Which one of the following s1( fkwmrn+c3+f pmf.vjc)(e*r- dlsis an example of a vector quantity?

  Which of the following operations will not change a vjbxv1 y f9xxu d/.lk2lo; 6(hdector?

  Which of the following is an accurate statemenl*x- :(q o my0ukh,ovtt?

  The resultant of two vectors is the smallest when the angle between them i1w;+u keq 3n.gf7qpq ms

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respect-qvnde. u ci):m9v, svively. When these two vectors are added, tqm.vuvienc d -):s,v 9he magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of tspvb90u5r) .,hj1 h:ir: byy ygyi8qnhe following is a possible answer for they ih0 8qsup):bryy1ryj 5nvig,h :9b. magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, mbd 7/2cfhll0pull on an object in directions that fm02lbc7/hdlare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tho w,a2cs/1o6 ni +o- xvmz4hxqe unknown vector is

  Ignoring air resistance, the horizontal component of a projectilelk7q5-9ptu x5l4j xq g's velocity

  A ball is thrown with a velocity of 20 m/s at an angle o*7)w3g viocyt f $60^{\circ}$ 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'sn+y emff;5g4 +hmw,wz acceleration+w;5fwfzyh eg,mn4 m+

  A soccer ball is kicked with a vel 3q-gwtipa8t4 ocity 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 an object is direct,t/*py5 vy hraed anti-parallel to the velocity v 5,yvhyrp/t *aector,

  If the acceleration of an object is04honi92shcb q/r t. y always directed perpendicular to its velocity4 snrioc/h tb0y. h9q2,

  At what angle should a water-gun be aimed in order for the water to land wivno7:rawp9 ts-+( wwca 2ce g*e4+zzcth the greatest :ac7-tvcgzo+w w(*2 4+ee9zp snawcr horizontal range?

  An Olympic athlete thrd7n,- q .aoatoows a javelin at four different angles above the horizontal, each with the same speed:dtao-o7a .qn, $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 vews +dtm- j-li30 )vrthe ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first selr t+3emviv-dj -) w0srve) would be

  A ball is thrown at an original r1;j9 qwr3bbk speed 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 attempt reaches3m*uk5z6 /5m vxmt ot abx-a-j its maximum height, how does its speed compare to its initial speexm5okz-m /*tja-xa t5 6b3vm ud?

  A stone is thrown horizontally fx y(:z8kqm 0ij .vlf 4xv.hms1rom the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits t8km: fhv( yi jmx0l41.qzxs.vhe level ground below?

  A bullet is fired horizontally, and at the s hd9hp )jgx:7aame instant a second bullet is dropped from the same height. Ignore air resistance. Compaxdg h9:)7a hjpre the times of fall of the two bullets.

  A plane flying horizontally at y9avfmk6t/;gsdc/ /y a speed of 66.3 m/s and at an elevation of 166 m drops a packy6; 9t g/makf//sy dvcage. 6.3 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 a plan/av ap tm8w9q n,k*+,d d .hmr;x(rdcde, and one second later a second package is dropped. Neglecting air resistance, ,9mk ,nr/8pvd+tc.d; d *dmqwxr(ahathe distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constantj h)k emvd3mcu5y5o9a put* 34 speed. Neglecting air resistance, when the bombcy 3m u5 pv45d)ut*9om3e hakj hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Ea v4hz zygi+5u/rth. If you hit a baseballz/+uihy5v zg4 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 rem(.f) mdhvi8/+ep tv nlative to a straight, level road and p.(vmi) fnt8v+h/dm peass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river tha0 h-/itx5mx tft flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should heatt/0xh f im-5xd your motorboat

  Your motorboat can move at 30 km/h in still water.l ) m idycsn*5:q7i0ell0xsb2l8w: q i How much time will it take you to move 12 km downstream, in a river flowing at 6*is8xw cse y mbli0:7ill2n5ql:0d )q .0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis.;. uqt7hf0wp(ga2zk -o)j th c The yaqo (cth.k; 0twzfu27 pj- gh) component of A is

  If a ball is thrown with a velocity of 25 m/s atrsh gx)g81bu / 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 north of east vm )n hj1bb 6- fiop5ywz3d1hb.2p6shand you end up 2.0 km noropjzb31-dhpb65s 6n.ihfw1v yh b 2)mth 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 its vel5ta06x ,o xtemocity is 8.00 m/s. The angle between the direction of its motion and the xxt560 te, xoam axis must be

  A 400-m tall tower cag lwjb::z0f lfi7z;: dsts a 600-m long shadow over a level ground. At what angle is the Sl7;bif: z 0jf:lwz:g dun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3 ;bm. hgpnfp)1), respectively. What are the c);nphgfm p. 1bomponents of the sum of these two vectors?

  Two vectors A and B )sgg6c q:uyd)u: a*6 ff a6jgihave components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectorsga*i cf q sa6 66)yud:jgfgu):?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mag n292 xonim/430nk qrmioo xy01 r8brnnitude0r4/nox019ixo m n2nm83ioknr b 2yrq of C ?

  A car travels 20 km Wn./ gzo z8kwh8est, then 20 km South. What is the magnitude of its displacemen8on/ zzwg.k h8t?

  Three vectors, expressed in Cartesian coordinatessxj8f -rxbz8a /wk e7w i8b*p;, 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 Ca g*- f5ita:u, qwfzhp4rtesian 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 ;clqh-qyvkgti2+(py9w85 nr B = (+3.0, -8.0), what is the magnitude of vector C = A 8t pi25l+ kc-w9nqqyhv;(r gy- B ?

  A runner runs halfway a0:odfryjpgs h2yp9+cgxq l 2l :b .38fround a circular path of radius 10 m. What is the displacemenrfl8+. cb3g9pjlgx 2dy syhpq: f:o 20t of the jogger?

  Two forces are acting on an object as shown in Fig. below. What iwi x01xd/ r*i jfc)(lis the magnitude of the resultant f*0l1r(fcwdix)/ j ixiorce?

  Two forces are acting on an object as shown in Fig. below. What ism) dy 8wwsf02 ia1i(fi the direction of the resultfiw( 8 2siday01w mfi)ant force?

  Vector A is 5.9 cm l 1nvdh .eo.bu-ong and points along the positive x axis. Vector B is 7.2 ced -. no1h.bvum long and points at $+60^{\circ}$ 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 60 cm long and points at/ ytewlv2; dvdxob3gf( p9/.q $30^{\circ}$ above the positive x axis. Vector B is 15 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 ao h2z3wfybj8 wfd(.* rn initial speed of 25 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 2.8 s. What is the height of thf8y bz2 f(3*jdoww. rhe cliff?

  A girl throws a rock horizontally, with a vel,a*-ctcb ad/focms er *0hd+)ocity of 19 m/s, from a bridge. It falls 28 m to the water below. How far does the rock -0d, c d *bf/sae+occh)*r mtatravel horizontally before striking the water?

  A ball thrown horizontally fro 9f8sz31jfbp )ah4vksm a point 18 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown?zfk vjsbhfs18p4 93a)

  A jumper in the long-jump goes into the jumpwyvks+xbgp dg0,e +jrb +58/k with a speed of 12 m/s at an angle ork+b xgy,+8 p5+wjvgk/d se 0bf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into zr;+cjbrb -vkqzf v8 1w(r5*q the jump with a speed of 12 m/s at an angle o;v+ kwzr-rr5c8vj 1b*(bf zqqf $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initiallv (,5 r*2kmuqjm z y s0cn0s1rv1xvk+ velocity of 30.5 m/s at an angle of $45.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 56.7 m/s a gg3q/6dm/ mpqt an angle of $40.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at 9qfz 80uu eek3an 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 horizont-t47sk-yz*)so+z 2 zyo no vizally at 27.1 $m/s$ from the roof of a building 50.9 $m$ 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 is u 9 w1 3v;.w0y ebpim3jmht.q1b3wnlnitial speed of 38.3 m/s at an antwws3blqej .9n m0myh1 3ib.3uvwp1;gle of $44.9^{\circ}$ 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 m/s. If o)3dkccl xp8 6gsg2j0f92orv you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/ko cgv3 pgc2j 60dxo)sf28lr9s, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due No+juc*y i-u 3xxrth, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grounx+-uc ui* yxj3d is

  A plane is flying du;b)z wqfn6,nw e South ($270^{\circ}$) 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 1v07e 8tf /*pxnd czi/p20 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 horj6 cyy0;0pqp ifx8j b 1b.cjw6izontally fires a projectile with speed 50.0 m/s injcijy bjq0w6 cp6 f0y;b .px18 a forward 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 stim 6n2+ horghd:ll water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is2ond: hh+r gm6 the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 18 m/s in still water wishes to t,2l 9p7cvnha,5gu oowravel directly across a river 1.7 km wide in which the current flows at 4.6 m/s. How long will it take to cross t,7uoal ghp5,oc nwv29he river?

  The driver of a motorboat r5*2yf3b/dff xosfs+bzf / t3 that 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 should the drivdbry 2s* s//5z+ ff3ofxt f3bfer head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank z)i3:f ) qda30k cknqtin 6 min 40 s. She is swept downstream 480 m. How fast can she swim i3fcz nqiq03) :ad) ktkn still water?

  A swimmer heading directly across +qz/.lp w z3lga river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 ./ pll+zgzw 3qm. What is the speed of the current?

  A boat, whose speed in still w kej1ysv9 .o2/k8voyexxda k;u r+bgf+t;4 y 5ater is 1.55 m/s, must aim upstream at an angle ofe +kb95dyok rfav v;g2;u4ot+8/s.1yxy jxk e $20.4^{\circ}$ (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)  $m/s$