Which one of the following is an examp( qroh.;rsx9wfh)* gpy tz4)ele of a vector quantity?

  Which of the following operationi nv2k5 hhxv0s-lo2 +j3b 9pnf w3pqy5s will not change a vector?

  Which of the following is an accurate s(gi5u7( pm/: lrkp 7q9pxzer1td 6z fftatement?

  The resultant of two vectors is the smallest when the angle betweew k n4uyl2tt(.b,v w/cn them is

  Two displacement vectors have magnitudes of 5.09nn, hkbygul37uv d9 ( m and 7.0 m, respectively. When these two vectors aru3dl7ygnbv,h (n99 ku e added, the magnitude of the sum

  Two vectors, of magnitudes 20 and /g0 zzmb 79le mq5fx9i(jlr 0r50, are added. Which one of the following is a possible answer for the magnitj57ef mzgxr9b/00irl m lz9 (qude of the resultant?

  Three forces, each having a magnitude of 30 N, pull 3.kyfp ygja 37on an object in directions t7.3jyap yfk3 ghat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector i9oul*(nb;50rrpu kr l s

  Ignoring air resistance, the horizontal component of a projj: k;i*p.uxmnectile's velocity

  A ball is thrown with a velocitc7qy(jt4 t8 ily of 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,ac 6 (85hpvkyucvs9o 2 the horizontal component of a projectile's acceleration 5vk8oca cv(p2hs69 uy

  A soccer ball is kicj86ckus x1:esked with 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 ofsu/ krkcdd75himu ,13 an object is directed anti-parallel to the velocity vectok3u57 1r ,im/dds uchkr,

  If the acceleration oarp pr2,hg: b7f an object is always directed perpendicular to its velocity,rra:,p bghp2 7

  At what angle should a water-gun be aimed in order fo7u wv(+, wdwvy zo5ol1r the water to land with the greatest,o wvvzu17d yoww(l+ 5 horizontal range?

  An Olympic athlete throws a javelin at four different angle .k x1+rucj xyluuu3g 3q8m* tc1yx(s:s above the horizontal, each with the sa8lxyju1(u.m31 qr gsx3y cxuu+c: t *kme 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 (qru: zei5eijcbjac 1ql://w z e/cvdk. ,i*1time. If the ball leaves your hand with twice the velocity it had on your first throw, its1ea/ribcjq*.5 k 1 (le/:qiz/:cwi j d,uvcze horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/sdpwdy*zy54n3 ftkgf 0nm /2m6 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 it haew6;a(k/ n27;s1ckmx r7fq.lyi wws maximum height, how does its spee w/;wies1kawrck;fa m n(y7 l6q7h2 .xd compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at thn)fw/if;b02ncck j p ,e same instant a ball is dropped vertica0nkfn,pbfc)2/; cjwilly. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet i*6j -kg/ tfnqre.yk2 vs dropped from the same height. Ignore air resistance. Compare thnkt yekjvgr26 -*/.fqe times of fall of the two bullets.

  A plane flying horizontally at a speed of 43.2 m/s and at an ele5z ux.ojbw8jye w 0g85drg(+u vation of 141 m drops a package. 3.1 seconds later it drops a .5gdu8zj(b5yj8eg0x +wr wou second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a secxrppgx0 mj:5ob3i 4 +pond package is dropped. Neglecting air resistance, the distance between the falling packages wpxj pgri3 +0opm:5xb4 ill

  A pilot drops a bomb from a plane flyinnslt.ei8*(rq/ iv*yr mt6;ga pu3g d+ g horizontally at a constant speed. Neglecting air resistance, when the bomb hits the grounsin38i6 tr+m/ r;u(tgg pqvaeyld* .*d the horizontal location of the plane will

  The acceleration of gravitwr. ub 9(myv:y,w widrv4 2s.jy on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (uww9,:rw ybvvi 4 mdsyjr2.(.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,cc/+c t8ade) de2e jz7t8s+vs level road and pass a car travelisat2 +8jee8dc7dvce)t +z c /sng 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 0:v2hc3(:d kie7diltlk h o3; r5spcmstrong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. Yous7d3 crhleh35(i kk2pimv ; :0c tod:l should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it takel) doau(6lq. e you to move 12 km downstream, in a river flowing at 6(eaulql)od 6 ..0 km/h?

  Vector A has magnitude 8.0 m at an ab,0p;xp . l*f u sg5qjb1xidf(ngle of 30 degrees below the +x axis. The y comfq b01lfps5 du,pg. bji;xx *(ponent of A is

  If a ball is thrown with awtkenb -l2tem*+ .p;m velocity of 25 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 direction northc5 zc,8 0p clh cn,13wpvp;jmm of east and you end up 2.0 km pp 8cc, mnpl c;c30wz5j1h,vm north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s0je8kjn9h jan;t;p6 s. The x component of its velocity is 8.00 m/s. The angle betweeat ;9jjsn0j8ek6 hp ;nn the direction 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 angl-y3sc9pp y 6 +kwh f*ibuf(ty/e is the Sun elevated above the hor3ffy/k +yb9p(ys 6 cp h*u-tiwizon?

  Two vectors A and B have components (0, 1) and (-1, 3), q4l0 fps0vy04bkfc2m ,*/whhwjasp-respectively. What are the components of the s m p-,b0aw2vclfks 0 *s fhhwjy40pq/4um of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), rfz)5tu t zpnd(8zpq7+ espectively. What is muzntpp7f )qzz td8(+5agnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Veci: d)nvvujiqk5 nd;(0tor C = A + B . What is the magnitude of C qv;n :iinu)kjddv 05(?

  A car travels 20 km West, then 20 kmk 50qo mk-xj,fb5g+fl South. What is the magnitude of its displak,f5 xgo5 + mjklq-fb0cement?

  Three vectors, expressed in Ca52hp 5*o7 qlyf qb) inevcc;.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 coordg8hr5zr4 0 m)h0lrgwdinates, 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) anb-+sz p-buekjoi8-d , d vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?d o-zjs8 -ike bu+pb-,

  A runner runs halfway around a circular path of radius 10 m. What is the dis1u+kq 8oh ebxm.yo h07placement ohh 7bo1 y 0uxe+qo.mk8f the jogger?

  Two forces are acting ono mn12k.h*(c c.+9dpkqb aki0zr zzn* an object as shown in Fig. below. What is the magnitude of the * qz0.p rankkd hk2cz(n.b c1im*+z9 oresultant force?

  Two forces are acting on an object as shown in Fig. below. What iaf ,94v+kk8ni- g vnwhuhwbx*9 b ,v8vs the direction of the resulta vhwv4 vu kb,v,kbn-* +8h899 xinafwgnt force?

  Vector A is 5.4 cm long and points j;j. qtqxxde,3 r: mpmke1():n yjg/yquh-g+ along the positive x axis. Vector B is 8.0 cm long and :g :hj(jxtng e;.r) ymqp3/m ky quje+xd 1,q-points at $+27^{\circ}$ 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 66 cm lo 4o q.1d)gbhdk z xpj*;i(.hjvng and points at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 20 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 speeanp8l:rv0w x5y+x4q4 lpls u4d of 22 m/s from the edge of a cliff. A stop watch measures th l +4x0pl85nrwupxlyvs:aq4 4e stone's trajectory time from the top of the cliff to the bottom to be 3.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 13yyu19 ,;+h;i s/hiearyc) r1mdhai ,i m/s, from a bridge. It falls 18 m touys)iea1hichy9,1y;i+ /h;,a irmdr the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a9nuedd98 ephu3 /q 2oc point 18 m above the ground, strikes the ground after traveling horizontally a distance of 23 m. With whed9u/oqh23 d8puec9 nat speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 nt .)l pyobyfanl 35n6)f) k)qm/s at an angle 6 f)5k oa n))nfq)yt3lp bnl.yof $20^{\circ}$ 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 wtwz/xhxu+ ;f +ith a speed of 13 m/s at an angle fwzhu+/+; xtxof $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 55.0 m/s at an angle oj k2j 2l3drm+u)sc*wro7fex6f $11.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veuq)ohz fl+0a/jd b/) flocity of 23.5 m/s at an angle of $42.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firbe)bfo pjl9-g 8 tyo(*bjhn 0/ed 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 hork ;w4p8nh ; oesn.b;gad(a-wbizontally at 25.8 $m/s$ from the roof of a building 52.8 $m$ 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 oftck(r)0r)1xoq0d g do )k -fa yl*4dsx 58.4 m/s at an an)trda 0l ksfk-(gqr)d*ood c0)4xy 1xgle of $38.2^{\circ}$ 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 velocm sdhhcvyosujl7;-0b.0czq0q p 5-: x ity of 4.0 m/s. If you ran the same race on a day when you had a constant headwindjsvqm ucx.:h50 - bl;0 qcyopzd 0h7s- 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 is in a wb5/:dy n;( mp6vch(awp 7vln bind of 50.0 m/s to the West. The plane's speed relative to the groundv7ml(na:pb nycd 65p w(;v bh/ is

  A plane is flying due Sou lg c:4 quc7j,d+(vpyrz-u/iath ($270^{\circ}$) 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 head .fz hs3tnd.8bed $30.0^{\circ}$ 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 pro0d ckus zc 9aew1+5;lkjectile with speed 50.0 m/s in a forward u0 wdzck csa 15;k+9ledirection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in stilo., nt xg7;8 b5whgecll water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the ; obw8nl 7 et,c5h.gxgspeed of the boat as it crosses the river?

  The driver of a motorboat that can move at 14 m/s in still water wish z6t0i:v1xk7l havs4 nes to travel directly across a river 0.6 km wide in which the currev6vznhlx a40iks 7 :t1nt flows at 4.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stw-k f:hchft4e* 9s r/we,h :xnill water wishes to travel directly across a narrow strait ishfc:-khew9 n,ew 4/rx* hf:tn 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 bae43)aaw4 tp y m57(29npfyl.f f fdkfdnk in 6 min 40 s. She is l7ddt am5f.wek42ff9pf )(y3 p4ayfnswept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite c/b5p kcoku3(n:q:l sbank in 6 min 40 s. She kqnbolks35: :(/cupc is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.35 e3-uk.+itt+r(woduu:e 0nfp: q i fk9 m/s, must aim upstream at an angle of+k nfudk urtei0 qwut:3pi(-foe .+9 : $27.4^{\circ}$ (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)  $m/s$