Which one of the following is an example of aqg ydnq9e 4 zda52ttx1p70e *woq v1,q vector quantity?

  Which of the following operations will not change a vectorqm6h 8p2)d1 kf osyklq -16roa?

  Which of the followinmyqgg318up 9u g is an accurate statement?

  The resultant of two vectors is the smallest when the angle be9k6 djou4uxr ;tween them is

  Two displacement vectors have mao*8e cefe0..j u 7zuyagnitudes of 5.0 m and 7.0 m, respectively. When these two vectors arj0.z8f *oau. eu eye7ce added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50,vq:qgfgv ; 2q; are added. Which one of the following is a possible answer for the magnitude qq:gf2g; v;vq of the resultant?

  Three forces, each having a magnitudex5:.h:17rmaui q,t3vseu gg t of 30 N, pull on an object in directions that ar7:1,amsuugg 5h. qe t t3v:rxie $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec)kswql; 2ci.pualjm:;-m f a:tor is

  Ignoring air resistance, the horizontal5 pj3(lds ut iwf)w+a1 component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at anzj.emigc 4nr+g20 kn 6 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 projectil3(no8 y7m a jcrmrdoywj)xwa8z2i*,,e's accelerationx(wary8yma)nw i7c 3 jzj,d2o ,o8mr *

  A soccer ball is kicked with a veloc5onq6/kt. j5usgy 4 qzos(9 --tfd*cakjx3 kgity 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 i l8ll9a.+adt is directed anti-parallel to the velocity vecto8i a9+ a.tllldr,

  If the acceleration of an obj;ddeh1( v:/zwkxu 5h nect is always directed perpendicular to its velocitdzh/ e1; d(5wux:knv hy,

  At what angle should a watdid- x x-nna.uy 0y2-aer-gun be aimed in order for the water to land with the greatx 2nnuya 0id.d-yx a--est horizontal range?

  An Olympic athlete throws a javelin at fonp+d . kv8xw re3to+7uur different angles above the horizontal, each with the voue+d83kx r7wt+p. n 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 yourvbly-xuom-:s 5a29 pu +*hfwk hand with twice the velocity it had on your first throw, its horizontal range R (compared9a h-s-ylpxfuw bum* 2:5 +kov to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s x h j9-cb7e 5hv53vjbmat 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 fx-.xon;gkzyrl 3lu doyp ydt. 2.0v56ield goal attempt reaches its maximum height, how does its speed comparylrd 0n zuo5gvtd .26o; ykp.lx3-yx. e to its initial speed?

  A stone is thrown horizotso,li. j;5iwntally from the top of a tower at the same instant a ball is dropped vertically. Which object is travtj,i ;oiw sl5.eling faster when it hits the level ground below?

  A bullet is fired horizontakc3vjtx /iqacat 2 8*5lly, and at the same instant a second bullet is dropped from the8cx*352ij cta/ tqva k same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 81.1 m/s andk 2r 7s(fckwadc(f i69 at an elevation of 299 m drops a package. 4.8 seconds latc7 c as6f(9fdk2wik r(er it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plag9vcyykrn/3s k:7k yc((9rv ,;zvt4-asa y dmne, and one second later a second package is dropped. Ne3v/ygvyat ; m d cazs-ky7 4(kv:9n9 y,crks(rglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying qw gk5:+p/ s:p*r+cqppn3ft bhorizontally at a constant speed. Neglecting air resistance, when the bomb hits th::qtpr3p+ c*/5sk p pqn+g bwfe ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one q1d*nf+tv .mrd6 o8pv/.imju (6zxxn -sixth of that on Earth. If you 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 r ..*zux1nv o6dv nm6+pf/(xdmit8jq

  You are traveling at 55 mi/h in the +x axis -6+o.aabydffx5.ng z 3,utgv relative to a straight, level road and6tv+.-uag f.z f n5,daxbg3yo pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river tujwulfs adyi62/e0 k-ufsn8e e 8-c:6hat flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank di fad6 u0ilk2 6wue-sef 8y:es8/ju-cnrectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How b 3i 52bdzhh10y: bufzmuch time will it take you to z2bd5uf : 1zbibhy0h3 move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees bel;;err orx(8vmow the +x axis. The y coorexm;v(8 r;rmponent of A is

  If a ball is thrown with a velocity oybyd18x)ul .t f 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 lineo dfk;r3;6hj krp40ap8p 2ict in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees npj p8f pr;6cr4i2kd oh3 t0a;korth of east have you walked?

  A butterfly moves with zebh*i* b +c s-lk7 2mkq*o4yya speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction*+mobb z* * k-c7lq hsy4yei2k of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a lev2pw1kutet 4h(ljft:caiac6 5+*lzw2el ground. At what angle is the Sun elevated aba( + 2kct2*wjh51ifw4 ttczal6ulpe:ove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. W asu(b fy r2rzdf9;p3 g+v5i5phat are the components of the rpb5;z(3 +v2uff s9p adi5ygrsum of these two vectors?

  Two vectors A and B have components (0, 1) and lwuw4f/b*t/kp2r( d k (-1, 3), respectively. What is magnitude of the sum of thes(w db2/p l*/kk fr4tuwe two vectors?

  Vector A = (1, 3). Vector B = (3, 0). j(z4 -otfb d9o Vector C = A + B . What is the magnitudejdoto94 z -bf( of C ?

  A car travels 20 km West, then 20 km Souz h9 m),kj gl;d(hqwd9th. What is the magnitude of its displacemd9m,;hhl j( )zgkqd 9went?

  Three vectors, expressed in Cartesian coordinates, ar0i.;+gml m atre
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 Cartscc hwum o+2ixh ,p6b8)m 3e(xesian coordinates, 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) and vector B = p(xwh,x. u g4)5qbu7pgspcf 69ru g2s (+3.0, -8.0), what is the magnitude of vector C = Ag7uc5 ps.pug,fxh2q w)sp 9(r g4bu6x - B ?

  A runner runs halfway w1+u raecyv,.around a circular path of radius 10 m. What is the displacement of the y+ew. , 1vcruajogger?

  Two forces are acting on an object as shown in Fig. below. What isz 0 1+e kvynki/8q/ou wvd0zc3 the magnitude of the resulwn10o/zqk+ 8i/yve0kdu 3czvtant force?

  Two forces are acting on an object as shown in Fig. below. Whmh7(6jim58 *1iu jkju epqqf,at is the direction of the resultant for758* (f1pmm6iei kuq ju,jqh jce?

  Vector A is 5.4 cm long and points along the positive x axis. Vecod(( oqud, n7m1+lybytor B is 9.2 cm long and points at o ,uynd1 7oqbl d(+(my$+41^{\circ}$ 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 71 cm long and points a(ay4crb1cu /2p l i5klt $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 49 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 withb c 2z- ;gbkujpo/vvh0o3+; ky an initial speed of 14 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time fromzb-j +gv0kbu ;c/voh k3op2y ; the top of the cliff to the bottom to be 2.7 s. What is the height of the cliff?

  A girl throws a rock horizontallyvn vw7 h.ek4a*, with a velocity of 16 m/s, from a bridge. It falls 27 m to the water below. How far does the rock travel horizontally ben ak*wh.7vv 4efore striking the water?

  A ball thrown horizontally from a point 29 m above tcglfo hsf2) (0he ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed wa g)f2ohfl( s0cs it thrown?

  A jumper in the long-jump goes into the jump with a speed of 1ggwn-4(b7 ims2 m/s at an angle mgwg4- 7ns(ibof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into t3f jd(4 l +nbcsda+2dfhe jump with a speed of 10 m/s at an angle of+sddj(a2b f4cn3df+l $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velku 8- q,o)f lk0l(b0 6lfoapcfocity of 46.7 m/s at an angle of $20.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialsoe yj9j+;(ghhcc ,3v velocity of 54.2 m/s at an angle of $36.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle buzy 2x cx/.u3of $30^{\circ}$ 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 horizontally at amy4ugb1 93 wo25.8 $m/s$ 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 firedy c r.:1zri4;ip/aicq2uw)vf from ground level with an initial speed of 45.2 m/s at an angle v /:zicp; wy21fc r.)qiairu4 of $40.6^{\circ}$ 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 a 1500-sr )mfuw -hl74.wh:hpm race at a velocity of 4.0 m/s. If you ran the same race on a day when m: w frwhh.)47-uplhsyou 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 s0 08c eiijpvx3z o;h2North, and is in a wind of 50.0 m/s to the West. The plane's speed relativec;j2hies 0p 0xv3i 8zo to the ground is

  A plane is flying due South (ku -d +eln8go lj+9+dv$270^{\circ}$) 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 ,4k+ 4kbyyv:rjmjbl9)y hz a3headed $30.0^{\circ}$ 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 -(yf8oaq9 ydifires a projectile with speed 50.0 m/s in a forward direction9a q8 fiy-dy(o $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in io2;fbqpn *4p1je),c2nom rybk( o1 d still water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the ore2jmy)f 1; * b kpqodn(c4o2n bi1,pspeed of the boat as it crosses the river?

  The driver of a motorboat that can move at 15 m/s in still water wishesll:xbd3.b2nwgvdc 1 mq g-.9y to travel directly a29by- 1g:v.dw lm n xg3.bqldccross a river 1.1 km wide in which the current flows at 3.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still wateq/7lqi99 q3zh ljhb4dr wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At qhi9 hbjzl7lq49 d/q3what angle upstream should the driver head the boat?

  A swimmer heading direcoop2h;)i 1 ho j+l ;dvb -iv170jkuxgbtly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreahu ovp;ljx dg)12h-bkvobi;o 0 i 7+1jm 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bao) e( cjq(*mx .(.pmfkm*pgwonk in 6 min 40 s. She is swept downstream 480 m. What is the speed o cp)( k*gq omope(xmjwf* (.m.f the current?

  A boat, whose speed in sf pvwx8p*g5t9c : zi/atill water is 0.91 m/s, must aim upstream at an angle off v9p8ia5x cwp tz/:*g $18.8^{\circ}$ (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)  $m/s$