Which one of the following is an example of a vectoyi.mvh5zwr h sid;4 k -o9e2b3r quantity?

  Which of the following operat*4a)sbnbvalqfse/0 d78ytp 6ions will not change a vector?

  Which of the following is an acqz 6 7qr1u :12fcnchiccurate statement?

  The resultant of two vectors is the old9/n 3, )bqguf+le hrj (xm)afdr6,smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 mgy sow(353c2tyncn) q7 ls/zq and 7.0 m, respectively. When these two vectors are added, the magnitude of the su2c sy3l wnz5sq/3gyt)(n7c o qm

  Two vectors, of magnitudes 20 and 50, are added. Whij7x7it6c;7jue6,o.eotz *w mu -a;h ov *dxgtch one of the following is a possible answer for the magn*z6ojt7eo gux6x.w * ej-7v,c; m7adou;t hititude of the resultant?

  Three forces, each having a mage c0h7dl yi 14fjnrw31nitude of 30 N, pull on an object in directions that ar4 1 70id3 yjw1lehfrcne $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,/vrbo3t. f 9pl the unknown vector is

  Ignoring air resistance, the horizontal component of a projectilei xn aoz-;f ::c41rg jes5tmi0's velocity

  A ball is thrown with a velocity of 20 m/+fzvszp80d k *7au pc:;x n4ces 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 horizobrgkzkc(:4r93cemx/ 6dh z 2fntal component of a projectile's accelerationf( 6/ hz cmr:9kcxk3 re4gb2zd

  A soccer ball is kicked with a velocity of 25 m/s at an angle of svs)ypkl5;0/m kiy5u $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector 98xmj8aeyd5j7by) ozdvx n:i -( 6fjk*ak+xj of an object is directed anti-parallel to the velocity ve)5(x j+mnyfd9iyada:z*x j8kb-x kov 8j7j 6ector,

  If the acceleration of an object is always directed perpendicnv s .x;1jzbl(ular to its velocitlsx;n1v( .zjb y,

  At what angle should0v)8o nz6pgj y a water-gun be aimed in order for the water to land with the yvgn)0 opjz68 greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the s+ox*vv/tja25nql)whorizontal, each with the same sp v2/jn a)wv5+tos*lq xeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secon1khrvpmz t y0,*lo,c8 d time. If the ball leaves your hand with twice the velocity it had on your first throw, i c rk1l ht80zvmo,,y*pts horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle of w 9qxvvi63.b. hjc+gw$35^{\circ}$ 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 /;gljbw y5 dsz-fg3t3 reaches its maximum height, how does its sg3zfg3bd/st- j;l w5ypeed compare to its initial speed?

  A stone is thrown hori,/n4 64afj hyv+len cszontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when ,6yjahv n+4 c4elsnf /it hits the level ground below?

  A bullet is fired horizontarxx;- 6i:x b 3bnk6kzjlly, and at the same instant a second bullet is dropped from the same height:3 6x 6nkjr x-bkbz;xi. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 61.2 m/s and at an d9 9sk66ca h(k 8sfbwb*utt:aelevation of 206 m drops a package. 4.1 seconds later it drops a second package. How far apart wil 9*k khbbfs689a:auwctt(s6 d l the two packages land on the ground?

  A package of supplies is dropped from a plan0zf:iz v7pch ,mm5zhnox b7(2kb nb*: e, and one second later a second package is dropped. Nego7p0 ki2:57:,(f mnnz zbhz vxbbcm*hlecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Newl u87f+j76 r hllf9+.gh4v iimvcm*iglecting air resistance, when the bomb hits the ground the horizontal location of the plane rvgfl7fv8l 7m mwiulhj.+6*+i i c9h 4will

  The acceleration of gravity on the Moon is only(kz3z lmjq 3x1fts rt*7kw.+m one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (a3jtt xlzqk7m.+smrwf3 ( z1*knd at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x ax l v 6yd:e0qyak(,ma.j-nydhf2nh0/m is relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to m ,v2k0 6/hqnyh-al:(feyad y. d j0nmthe other car is

  You are trying to cross a river that flows/ku2whfz(.v 9ubv n ,e 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 shouldw(hk2ue zbv.n /9 fuv, head your motorboat

  Your motorboat can mol ypd )4eu2wycg(j-8 jg,;wxuve at 30 km/h in still water. How much time will it take you to move 12 km downstream, in a rive;2-jpy4u8ww ,ud gjx cl)gey (r flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +xynwvvh3rzw * /y5*6vt axis. The y component of*v/*h5v yy3t w zn6rvw A is

  If a ball is thrown with a velocity of 25 m/s at an angle xo 1j ybk;-z + kcm/bnngjh+ 3bt*soh3h7z9-f of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight 9; /12p )*srg7zpiqbly tpdxnline in a direction north of east and you end up 2.0 km north and several t79n2*drs/;1qyzlb)xp gpip kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x componuh47iwb , g)bl cf.n6uent of its velocity is 8.00 m/s. The angle between the direccfi ubn), g6ulw h74.btion of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadklekt.ka2 a74 ow over a level ground. At what angle is the Sun elevated above the horizkkkl 2t.a7e4 aon?

  Two vectors A and B have components (0, 1) and (-1, 3), respql2a)cf/j.v 13in9 vkwthtf /ectively. What are the components o1vnkvqf3h/ . jiwfc9 at )2tl/f the sum of these two vectors?

  Two vectors A and B2c0 sjy /n0vindd bi;i4yorfn8 :+ mk4 have components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vect;cd+ny0v 80iy44j :bnsn romk/i df2iors?

  Vector A = (1, 3). Vector B = (3, 0)b1:bz*oz7ww imy8m 6h. Vector C = A + B . What is the magnitude of b7:86z* 1zmoybiw hw mC ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disirv0gusm5 pfya19 f. ,placemrgap5vfsmy,0u 1 . 9ifent?

  Three vectors, expressed in Caa:l*4k fr,t4c*.dfw b1 hfum drtesian 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 mo+atmgoce p8 )nykq, k(7**pcoordinates, 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, -n 7yyyh/k0p -v4.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - y-yvnkh/70 yp B ?

  A runner runs halfway around a circular path of radius 10 m. /s ch75wfep 0 v*sulq(oao8z6zf vl.8What is the displah (plfvl 7ov8uazqs8.* 05f ez sw6oc/cement of the jogger?

  Two forces are acting on an obje zs.;zykj; y:bqj+ /zfct as shown in Fig. below. What is the magnitude q;zjf. +kb ys;z:jz/yof the resultant force?

  Two forces are acting on an object as show45e39ma bx h-;v cybfok5zpjbs+6 x :wn in Fig. below. What is the direction of tho b:mcb54a9p-eyz fbkv w;xx +s3 5h6je resultant force?

  Vector A is 6.0 cm long and points along the pdw;v )/h: wjx1adyqyrop35k( ositive x axis. Vector B is 8.3 cm long and poin5 dyx p:o h/kr)yv 13qj(wwa;dts at $+21^{\circ}$ 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 65 cm lofn4f j4u0 /cfjvys43ung and points at $30^{\circ}$ above the positive x axis. Vector B is 18 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 28 m/s from th-p:6bza yq9jw ln.6pje edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.6 s. What is the npjpq:9.6y w aljzb6- height of the cliff?

  A girl throws a rock hof:z b)km mi;gv2)bm9 hrizontally, with a velocity of 12 m/s, from a bridge. It falls 11 m to the water below. How far does the rock travel horizontally)k:mg9mfhz;) ibmv b2 before striking the water?

  A ball thrown horizontally from a point 28 m above/;y .rz;cixcc sedi/u33 vtx1 the ground, strikes the ground after traveling horizon3cr z/uv exdts;x1i cc3.;i /ytally a distance of 16 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at aydg,*u nla 5n8n angle *,lyu5 dngan8of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into thti3y/tg-fvmap u, 1d;e jump with a speed of 14 m/s at an angle oy; ptv3 t ,i1umgfa-d/f $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initiay5yjcq.h7 ; a),ljtevl velocity of 31.7 m/s at an angle of $36.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is laun/a v5cjey9eif 12mj.h ched with an initial velocity of 36.2 m/s at an angle of $42.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an q bo 9jjk5toi-24f3bngle 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 horizo2yb,(8n w lsumntally at 20.7 $m/s$ from the roof of a building 37.0 $m$ 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 st8; fb gked1jwjc1hfx w-( fj65 lb-/dpeed of 53.5 m/s at an anf1eb t; bj8cw651x--dlj fwdkhj/ g(fgle of $45.8^{\circ}$ 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), you can run a 1500-m5 7g,mlz3g+sxhvt a 3bl9cv2a race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwindac3325lv9zxlb7g vt ,am +gh s 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 m/s due North, and rnk + 09bezbvqun1wl.pt w- ybx4/:g+is in a wind of 50.0 m/s to the West. Thenqb + yn0z/e.blv+wxk -:gtw9bru4p1 plane's speed relative to the ground is

  A plane is flying due S3yr9h6 bi,yqpouth ($270^{\circ}$) 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,z o v l4v: d7pr)i- rzc06o(y8ltoppc 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 firc n09c2ad j1 ofn5c5tdes a projectile with speed 50.0 m/s in a forward dir12 n95a0 cdtnfcc do5jection $30.0^{\circ}$ 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 directe5s rci* 4x3m8 .yrdfbvd across a river with a current of 6.0 m/s. What is the speed of th 8rmvx3d 5*fb .i4cyrse boat as it crosses the river?

  The driver of a motorboat that can move at 9 m/s in still water wishew-fl 9d h ,1pqfg7ye9ys to travel directly across a river 1.5 km wide in which the 9h, w eq1f-y79l dfpgycurrent flows at 4.1 m/s. How long will it take to cross the river?

  The driver of a motorboat ezpt /upf2 uogg*+-j4that can move at 10 m/s in still water wishes to travel diggjfz*/eup4+-t 2opu rectly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank *b wliqjd2y; 85dw9izin 6 min 40 s. She is swept downstream 480 m.2djw;qi8 d9l* yiw5zb How fast can she swim in still water?

  A swimmer heading directly acrrl c /zl9.*bd u/*vi5 x/lninqoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the currentil*.ld5n/zbvqx i*cnlu/9 r/ ?

  A boat, whose speed in still water is 1 -4;wlon hhgo9.09 m/s, must aim upstream at an angle of gl-ho4h;o 9 nw$26.7^{\circ}$ (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)  $m/s$