Which one of the following is an example of a vector quantilkg rpzm 7*-hb48zin 1n; *p20s elozwty?

  Which of the following operations will notk wbpf2au *iafr7ak/f /5wmpns2,)/d change a vector?

  Which of the following is an accurate k8*5h .bhwdk1, c2fgr 4sn ovjstatement?

  The resultant of two vectors is the smallest when the angle 8 x0yz;w2hcf oiu*kr h 3w 6kfv:hp1u)between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0fff )z1x r8ievny; (s0 m, respectively. When thesnfxe izyf 8)s1fr0(v;e two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are c+2ycc1 *z *m)rgsfm s9gjaj6added. Which one of the following is a pozr yjm m2c+9fcsg1js6*g )*a cssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an1g+uvul9p6 t z object in directions thaz6g+ lup u91tvt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vect2cwx*c 8fjh,qywzq3f9; sbx/sf; vc0xuw72 jor is

  Ignoring air resistance, the horizontal component of a projectile's x4r 5wqpk2idhl+m :y-9i o3s hvelocity

  A ball is thrown with a velocity oyjejo 6ws8ypxl4 /4s 5f 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 ctwgv8l a8;1g6cc: phcomponent of a projectile's acceleration:68tc ;vgw ga8lccp1 h

  A soccer ball is kicked with a velocity f3vzz l2r/g.ijhi yn/ n1z+tgr-w,-i 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 5e -1v (7c sj9wwmpmbeis directed anti-parallel to the velocity vmbs(cep -9e5j 17w wmvector,

  If the acceleration of an object is always directed perpendicular to its vel z y:0 ox(cwnedp-sndtv)4:w+ocity,zd-:o4t wx(v +)d: nysp0 ncwe

  At what angle should a water-gun be aimed in ortvd :cpehj ,5ps:kiqq; 9fg;, bzu h+- rn8+whder for the water to land with the greatest horizv,jp qi9sd- qchz8;:,h g:;bp t 5nhfku+wre+ontal range?

  An Olympic athlete throws a javelin at four different 2o+c:,usjf xe.; 9ov+ls 6fqathwh6m angles above the horizontal, each withc o.q mh;s fae++,: h6wtosv6j9lufx2 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 1esgyk )4t4xhzjfpo4f1- sr 2t(a k4vhand with twice hk2 e1txyato4fs 1gz(k-r)4sj4fvp 4 the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of .br/( c ql.9zi0m:r1dmeacws 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 reaches its maximum h0c q 1/ez ex,rj yeg-si80 dhcstn4*:meight, how does its speed compare to its ini*eig8t/jm,- z4ne: qx 0 y sdcsr0ech1tial speed?

  A stone is thrown horizontally from the top of a tower at the same instantw/8 duli1c e6 /je )d3fzwqho5 a ball is dropped vertically. Which object is traveling faster when it hits the level o61dweu jh3 )/z5dwq clf/ei8ground below?

  A bullet is fired horizontally, a7go*.f 3:ev.-;)md lwaio n.vdn sie ind at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bu*-io eon vwgefila. s :;.i).dndvm 37llets.

  A plane flying horizontally at a speed oh98hw gfe* c.groa6n;f 40.7 m/s and at an elevation of 290 m drops a package. 3.0 seconds later it drops a second package. How far apartfcn8*ow ggh9 he.;6ra will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pac xpt*81 ofh0ftkage is dro ftf 8oh*1x0tppped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a oa3 6emr4t(vzc ckg,wfd 55nx: nxn: 8constant speed. Neglecting air resistance, when the bomb hits the ground thenogvtxc5 :4an: xm w8df,n(5 zrec 6k3 horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth oz+q( fu 7cdqbj: /qzo5f that on Earth. If you hit a baseball on the Moon with the same effort z /:7of5+qc(jq quz db(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 relat (1jzeel e rabvb1b,;/ive to a straight, level road an eebjb(1abvl/z e;1 r,d pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to crossax0jt 4 ma;y2ur:3q bu a river that 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 head your motorbo34aau mu2xt0; rqy: bjat

  Your motorboat can move at 30 km/h in still was 1 2slvgs8f7mter. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/h7 s18vmgf2sls?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below .suxhd9 8o h7nthe +x axis. The y component nh798.o shxduof A is

  If a ball is thrown with a velocity of 25 i;ej+bw e0v 2r +k:u3so ig,vcm/s at an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km inj3( :x (c:6b/ hg-ymf*esbdcc2eo ega a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of - f:mbe dohaeb(c2cxg y6gj*sc/: e(3 east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component onp4;uucyz z1ax:o 55h xim0i ;f its velocity is 8.00 m/s. The angle between the direction of its motion and the x aix0yucu:mzz;1o 5 p4i;hax5n xis must be

  A 400-m tall tower casts u7vf5w+yo fqe4 72fhia 600-m long shadow over a level ground. At what angle is the Sun elqh f7wf i+e4u2f 7vy5oevated above the horizon?

  Two vectors A and rgl08* wv p(3g4nalloB have components (0, 1) and (-1, 3), respectively. What are the components of th lwn0v43 *8lg rlpoa(ge sum of these two vectors?

  Two vectors A and B have components (0, 1), 6fg- tnj3+2daoqtrh and (-1, 3), respectively. What is magnitu2o rng3a,qtdfh 6j-t +de of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magn3*zcl jv - znwyhv0s7hl)5+y. -gygas itude of Csc30yg as)n.g+ ll--5hw7j*zvyhvyz ?

  A car travels 20 km West, then 20 km South. What is the magnitudeyr+ p-l,rj h8y of its displac hpy, yrl-8+rjement?

  Three vectors, expressed in Cartesian coordinatj 2f(0w gv,9y,ayyf kees, 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 coordi lm,,/afxym6)tj f*opnates, 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 i ap7 3+n,r4xupz(fpwus the magnitude of vector ,x7 pu+r u4papfz3(wn C = A - B ?

  A runner runs halfway around7pfe9vuu2,z y a circular path of radius 10 m. What is the displacement of th9ue , f7up2vyze jogger?

  Two forces are acting on an object as shown in Fig. below. What is the muvp;7dd.sb1 r2 ,)yv ykg5axhagnitude of ;badu5 vd7yph ,gvsk2y.1 rx)the resultant force?

  Two forces are acting on an object as shown in Fig. below. What bfpms5irh9 v9(o, y(nis the direction on vs m(5of(py9,ribh 9f the resultant force?

  Vector A is 3.8 cm long and points along the positive x axis. Vector ibkicy1a;:. qB is 6.9 cm long and c:;a kiqi.1 ybpoints at $+50^{\circ}$ 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 82 cm lonobjmr 2w ;ba37ac1 (j/fa7hxx g and points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 48 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 17 m/s from the edb61aziuay1s,09k lka ge of a cliff. A stop a , yaks16 zbul0aki19watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocihpr )jbt7261l9k abp sty of 9 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the t)b67aj2l9p1rbks p hwater?

  A ball thrown horizontally a * /n.na5mkbk. 2wrbsfrom a point 22 m above the ground, strikes the ground after traveling horizontally a distance of 23 m.*n/mn a..bkb wk2sra5 With what speed was it thrown?

  A jumper in the long-jump goes intpdl 1qc-p-(2is(shs no the jump with a speed of 12 m/s at an angle ofpds ps-1lh-(( q2icns $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into th2z4lwna xp3/ ve jump with a speed of 12 m/s at an angle of /l3pnv z 24xwa$31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 40.0 m/s od m:f2 amai3l89* b4tqhs,dhat an angle of $22.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 28.0 m/s at an angle ofxzj08f f0jb z( $37.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle *trh/l)l a-twmp2 wjy,ab t( .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 b3./(zq*sd n wevev.omr/n zj,ia0( jhorizontally at 23.7 $m/s$ from the roof of a building 37.7 $m$ 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 speed ovjtm xp zr,77g)xmjc wd39-do4 oi( m-f 59.4 m/s at an angle m, p)d7 vj94co3xmjztxo 7w-g rm(-idof $42.6^{\circ}$ 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+tx z,uxhh ji.v-yg.-p-5rox 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 -j igrhyhu+5x,zx-ox-v.. tp, the time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of6e :irlkk3(hi 50.0 m/s to the West. The plane'se:kr(3 ih6kl i speed relative to the ground is

  A plane is flying due So7mwo5 363rqc mt,6wvzjsqre 1uth ($270^{\circ}$) 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 175 l4mnhtt v5o20 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.ie ul4k :n5.k/xaivn projectile with speed 50.0 m/s in a forward directiouivnil: ke 4a/.5knx.n $30.0^{\circ}$ 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 a:9303. zhqf k9ifpug abz 1nbj current of 6.0 m/s. What is the u3h: ib9fzbznagjf93 pkq0. 1speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s ilg62 ,td mo)-k)+v- p eyhoahtn still water wishes to travel directly across a river 1.8 km wide in which the current flows at 7.8 m/s. 6tg+a-d h e-hto)m, koy)2lpv How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s j7:or 8m3q;lyz 9wg9mm .xmrj rrgg vimw- ;89in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. mr m gigyr8 r9:wj79q r-xwm;mo98 zjmgvl.3;At what angle upstream should the driver head the boat?

  A swimmer heading di9u) h94v y,ijlssss.prectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast ca hvs94ip su).9ysls,jn she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches x* 0ifg26f o.ukl4i yvthe opposite bank in o.kfvuii y6f g204lx*6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.46 m/s, must aim upstream at an anglexlb .lj fmtl* u6*mv0( of 6lmm u x0f(b.l*t*lvj$14.7^{\circ}$ (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)  $m/s$