Which one of the following is an exbzpe) 5(;/qd*dcth n pample of a vector quantity?

  Which of the following operations will not changetb o5mv9z1hf9 a vector?

  Which of the followingnf4sb q9, qgdx) 3h)gf is an accurate statement?

  The resultant of two vectors is the u 0pj6;zlc3 lwccg.11en ;xnzsmallest when the angle between them is

  Two displacement vectors have ma.yf7lv yomb tgy1, .-fgnitudes of 5.0 m and 7.0 m, respectively. When these twogf 1v -lyftoy,y.b7 m. vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following is og8b5j(4vhq f rocmze:x/5gmoss)+2a possible answero/5mrzsfgsb(q o4) 8+ ocj hx5m2vg:e for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objecfv+gf n gozu0z9/3pu(t in directions that a 3un gfo+pz(gu9 zv/0fre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, th**..os,,vbop d vmx.cdieh-v.a ; kkse unknown vector is

  Ignoring air resistance, the horizontal component of a proje xbieq 62q-z:yctile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle ov2 wje 8n02rhhf $60^{\circ}$ 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 projecvl3s*k8j*bql0/ fm(dga )zu b.. yvef tile's accelerationv0yk 3z8*fl vgmd/ aul)jf.q.e(s* bb

  A soccer ball is kicked withfz ( * kmwgdqcwcj-i+ f9316xh 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 vector ofbzco (2rt9/fl an object is directed anti-parallel to the velocity(/ ol9b2tczrf vector,

  If the acceleration of an object is 1/tzvglwrq 57always directed perpendicular to its velocity,z 1trv7q g/lw5

  At what angle should a water-gui czj*rz.ck 20n be aimed in order for the water to land with the greatest horii 0r*zz.jk 2cczontal range?

  An Olympic athlete throws a javelin at four different:6gfwpxm s:wxxwvk ;,ld )w/0z)sk7r angles above the horizontal, each with thf :xwwz7gsk:px/x)r w6 v ;s,dw0klm)e 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 hq8s ;-qhu6vzsecond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first s s8-h6hqq;z vuerve) would be

  A ball is thrown at an origw 8(*9+lg jb p /yhgjat47uvr u*luy7dinal 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 reaches its maa w pmmr/ w8j3 0vd/xt4a9pwd,ro(cg0ximum height, how does its speed compare r8xta,p0ca/4ww3vr od m mwp09/jdg(to its initial speed?

  A stone is thrown horizontally from the top of a t3) opcw/ 3l+(*jmhc rg;wsbs3w3vocy ower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level grounbpos3;vwjsm h3lw( 3yc)g+3*o w/ crcd below?

  A bullet is fired horizont8 02)sjhpgavu; bst;z+*a;poyziv 0wally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the timesabw8z*y; p; zsti+o p2 ;j)avhg s0vu0 of fall of the two bullets.

  A plane flying horizontally at a speed of 118.4 m/s and at an elevation of 246 s r:bhxfke od73-)y8 jm drops a package. 2.7 seconds later it :h7-o38 fdj)erx bysk drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from at 1/hd10dpb x lne5so6 plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fallto/ddsn5p6h1xb 0e l 1ing packages will

  A pilot drops a bomb from a plane flying horizontally at a constant spelvt/jy0o2uq ) ed. Neglecting air resistance, when the bomb hits the ground tvtu)/lyj0oq 2he horizontal location of the plane will

  The acceleration of 808h 4wdzzmcx :w)dtb2 dees *gravity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball wouldm4ecsdx zwt:0ed8d2b8h )* zw land

  You are traveling at 55 mi/h in the +x axi9i jj9bd//d5eg .buijs relative to a straight, level road and pa9uj/.ij jebb d9i 5g/dss 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 that flows due south with a strong current. Youxqjak e) n9i1* start out in your motorboat on the east bank desiq 1k)j einxa*9ring 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/a gnhw. jjzdjo(8;2t still water. How much time will it take you to move 12 km downstream, in;j hzatgn./ojd(2 j w8 a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belo9 8*m lxrfsksf+zo)r u87/-z/b ntfcvw the +x axis. The y component of A c//o )xf9t- 7zus sn8 vf fkbrzrml+8*is

  If a ball is thrown with a velocity of 2597fm9kyy6aq.t 0d yxd 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 direc8 x)1l5 qpj r4qypit.ption north of east and you end up 2.0 km north and several kilometers east. How many degy 8p q1lir5 4qp).xjptrees north of east have you walked?

  A butterfly moves wit f:q:ri wia:/th a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direc/iaif: qr:w :ttion of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what nah5ne qakz7,hd* 5k1rw6 1o5 cyd,zyangle is the Sun elevata5 5k,hk5yn71zdy c rqn6 he*wo,z1daed above the horizon?

  Two vectors A and B havecxx1 c9i323wxvczajz8j g /x+ components (0, 1) and (-1, 3), respectively. What are the components of the sum of these t2gcx x1 xj3zia9vwxcj8c/ 3 z+wo vectors?

  Two vectors A and B have components (0, 1e ;j:7*cnobn 4pzptj() and (-1, 3), respectively. What is magnitude4en7cn*pp:zbo j (tj ; of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (i+j ngt*wt/ 8qg33jtnb s1 o-m3, 0). Vector C = A + B . What is the magnitude of C ?st*iqjj3g+ nn3t/g1 bt8om-w

  A car travels 20 km West, then 2 z4d(xxcs/g 9j0 km South. What is the magnitude of its displacement?4 (gjxszdx9/c

  Three vectors, expressed in Cartesian coordinates, azge xo6e y.6g7s.gvt) re
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 coordc/s5 i1k)n3vy g(/5xv eduy iginates, 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)-8lj q4hrxgcsd0k+/8m y 9jfr and vector B = (+3.0, -8.0), what is the magnitude of vector C = A -yjk hx9sgrr m048l fcq d8/j-+ B ?

  A runner runs halfway around a circular path of radius 10 m. Whai 3cqp7cjc i(6t is the displaceme( 7ic3cqcipj6nt of the jogger?

  Two forces are acting on an object as shown in Fig. bek0p )/m7aqh wz94rk x */uv+ )bppbenvlow. What is the magnitude of the resultant forcw hrp+7/b4 qa0muz k/pve)n 9kp)bv x*e?

  Two forces are acting on an object as shown in Fig. belo9p29p 4/g5:dauxelguzkm vz + w. What is the direction of the resultak +ud v5pzgz4:ae92l/g9mpuxnt force?

  Vector A is 4.7 cm long and points along the positive x axis. Vector B icjul 3m: b*gn)s 6.5 cm long and l*u:m )cn3jgb points at $+45^{\circ}$ 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 68 cm long anea2ye rn6(hs* d points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 42 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 horiz x20qans, f xpe:dfp4fc 922i:k1 le+oemx 8juontally with an initial speed of 24 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 3.0 s. What is the height f 8 usxaq:2p:npe,el2j i1 k09fxemx+ c od2f4of the cliff?

  A girl throws a rock horizontally, with a velocity of 20 m/s, x1 e zu;dr/ow *os)ln0from a bridge. It falls 11 m to the water below. How far does the rock travel horizontally befor 1)0/o xewl*nzd; sorue striking the water?

  A ball thrown horizontally from a* v1;x6pc-rdd ybu) zt59efh u point 22 m above the ground, strikes the ground after traveling horizontaluvyz*ut;1prddx f 5b 9c )6e-hly a distance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into t lj 1mwjn:x.p8he jump with a speed of 12 m/s at an angle of:px8 jlw1j.n m $20^{\circ}$ 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 upd c0bq*5,wjth a speed of 11 m/s at an angle o0, bjc5dwq* upf $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 23.4 m/s at an anglend7rs4u ix6s/lrh*oa*;q h s; of $37.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity ot opz/7d *yj/bf 56.1 m/s at an angle of $27.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired atjhf bx*(6 r,d9lxfz0 t 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 :28zg/u zu2zlzob a1pat 26.5 $m/s$ from the roof of a building 36.9 $m$ 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 am+(lr/bhyra( n initial speed of 67.8 m/s at an angle of r+lra/mhy ( (b$47.3^{\circ}$ 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 can run a 1500-m race at a velocity of 4.0 m/s. tm2xuvoj gkrd3: -*gt, +ld4a)0bhz* ilu6qwIf you ran the same race on a day when you had a c*6l4bmudgzx) :j it-* ,w oqh+0kuadl2rtv 3gonstant 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 1g gu *ppa*x/4hm rha.qsq+8o 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relatia+ag/m.up p *gh qr18x*qsh4 ove to the ground is

  A plane is flying due Sa/ mvk cfx-6hty);v6m 0oxew /outh ($270^{\circ}$) 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 headeu8t tid )ww-g+d $30.0^{\circ}$ 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 5 b(jb yzw5 )wldg,mv2v/ fkh+projectile with speed 50.0 m/s in a forwal5,kj()b2d mhbv yg5 wz fw/v+rd 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 dino6t m2+e x5ben. :/rw q+nyctrected across a river with a current of 6.0nwt/ .bctx6en2 +m+on:r5qye m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move a8c wtwg4n7vgt94o0. a c ,vfgdt 12 m/s in still water wishes to travel directly across a river 1.1 km wide in which tag8cg0t cd. 4 ,ftg9vw7v4n owhe current flows at 5.0 m/s. How long will it take to cross the river?

  The driver of a motok3 e;up1 szxt8rboat 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/8;ps zet 3x1uks. At what angle upstream should the driver head the boat?

  A swimmer heading direc qxibn 4mqfcp1:2c9bb6w- rr ,tly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept dow6,fm41xrib-cqc2 bq wbn: pr 9nstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a :nuksacg/wv(vzt c 9 0w1)ne9 river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreameg :/ nnuzv1ws0)9(cw9t kc av 480 m. What is the speed of the current?

  A boat, whose speed in stiik g2,d)gwt- mah/w 9tll water is 0.97 m/s, must aim upstream at an angle of ihw,2gda)t-twg/mk9 $20.8^{\circ}$ (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)  $m/s$