Which one of the following is an example of a vector quantizq tq 9wbxe;;ufgh9-t xx,0p-ty?

  Which of the following operations will not change a vemeu) szacn hqke9.. 0y f k0m/,8lx-swctor?

  Which of the following is an accur sl j8(* c6y7idt7otj hean.,sate statement?

  The resultant of two vectors is the smallest when the angle betweap+*c 5nm3u2bclh cmug 3 *kz+en them is

  Two displacement vectorsr-a tyv. w106;,993hhbs7;pgjiygmuojjkv v have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude ob s;r7 jv30 u ;gjv91w6hv.,jm-yaykph9ito g f the sum

  Two vectors, of magnitu+p v2n,rlc6bpdes 20 and 50, are added. Which one of the following is a possible answer for the magnitude l n2+c6vp,rbpof the resultant?

  Three forces, each having a magnitude of 30 N, pull on an ob+zm yek(aphu: e-j+s3hn v(th) rv1r)ject in directions that are rvpe)uav)y1-+ nts(e3kzh(+rhm hj:$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tiwv9mkus.)yc0 9qpb/ zv1 (oz he unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's g zfh5ilt0hd71m71k -fl4iub velocity

  A ball is thrown with a velocity of 20 m/s atl9;lp7kolnb 2fdgms cj24 0)w c4ew1o 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 of a projectile's acp(*tc dbsc u33celeration(cu 3sp3b*d ct

  A soccer ball is kicked with a veld)x i-2 wpj94plo6s tkocity 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 directed anti-parallel to the vep 1 ,2bhlwzvn ixj/clj41yi07)cx5 zrlocitzzlb5xijh x27y,v )rc 1c0 l/pi4n1jwy vector,

  If the acceleration of an o6hha z8zt*4 ka69 aluk eiv:+jbject is always directed perpendicular to its velocity6tae8*laia: kjzk 4v9h huz 6+,

  At what angle should a water-gun be aimed in oj//4i.lmabr jfg;c e0rder for the water to land with the greatest horizfl.4/ cr /;ejjmg0bia ontal range?

  An Olympic athlete throws a javelin at four different angles above the hos3-iexrr w771zdww5, o) q2)m dg rysmrizontal, each withqrs71dyexmr2-mgzo73r ),5iw wd)w s 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 hand w)/:v f q1 ws:foavy0 p+a5qntxith twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would aqfsyn/v+0 vt1o)pq 5:wf:ax be

  A ball is thrown at an original speed of 8. jnh*0fo t e adfn(6tn6-szp4.0 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 m36 u d4u:p1*nsdfjzk daximum height, how does its spee 1u*s3 dpkjuzf64dn:dd compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at t 0hz,h5nos edgov750uhe same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground below?g0z h7h5vu,se on0od5

  A bullet is fired horizl7d i.e*3 x6dxos+n yuontally, and at the same instant a second bullet is dropped fl7sx3*y6eoudid+nx .rom the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of d8+f; zxql*u. aah ao954.7 m/s and at an elevation of 156 m drops a package. 5.7 seconds later it drops a second package.+hq . f*ad laouzx8;9a How far apart will the two packages land on the ground?

  A package of supplies is v/ /pvlq 4 kh-1abggy)dropped from a plane, and one second later a second package is drg)yp v /kah1-vbg4/qlopped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constantjvdo f0s/m3 j2 speed. Neglecting air resistance, when the bomb hits the gro3 jf0d/2 svjmound the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sx q1r aanmy/o ir9oo5/n18y5j ixth of that on Earth. If ajn m8 9yo/1/i5roayro5 xqn1you hit a baseball 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 relative to a straight,(t8 i dkc20f;;jqx zbs level road and pass a car traveling at 45 mi/h. The relative velocity of0bq i xj2(sd; fktz8c; your car to the other car is

  You are trying to cross a river that flowy1 r r6*7vq*kph;4nz kcqv x9as due south with a strong current. You start out in your motorboat on the east bank desiring to reach the westknvzpcha*vk9q*rx47r;6 y q1 bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Homm pcjbv5)tb4,t; c 3tw much time will it take you to move 12 km downstream, b4 ,c)pt j5tvmtmbc3; in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees bel sj34qura ufo04 yoy)(ow the +x axis. The y componejf0y o ao(u)sy43r4uqnt of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of 96q5a4 ugfe by. 2+itdvwmal:$37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight /e3 m9tjyv4q9auqe/0a hu ct/ u:frx;line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees nor/t9qxv;e q0rmc9 yaju uut/3 4fe:/hath of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity isabn)-a4imelts/1 s.q0czjrhe 1/c:n 8.00 m/s. The angle bh1 -/t bq/r10a :.cic)ale zmjs 4esnnetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow oq1 rg vy (b-iosk3k+g7(jo zwrc)l7(wver a level ground. At what angle is orw7zs7kqg cv(r1l o j((k gi -by+3)wthe Sun elevated above the horizon?

  Two vectors A and B have*k+re qngit78q0lz u4 components (0, 1) and (-1, 3), respectively. What are the components of the sum of these trl zgt 740+nkuie qq*8wo vectors?

  Two vectors A and B have components (0, 1) and (-bcf c; rn cf5fa-o*e661, 3), respectively. What is magnitude of the sum of theseb ocnar cf ec*56;ff-6 two vectors?

  Vector A = (1, 3). Veql )z vd9b9wr- ns;,rkctor B = (3, 0). Vector C = A + B . What is the magnitude of C v;lnq 9)w zr,r9- kbsd?

  A car travels 20 km West, then 20 km South.9e3xg qs pk2qu )e85xk What is the magnitude of its displacee2 pe8q) 3s u9kq5kgxxment?

  Three vectors, expressed in Cartesian coordinatzmg2b/(i .p10a hneei, quvmi7j a/p4es, 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 coordin e gh4ty+od*a97 ixc)qates, 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, -4.0oi; ,u)g (/c4xwgw.9cee;gw:mxn wii ) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A9 xe(w wi;iw ,gc.4c i)m/nugxew:;go - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the d nxeigoe5a: 3 (+*,uiassgn k*isplacement of the jogger?xi*+eoek i*g5(ssa3, a ung n:

  Two forces are acting on an object as shown in Fi7u,msgy 0r w: yuzi14gg. below. What is the magnitude of the rguiy wym:rs7 ,41 g0zuesultant force?

  Two forces are acting on an object as shownnm: dgwm90u*hhmoz7gte kgsk . ) z;-1 in Fig. below. What is the direction of t9gms-z*nkz).ohewt0g;mk1 h7m gud :he resultant force?

  Vector A is 5.2 cm long and points along the positive x axis. Vector B is 9.4n2ki78g g0 nclgs dm+7 cm lon7lng+ igm0gsnc7 k8 d2g and points at $+34^{\circ}$ 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 63 cm long and points at yw q:m*: z-yif dh46ro$30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 41 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 withrh8u m//f8kt +di2f kbg+ cg.j/xg lc* an initial speed of 22 m/s from the edge of a cliff. A stop watch measures the stbl it+/kc fc2* 8u/gxm.grhfg/jkd +8one's trajectory time from the top of the cliff to the bottom to be 3.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 13 m/s, from a brils(o ekfv.+ kr zix6n1mc24)idge. It falls 13 m to the wamc v 6+rexsiifzl.k(2n o1 4)kter below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from17h:ifv*( o b2bs+icsztka 0c a point 20 m above the ground, strikes the ground after traveling horizontally a distance of 13*0a:b+ohs sz f1i7t ic2cv(b k m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of pfead-n5bqu9fj*j y80 ) :zyf 12 m/s at an angle of *b n9a:ezqf-50p yjf fud) j8y$20^{\circ}$ 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 wit- dirxku - q qf*hu-c*gl/*ny+h a speed of 13 m/s at an angle fy*i+ l nu-qgurh*/x *k-cd-qof $40^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity 81xan 3gkmoa1jfx2 o9 of 36.2 m/s at an angle of $38.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 4 -fso+:hdv+c vob0:ov7.2 m/s at an angle of $16.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firn*u-)s 375ut njp c i;8mp qg6qgkya3bed at 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 horizontahm:*a93da6*pjq d dooli pv- )lly at 23.1 $m/s$ from the roof of a building 40.8 $m$ 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 of k.6 (wjrewwl z j,(gg661.5 m/s at an ar(,gl. zjkj6 wge w6w(ngle of $37.7^{\circ}$ 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 velocit ddgco /6os,1yy of 4.0 m/s. If you ran the same race on a day wheno,y6g/1soddc you had a constant 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 s db8:j.7ca nl200 m/s due North, and is in a wind of 50.0 m/s to the West. The pla8cbds ln.aj7: ne's speed relative to the ground is

  A plane is flying due South 8vsyf rq8;/qh8i hg2k)m0h .frcocj 5($270^{\circ}$) 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 kn gr(pwc9*z0 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 20tl16w7sm) cph)d g )zq0 m/s horizontally fires a projectile with speed 50.0 m/s in a forwarphzqlst)7wd) 6 g)1cmd 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 acrossvznw.lo,u fs zd *8/wko/e 1-s a river with a current of 6.0 m/s. What is the speed of the boat as it crossw.* nfzsud1kezo,s/ / lwv- 8oes the river?

  The driver of a motorboat that can move at 13 m/s in still waterdqc)0j *7e gfr wishes to travel directly across a river 0.9 km wide in which the current fcfd )q7rg 0e*jlows at 3.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can mo,ej q5ax8. xje blgg61tk: 47kmzthl9 ve 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 upl : tgxej.7z4t6gqh8kk balej9m15x ,stream should the driver head the boat?

  A swimmer heading directly acroeiqe cobs,67 +ss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is 6q,e io+scbe7swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly acroh/ze9u n9vla z2o5:a( ejdl:8,umy vv ss 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 dl uz,e hv/mv8n 2:v9 zuayjl5:9 ae(ocurrent?

  A boat, whose speed in still waterfoit e q;b xo1(7 ydm0jh0 .kk;o4c2xs is 1.42 m/s, must aim upstream at an angle of 7 siqjkkoh bc0.0d( 2o;;yfx4xmt1oe$25.3^{\circ}$ (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)  $m/s$