Which one of the follow3ouiatqm /z z 4h/l-,uing is an example of a vector quantity?

  Which of the following operations will notp75h 5e8mypxf change a vector?

  Which of the following is an accuratey jg+0*+f9gc d el ykh63zf.dg statement?

  The resultant of two vectors is the smallest when the angle between thy p+los p8,f5hem is

  Two displacement vectors have i lf50l(am 3riq7oj9 tmagnitudes of 5.0 m and 7.0 m, respectively. When these two vectorl( 7i0mljr9fq5a i to3s are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of theb4+enaia8 eyb+w9e en6s(9q4a vko x( following is a possible answer for the magnit beakeinws9(8y(4qb6x4e9oa+ a+venude of the resultant?

  Three forces, each having a magni2 lho(lq,hb xb:.ph 0ctude of 30 N, pull on an object in directions that lq: hhb(2c0p b hx,.loare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector omy+a o/6uvg 8w;xxr2is

  Ignoring air resistance, uuivu bh:j 71ow,/9 ijthe horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 2n--4tgszjxj 7 0 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 component of a projectiq7scw5y hrn-v9- )en lle's acceleration 5 eqlwyn9-v-c)nhrs7

  A soccer ball is kicked with a veloc: y 1zmut05iwxity 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-anc2s8d4 ye,x g h9* xl2fnch)parallel to the velocity vecayh9xf gh4) 2n 8c,s ndx2*elctor,

  If the acceleration of an object is always directed perpendicular to i(;7t9k-ov od icb8 0 talkawd.ts velocity,ta- tkd0 8 9l; acbwi7.o(vodk

  At what angle should a water-gun be aimed in order for the water to land with9v v s43lecun7 the greatest horizontal rangec9 l4u7evv ns3?

  An Olympic athlete throws a javelin at four diojdu;:xbi41 jq5o wtv 3+ tj4ifferent angles above the horizontal, eachdo jqx15+it4; w uj:4ijt3bvo with 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 ba1h 5jcb k.7ho u,y7gdkkrxc4+ll for the second time. If the ball leaves your hand with k g7hk1d5 .j h b+7rco,xkuyc4twice 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 8.0 m/s a8ofi 4j iwu8nf9hw;0m t 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 fms i8372ih+g li6ewqits maximum height, how does its speed compare to its iniih3m 8i7qw+s il2eg6f tial speed?

  A stone is thrown horiz.yjdib l+ x woa/w*0)inpr 0s4ontally from the top of a tower at the same instant a ball is droppedjx0 wyd/iow*) +n0 .parlb4si vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a sdc6qq6g)bef ; 1sg.yaecond bullet is dropped from the same heighb q).yqd g1ce6a;g 6sft. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 116.1 m/sv ;t56qnjr6 gp21tc4 g xnis0a and at an elevation of 130 m drops a package. 2.5 seconds later it drops a secon65js1x0 pniav6r;g2t 4c qgt nd package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second:s /b- fnow;jh +rp+th later a second package is dropped. Neglecting air resistance, the distance between the falling packages:+ftb; wjh-nrs/o+hp will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. N :d1ja6kw(5zu3 c ppoxeglecting air resistancexk:5uja1c6od3( wz pp, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is q..sn ob6 kd) 0vw9hfnonly one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort ( b)w 9nd vnoh6qf.0s.kand 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 straightz -s( v*yakzce 8qe5 *eal0wumo9v0,j , level road and pass a car traveling at 45 mi/h. The relative velocity of yw,kvj eu( sy-0*ale z 5 89oqz*c0aevmour car to the other car is

  You are trying to cross a rivb2g b-e16skft q-dt1per that flows due south with a strong current. You start out -gtb k1sbdpf-q12e 6t in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h i7cu1d nz b6j.0 zs+nkin still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km67jzdi1 cknu +0szb.n /h?

  Vector A has magnitude 8.0 m ,fw fb2-b ah vvyh/l20at an angle of 30 degrees below the +x axis. The y component of y 02- ,hbv2bafhvf /lwA is

  If a ball is thrown with a velocity of 25 m/s at an angle /hz xmanwi4-zg c5s:* 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 norh rpy22oicd0b0 af )a7th of east and you end up 2.0 km north and several kilometers east. How many degrees north of east h by720o a0)rp2cidfahave you walked?

  A butterfly moves with a speed of 12.0 mz7cp5+s wiqnw(;ad5cz7 sg y4 /s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion asq7i5cg p +(waw4s5 zyczn 7;dnd the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a lw3rlpt*imq2w4)d /v.oot*z 6 os d) fdevel ground. At what angle is the Sun elevated abovt3t s .6*o/m lozrdqfi ow42w)vdpd*)e the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivel1* lmqrh*e)c6* jmukn y. What are the components of the sum om*elq1*mj6n*k c )urhf these two vectors?

  Two vectors A and B have compone. -)mdj;zcet2 tu4rmknts (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two v2c. ktr)- ;dtmz j4emuectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnmhj*t6 0xcxv 8itude 6hm 8x tjv*0xcof C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its dr t4bx f1fntxg +z l1w3s9ho3:5oj 5tdisplacementn4 djr1 xxf3 3:zt1+95bttgwh5olf os?

  Three vectors, expressed in Carte 5q.cyrr0ogqo c34v/rsian 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 coordinates, aryx 8/clqgmfi 8l ,r;o1e
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) aa /b jv05fznv:nd vector B = (+3.0, -8.0), what is the magnitude of vector C /f znva 0v:bj5= A - B ?

  A runner runs halfway arr*jw vgm.9 r6yound a circular path of radius 10 m. What is the displacemerj9 wy .6mg*rvnt of the jogger?

  Two forces are acting on an object as shown in Fig. below. What 0,a89khmm icqis the magnitude of the resultantqmc0 ika9h8m, force?

  Two forces are acting on an (nfc2cgr: 0p 7sxm fv+7*pcte object as shown in Fig. below. What is the direction of the resultant forcet7sf7+ c f pmc*x2nvrec(g:p0?

  Vector A is 4.8 cm long and points along the positive x axis. V:so 3: y8jgqunector B is 7.4 cm long and poing osu8q::jn3 yts at $+41^{\circ}$ 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 78 cm long and poin, ;f6w0zrk zojy;uk8c9jnporh+d*m x- a+ 1 amts at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 45 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 sp* 9vs w48 3efto:davdaeed of 11 m/s from the edge of a clid3a4 ts8: aw9evo*fvdff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.1 s. What is the height of the cliff?

  A girl throws a rock horizontalb1* xmb bt7 2wt2+jlzzly, with a velocity of 8 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before strt7+ mtjb1bx z2z*2wlbiking the water?

  A ball thrown horizontaepe,7y.(: dypgzk 8killy from a point 29 m above the ground, strikes the ground after traveling horizontally a distance of 14 m. With whp yezyi: pkde .g8k7(,at speed was it thrown?

  A jumper in the long-jump goes into the jump with a y), f82ii z*eyi c ynfmc dtw,53ls94xspeed of 12 m/s at an angle oxcd8te9cf2 yfilnis 4i*m,53 z)yw,yf $20^{\circ}$ 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 with au*dzf)oxf38gpdb48 / nfsis) speed of 12 m/s at an angle ofsn 4sf)bx3iu )zfdof/* d 88pg $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 39.6 m/s at an angfyh hntj.f: (2le of $15.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 46.5 m/s at an ans98b)g)h0lgduk vgu:v el+:y-9aw0d f f u; izgle of $30.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofef* u gx97djk3 e4a-dr $30^{\circ}$ 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 horizonx1wip 3+,esag- kwj)wd4 sp+ stally at 24.1 $m/s$ from the roof of a building 67.1 $m$ 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 fi .z-bvw98 bxav8ri0doov+t 0e 03vo 44.3 m/s at an angle 0i0 bvvdze3-x 9bi +oo 8vvt80w .raofof $43.4^{\circ}$ 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), ye- f tqf8wjia44he+f- sm) +rnou can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race +maief -hrj4) tfs -8+eq4fwn on a day when 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 200 m/s due imhy ,4. wr(p,yjq,mvh-5vqgNorth, and is in a wind of 50.0 m/s to the West. The plane's s-y i,m5m4q,(wy pg rvhvq.,h jpeed relative to the ground is

  A plane is flying due e yyjtezcuu.n -+/8q)*i 5nyc 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 120 km/h is heade, l6xtjy+x),bofcg76 cxy d0m 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 hor/5v2ahdhrv - / c6a3c5o pyoxlizontally fires a projectile with speed 50.0 m/s in aav /xo6vo dh2rl /acc5yh5 -p3 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 still water is 8.0 m/s, is phn5; ki(fm)b.v zbh1jaa,3c3 2ti otdirected across a river with a current of 6.0 m/s. What is the sb(2a f ,zm.)t tob3j3ihn khc pi1av;5peed of the boat as it crosses the river?

  The driver of a motorboat that ccd) +yxtftx+6j/kwb w6yziuz y4 n);/an move at 9 m/s in still water wishes to travel directly across a river 1.0 km wide in which the current flows at 7.0 m/s. 6 +jzk ;y nwi y) tzybw/u6t4fxd/)c+xHow long will it take to cross the river?

  The driver of a motorboat that can movdmt3utjc gz axq . m3*,jm:0b* a12kzde at 10 m/s in still water wishes to travel directly acros0xj* 3c 2uzzj,mg.tq: kt adm3*dab m1s 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 uqd*sbou9nc; (:jm in 6 min 40 s. She is sweptmud9;sqnju :(*bb( oc downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wid2e oi . x9 wr6vnkyz;/vt8ro9me reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the curreorwv ;.kit 8xv/r zm2y 96on9ent?

  A boat, whose speed in still water is 1.71 m/s, must aim upstream at an angle o08 vqfq1a;sx yf a0s8xfq y;q1v$29.6^{\circ}$ (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)  $m/s$