Which one of the following is an exa rpi1w)cghm70mple of a vector quantity?

  Which of the following operations will l,a p hafd;3(pnot change a vector?

  Which of the following is an accurate statemen3-4cua*r3v r mxk-v iat?

  The resultant of two vectors is the smallest when the 5xesmdw9jxm*1)p7oo 9 ud ikfk/rk-8 angle between them is

  Two displacement vectors have ui vl8j2s o0ml cy23ttl+4vm8magnitudes of 5.0 m and 7.0 m, respectively. When thes+8m8su 0ljv tyi3m4 vlocl 2t2e two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followi7yu0w kz3ukk *evg9/rng is azu vkk/gr9*y u3w ek70 possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dirgg32m3 d/kb2d ooj 9mry e(oc*ections that are e3y2 go2jgr*/mc dm3dkbo9o( $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector iskcpkem0- n8 xd84xz k.

  Ignoring air resistance, the hori+nh5er,fv/vq h ./ ftutt+bg;ngi s, 7zontal component of a projectile's velocity

  A ball is thrown with a velocity of hh)5l:m8giu4f h d/f-2qo ajo 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, the horizontal compone ;.llw. zh 1d/ml;cqmpnt of a projectile's accelerationlz;d q /mpll.h.;1wcm

  A soccer ball is kicked with a velocity of 25 m2( vjk7vzq 8y8xln/k q/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 3;x:pcvw *q,n tfmm3vobject is directed anti-parallel to the velocity3 qvpvfc mt,;wn3x *:m vector,

  If the acceleration of an object is always directed perpendicular to itsd*b 2b (mru252r su3 sqfircn9 velocityu229rrb c3qns(b5 2ufmi sr*d ,

  At what angle should a water-gun be aimed in order for /7datuhjd t -9the water to land with the grhuj -at/ 9dtd7eatest horizontal range?

  An Olympic athlete throws a javelin at jtj g6rw3df uiey/u4b9)yepd(; +6cn four different angles above the horizontal, enjeutc/j w;4 r9 y gfiddye+3p()ub66 ach 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 ball for the second time. If the ball leavi .z8xli: bj uy,j;:bti90toy es your hand with twice the velocity it had on yl 8;t z,y.jotj09:uiibxib :your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an ori*sc6ksy r1l0h4ljnaqm;.ocw . f 6 3dnginal 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 maximum height, (9 ofrpb3b*/ wepn. mfhow does its s/r9pm p.*fwb( 3 obfenpeed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same ins8 )7hhjmvxy(2e3k ttl tant a ball is dropped tk(y7 h 3vj)8et xhlm2vertically. 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 6qmvxshcgs1(1 e7q o0is dropped from the same height. Ignorsgo6qx 7ch(eqm1 0 vs1e air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 75.0 m/s and at an elevationy ;(aafqh6t, jn0aa w)jq7ln. of 130 m drops a package. 5.0 second)aj7 ltnw(ay nq;6ajfqa0 h.,s later it drops a 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 late i 6n/niyg 2gzko9f e7t1v(3qw -mo(obr a second package is droppet -zi/((2 fi g o1gmvokn3nbe9wo6 qy7d. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flyi+ls t1 x7vlu vgwn.03z2fdw i)ng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wix )wzluw0fl g3.v s1+dti7vn 2ll

  The acceleration of gravity oroazg o9m z 9)(zap3a9n the Moon is only one-sixth of that on Earth. If you hit a baseball 99)p(a9agzzr zo mo3a 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, lev5w .yevv d8ebw4u3f;t 1 8kzpxel road and pass a car traveliefpw83;d1v8.4xbe v k utw 5zyng 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 strt/0y6p akczo x ( dicg://e0pbong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motot 00b :eigda/pko cx6zy (c/p/rboat

  Your motorboat can move a; )y 0-m drz7*rybynoht 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flow7yo )dy zmyrrb*-n0h; ing at 6.0 km/h?

  Vector A has magnitude 8.0 m yk8 y. w7tpp2vj8 yl kt4yp-*iat an angle of 30 degrees below the +x axis. The y component of v 24 7-8k*ytlt pk8y.ypjipyw A is

  If a ball is thrown with a veloci gifa6y83h k,wty 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 northbt/s .wqtrf 43 of east and you end up 2.0 km north and several kilometers east. How many degrees norf4 /qb. t3wsrtth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The *xq5 kpcx8o ,, ,*zhxe/vxdzhx component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must*h/v kc,pz*,x xdx8e q,o5 hzx be

  A 400-m tall tower casts a 600-m ln* isqy+v)py/(t/ wrq z u+nb5ong shadow over a level ground. At what angle is the Sun elevated above the hu *n/y (/t+sprwzyqiqb5+ n v)orizon?

  Two vectors A and B have components k hbp36k : .9sptf7cxa(0, 1) and (-1, 3), respectively. What are the components of the . bx hf6ast7 9p3pkck:sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. y vc 2:yokwd h6 v5b;pfa))pn: What is magnitude of the sum of tkwony; :vvabd6)f 5y :2p) hpchese two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C) h rtad4 06(b/ a+ptxnaij2dr = A + B . What is the magnitude of C rhpi)td+ 4x r/ndbat a2(j 0a6?

  A car travels 20 km West, then 20 km South. What is the magnitude nv:l-4rfn)c ;oh1 4sg5 jsvtv4qiwn5of its displacemehn 41:cqvg-v 4; 5nsnv)rwos 5fi4j ltnt?

  Three vectors, expressed gxb aj;g)q(ljtya p56r,/)lt in Cartesian 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 coordinate o+gf7vi2b 9tmz743l0ib8) uzbpgzvbs, 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)gkn.cy wukpi +1)+3 ei and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - 3ikgu.p1+ e wykcn+) iB ?

  A runner runs halfway around a circular path of radius 10 m. What is the dscdm(-mnjnqp j8,2 6 kisplacement of thmpm jnd8-2ks, c(n6qj e jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitudemmhqpb-( qlk4 5. 1rlw of the resultant forcehwr4qlm.p (k5q1 l-mb ?

  Two forces are acting on an object as shown in Fig. belowu v bt pht-8;jo:if1p,-hyp.s . What is the direction of the result st:pit1;8hj- hv.ppbyu f,o -ant force?

  Vector A is 5.2 cm long and points along the peq*,+zy im-y;klbu i. ositive x axis. Vector B is 9.3 cm lb,l* -kqiu+z ime;.yyong and points at $+51^{\circ}$ 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 59 cm long andh*kss1 hx ,zu0u:we5 t points at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 50 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 17 m/s fr38uan,mlh20cy r b*n rom 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 3.1 ,u r *bcrn0nm82lyh3as. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity m(efb1p- dxgh, 416 rru zink;of 11 m/s, from a bridge. It falls 20 m to te1,hk- b6fndrr x(1z pim;4 ughe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m aboa pzaimt6 i l-8h-o/l)ve the ground, strikes the ground after traveling horizontallytlz8/m) -ah 6pil-oai a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed dkee03f pdl/eg9 zwb 69c: lv(of 12 m/s at an angle ofep6lze9:ew( /9 d g0cvfkld3b $20^{\circ}$ 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 ki**i+0 zhi,a,z0qkv yx -(:fmvvl pwjump with a speed of 15 m/s at an angle of+ iw:xk,lkf(0yi qh, a* vvi*pzvzm0- $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with anc.0e 5tm yexqrx32 x,i initial velocity of 51.2 m/s at an angle of $44.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velod i/)*dfhb;i.znpe(zff,c,r city of 34.6 m/s at an angle of $39.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fireda7a1n +,.hn m3maa ihb 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 h) z. bd kt(zuhb:+ehv2orizontally at 20.9 $m/s$ from the roof of a building 62.1 $m$ 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 levelv/-k p , zqws fexqbdr2uk8n3w5 3k9.g with an initial speed of 49.9 m/s at an ankb5fxp zrvg 9 /dkq33u 8s,-qkwew.n2gle of $42.6^{\circ}$ 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 ad :atkv*7.xqdhcw hi)5 -(f fan4em,w 1500-m race at a velocity of 4.0 m/s. If you ran the same race 7wddnfeft)aw4q( xh*h.,-mvk:i a5con 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 North, and is in a wind of 50.0 m/8ubfdg9,he t/s to the West. The plane's speed relative tob9,8gf/ t uedh the ground is

  A plane is flying dueqf +q c0el tml1kg,7eukdzd3b +0ha++ 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 ge0s- i689el/* ke 6nfykgd zr120 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 fires a projectile with speed 50.. eq; dy;tzwn;0 m/s in a yd;wtn;zq e.;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 directed across a river with qmzu5jg 13*l sa current of 6.0 m/s. What is the speed of the boat as it cr3* ul 1q5sgjmzosses the river?

  The driver of a motorboat that can move at 19 m/s in still water wishes tlguk) *n9p fu:onn rv.bt rm.-gfs *59o travel directly across a river 1.3 km wide in which the current flows at 6st rm.of:nbf *n gk* )- 9r.vgn5lupu9.4 m/s. How long will it take to cross the river?

  The driver of a motorboat tha( g dna2j(agel9)qgq2 t 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/s.n 9g 2( (lageaq)2qjgd At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposits 4f9tja izan,:prksmz 92.m2e bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swsm,air:j.azkszp mn2 429 f9tim in still water?

  A swimmer heading directly acrz/ke5sec .4esx q1c mkwcw*y r .1)fz+oss 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 thfsk 1q.4smcxzewe / c1 +k.)*zey w5cre current?

  A boat, whose speed in still water is 1.74*8 n8b9cg bawxb ,usv) m/s, must aim upstream at an angle ofu89b)g ,abb*8 v ncwxs $13.6^{\circ}$ (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)  $m/s$