Which one of the following is an example of 0rfb:k6 r.dk;vc)kzoa vector quantity?

  Which of the following operations will not change a vd )6dt2d0nykl ector?

  Which of the following v ,rg9mhoc7 z poj5nq,/ko 4l+is an accurate statement?

  The resultant of two vectors izy h:up.9zva0phko o *cm7*6hs the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respevo.f3 66-pndu-kl oqg ctively. When these two vectors are added, the magv-qfuo -dk.lon6g6 3 pnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the:xklzo+aw,-z5b d z8c following is a possible answer for the magnitude of tl-o b,cd w8z+az k5:xzhe resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direction t/r kuk u+;tfiyz73em i,*u(us thieuiku, fu/u+mt*r;7z ty 3( kat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecto7 aexpp 1sgf01hlt ..sr is

  Ignoring air resistance, the horizontal com,7 js+fxf2ix iponent of a projectile's velocity

  A ball is thrown with a velocityq *pprh3k8wv ;ji1eu5 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 tb cx05tod *-gat3-br of a projectile's accelerationt50b b3-aotcgx- *rt d

  A soccer ball is kicke(w yg*aw1ome -*uscut2w-)ri d with a velocity 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 veokm0g,m6lw6 ;; hej 09lwrs h,dpx9frctor of an object is directed anti-parallel to the velocity ve;jpde o909srh, 6x l;grmw60, hkmwlfctor,

  If the acceleration of an object is always diopqfxx1a / e28rected perpendicular to its velocity,e8 aq1/pfxox2

  At what angle should a water-gun be aimed ltu3:mqc - .ybm3 +oecin order for the water to land with the gbc :.cuy-o 3m qle+3tmreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the hhato3d xs *;8horizontal, each with the s8 3had s;toxh*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 second time. If the ball leavebe48ln) qtw(qm(q;c gs your hand with twice the velocity it had on your first throw, its horizontal range R (compaq;(bn(clewq tqm 84)g red to your first serve) would be

  A ball is thrown at an original speed ofm8h s.+niyq b9 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 t03:p dny( gq*zeyye1 *ga,nu field goal attempt reaches its maximum height, how does its speed com*qtugyg y*nypa(:3ee1,z d n0pare to its initial speed?

  A stone is thrown horizontally from the top o 6k-bq0 tsnh*g8j1 lb)) fk jc+l4rgjgf a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it higb f8c)ggtq6 0jsnj1kl rk hb+ j)*-4lts the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet isi8df ex4/ iq,;0gjedy dropped from the same height. Ignore air resistance. Compare the times of fgqedj, iy;8dx4if/e 0all of the two bullets.

  A plane flying horizontallyr(3htl qq+ miqohsi6g68 5iu8 at a speed of 67.3 m/s and at an elevation of 273 m drops a package. 6.3 seconds later it drops a second package. How far apart will the two packages land on the lri+qhm8t (su 68hqg6oq 5ii3ground?

  A package of supplies is dropped from a plane, and one second late*h- +xtpuxkkh tk5x 7+r a second package is dropped. Neglecting air resistan5khk7*+ k -h+pxu xtxtce, the distance between the falling packages will

  A pilot drops a bomb80tea urtr 9f :l:dvd; from a plane flying horizontally at a constant speed. Neglecting air resistance, when the 9v fd8t;l0::ad rer tubomb hits the ground the horizontal location of the plane will

  The acceleration of gravitz;uo 0rdik+vsng88* m/:bcn5i ygq)o y on the Moon is only one-sixth of that on Earth. If you hit a ba ncob +*)kyg/8g zo0s5m;i8vn rdi:q useball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis re-c 2le /t 7boor:/b-urnfnrz besx44-lative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is:r7-/ecn s z4 xe otbn24o/u-frr bbl-

  You are trying to cross a river that flows due south witge9kgy d4*;y ch a strong current. You start out in your motorboat on the east bank desiring to reach the west bank d gy4 kcgd9ey*;irectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h i-ud;py i:5ik w)p4gm un still water. How much time will it take you to i k p;i)d5wu: p4guym-move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees8xpmr:1 gsamxe3:vc + below the +x axis. The y comgm xem+:r xs:p1 a3v8cponent of A is

  If a ball is thrown with a velocity of (.0f uu - x9fbrlut 8krhq1;ch25 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 directioa46 mfze8rlmm d03yu; n north of east and you end up 2.0 4ymfa;0m6ze3u l 8dm rkm 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 component of i2xsh0+j:pdj j ts velocity is 8.00 m/s. The angle between the direction of its motionh+0jpj : j2xds and the x axis must be

  A 400-m tall tower cx80en 5uc bz8qasts a 600-m long shadow over a level ground. At what angle q 5eu8x08nzbcis the Sun elevated above the horizon?

  Two vectors A and B have components (0y(ahnfl u9s4647b wu y12pxl c-gkc x6, 1) and (-1, 3), respectively. What are the components of the sum of tkl9pyhsycu64b471w6(xxg-n fu2c la hese two vectors?

  Two vectors A and B have components (0, 1) and (-c xkl/im*:a vi1dm(c/1, 3), respectively. What is magnitude of thev c:1(c*mmk/aix l d/i sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A +xpp2wrx,2 i5f B . What is the magnitude off ipxp2rxw52 , C ?

  A car travels 20 km We63rmm ;mj) :lxoth /f yg4nts8st, then 20 km South. What is the magnitude of its displacementtxjsr3;lo: mm) /64mhfn 8gyt?

  Three vectors, expressed in Cartesians8,6zc. 6bvkf 3n qbukf v2a1s 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,(z :n 91 q:3zul)byfloyj d+gd 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), wha+ /5gysk2 j6xjehatx1 t is the magnitude of ve+1xej tk/yxgjsa 562hctor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. Whatk dr(op 614oylb.bnj7 is the displa(n41o6y okbbjl .p7drcement of the jogger?

  Two forces are acting on an object as shown in Fig. below. What l)ew(tcb rgbx16h4-y is the magnitude of the resultant forceerl-1gy6th(4 x bc)wb?

  Two forces are acting on an object as shown in Fig. below. -,m c8w6vg c4fy f.vvxWhat is the direction of c-4f8 w.mvf ycv6gvx,the resultant force?

  Vector A is 5.6 cm long and points along the positive x axis. Vectobm)f i i9*rrsk hfx)/u 6za 1xm34um)or B is 5.6 cm longr3iukso9z 4r f )bfxu1mh m*x /a)im)6 and points at $+36^{\circ}$ 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 81 cm lo 6 1iz2fwspf) 6eedv3-y n*jcqng and points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 24 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 t9z n1mf)dq ,zb(/xihu6 bk)yjhe edge of a cliff. A stopbd /9qikzz nx hu),)mfbyj61 ( watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a bridge. 90vl9)vg,xc;l sq lrm It falls 20 m to the water below. How far does the rock travel horizontally before striki9;,rg 9l0)vxc sqlv mlng the water?

  A ball thrown horizontally from a point 23 m above the ground, s3zt w7 o5nb(*vue;lft r( v)lutrikes the ground after traveling horiu(z)v(ou7 *tw3 ;vltfer n5lbzontally a distance of 13 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with 8:keb+f.l7g m;b wz3jc x2 svha speed of 12 m/s at an angle of.jhlekv+ 7 sgc2:bx8mzbf;3w $20^{\circ}$ 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 speed of 12 u p7gu o8 pv(msek.*j1m/s at an angle of71( v jgkp*upom e.s8u $30^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velo -t./k wwlpstvxx 3ee)z1z6(wcity of 20.2 m/s at an angle of $30.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 42.3 mo jkdu29k(: lwp .gfdl n1e7w-/s at an angle of $19.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at r c(bl*ptq7*i h3t4og 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 horizontally at 21.7 e,5ay wn/ .-croleg5o $m/s$ from the roof of a building 56.5 $m$ 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 groqls8.z rwe r: p n/6*9+ f)mmdcr7jtj)twq:kwund level with an initial speed of 63.3 m/s at an )f7pjm : wsle +w)9drq:.n r*rm6jqztc8wt k/angle of $44.8^{\circ}$ 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 p;9zyo (e-hvh3y(u23sos akg), you can 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,(p;ho k 3v u(sgoy92y 3e-hzas the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, f :xb. +u)hfee:+y-zoge2 eiyand is in a wind of 50.0 m/s to the West. The plane's speed r+ g fioyf2y hee -z:ux.:ebe)+elative to the ground is

  A plane is flying due South*js7 sqa:paqf m41h)7uvcg c*jn s*yl7aq,*m ($270^{\circ}$) 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 headed yya z9xf26dtn 4qvz;z;q5vf: $30.0^{\circ}$ 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(6+,xjtjp2l 1mew4dqiwle2 9y9ac)xj7p u q c fires a projectile with speed 50.0 m/s in a forwarqmj+p6l 1etj9xy,9)j4diucq2(p acw2w x7l 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 in still water is 8.0 m/s, is directed acrost4tu7),wx l kdsltv * wdx0t 7+e.a6mls a river with a current of 6.0 m/s. What is the speed of the boat as il tuxdmtt7d0,av*4klw7t6x ews.)l+t crosses the river?

  The driver of a motorboat that can move at 14 m/s in still water w/b kgpfe1,b+4y eg id xjm(j12ishes to travel directly across a river 0.7 km wide in which the current flows at 6.8 m/ f4j+xe ge(kbi pd2myb/gj1 1,s. How long will it take to cross the river?

  The driver of a motorboat that hh 57u,)splan /fzuz5can 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 should the driver head the b,z) nh /5hspa z5lu7ufoat?

  A swimmer heading directly across a river 2diym3 qk03swkg7vi (a 1pk6 ,h00 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream h v 6siyi k17k3p,d3wgmqak0(480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reachekh-; np6b*2nxyi ehfe 4hq61as the opposite bank in 6 min2e6;hf*hikqp16-xen ha4 y n b 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water ivuv lq(, 1drw im,e59zx5oud,s 1.39 m/s, must aim upstream at an angle ofir,uxzv ,dmew5 q d9(1vu,o5l $29.0^{\circ}$ (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)  $m/s$