9 /taog5sg kh6 n77b +v(yised 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), what8v(as t0til 1t oq;2lg is the magnitude of vector(g8oqltvt0st2i ; la 1 C = A - B ?

  A runner runs halfway around a circular path of rju4*txtq-7w sj mo c g(k.*;uoadius 10 m. What is the displacws c*jgxtm.- t*;qku4uo (jo7ement of the jogger?

  Two forces are acting on an object as shown in F 3hri 7e.f-x qax79dksig. below. What is the magnitude of t 9ki.xd3 7 -frh7qxsaehe resultant force?

  Two forces are acting on an object as shown in Fig. belo7h,r, ,kzdru bw. What is the direction 7rbz rk,du,h, of the resultant force?

  Vector A is 4.8 cm long and points along the positive x axis. Vector Ba8e x0u:(o h7 vtiu-vp is 6.1 cm long and poiuh8o : vpxaut(vie0 7-nts at $+49^{\circ}$ 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 57 cm long and points at rfe/2v4agnvmf o be 83w1b:;x $30^{\circ}$ 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 horizontally with an initial speed of 15 m/s from the edg a2tb.alsmy82gk*3 cee of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.5 s. What is themb c.a 8lks2a3eyg*t 2 height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, froml 8q(i.5*b 5 o yxj)ve;zucnen a bridge. It falls 29 m to the water below. How far does the*o .u e q)i5vc8jbxzeyn; n5l( rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 18 m abovcsih5( s+p ;fxy8uin5 e the ground, strikes the ground after traveling horizontally a +ixh5 ssf 8n;i5yc(updistance of 16 m. With what speed was it thrown?

  A jumper in the long-jump goes into ( enm9l xt -5,k5qcfbl. v.notthe jump with a speed of 12 m/s at an angle nok n c le9.(m5xq5.vb-tlt f,of $20^{\circ}$ 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(w33ojqjp 4fiv43 utp th a speed of 11 m/s at an angle q jj(p43f4ivw3pt u3o of $33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocityokp3 t)*e a7d-06ryrvcs52w vbz nz0c of 41.6 m/s at an angle of $12.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 20.4 m/s at an syb y,o9 lxrhkb:.5 ;wangle of $31.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fif g x)6qh cu30dvm,a.; +ggtdjred at an 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 hori/ liiculm2mc -th: :a/zontally at 25.5 $m/s$ from the roof of a building 49.2 $m$ 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 wo3ngm*ak5 )+r hngh7g,c txc(ith an initial speed of 66.7 m/s at an angle of h +7 rcnc tg*5(gm h)ogxa3,nk$44.6^{\circ}$ 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 velot;iu e , *lkbovgzmh;(v .kw.aew., w/city of 4.0 m/s. If you ran the same r w/.(;o .l wzhkg.te, ;abmvvw *i,eukace 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 m1z g05 uh8p78sxa8 qmhuie4uy/s due North, and is in a wind of 50.0 m/s to the West. 1p4hgz7uuqxs m80i ahey588u The plane's speed relative to the ground is

  A plane is flying due Sou)atw,ap hzl(vd+e5+ a .- 4hzg ;gqlmrth ($270^{\circ}$) 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 headejavg*8bc y +-ed $30.0^{\circ}$ 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 i*n70 v teabe+projectile with speed 50.0 m/s in a forn70ea*te+iv bward 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 water is 8.0 m/s, is directed across a river witq+qjtbpya:,tv 2 dp, +h a cud:vpqj2t aqyt b+,,p +rrent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 16 m/-yw6 30rxrfcidp6(v4 u.no(qt u4qr ss in still water wishes to travel directly across a river x u6 -vfs i yot4360drqrcpu(n (q4.wr1.7 km wide in which the current flows at 6.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still wmr) typfb 91e3ater wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle ups3r1y9pbtmef ) tream should the driver head the boat?

  A swimmer heading directly across a river 20zi4iqvfw8 do9 grk)6i+zwm +s o;fl;)+xqw z00 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast 8i)ww+ rl 9qffwizg;+oxszk o06+ );zv qd m4ican she swim in still water?

  A swimmer heading directly across a river 20pfa.be/zgksqvks.i7b(06zo e+/ me4 0 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. Whag v/.k m04(e6pkqze/s+zf. eb sob7i at is the speed of the current?

  A boat, whose speed in still water is 1.90 m/s, must aim/f lrq jrllwk(h7f1 dz fe222e .h;n.l upstream at an angle ofwl 2.hfrnlqd7 lel;kf/ fj2ezrh21( . $29.4^{\circ}$ (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)  $m/s$