Which one of the follow6(exz dx-sm0ayavv,: ing is an example of a vector quantity?

  Which of the following operat(dpru/+wmhrz95k ;lmuc4 l 0p ions will not change a vector?

  Which of the following is an accurate statempp,r/ pnjhc04i 80h cmr rtk78ent?

  The resultant of two vectors is the smallest when thwd0zw ,pvb6+p07zij je angle between them is

  Two displacement vectors have magnitudes of 5.0 m and, (h mejw( 2(s gzl2pjf.7frdmv )ws4j qio17r 7.0 m, respectively. When these two vectors are added, the magnitude of the sf rjw4(g,)j e1.f7dqlzrj2 p ( hv2i7m(msowsum

  Two vectors, of magnitudes 20 and 50, are addzoda 1z+ha32s v8i);oie ka+tr)pro 3 ed. Which one of the following is a possible answezaa1t+o+a3rv2o8dps h iire;koz3 ) )r for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 6 :lz4 :qlh2ggevuh48md(fxj N, pull on an object in directions thald6h xul2q :j z:4v(4mg8fh egt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vssf2jira*l pr*e6-8z :tjuq,ector is

  Ignoring air resistance, the horizontalz l,8a1l rh7p 7mp5q wfo+gv5p component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an a, yern:rcb4. fv6;w bxngle 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 horizontaa-t l4 ncji1-sssllw3jy p/ )s(lf +x/l component of a projectile's acceleration+pjxl14-jys 3snts/i/c-)f (lsaw ll

  A soccer ball is kicked with a velocity of 25 m/s at al;l-tq:m pl0 zci,a(n,x ywn; n 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-para xgnot/0hv(cz6uyei-8 f ; r1allel to the velocity vect08 ta n1 6ru/v xoeh;gziycf-(or,

  If the acceleration of an object is always directed perpendsr d62y)bo)8x*s/6 i l avrpgnicular to its velocit*xn6) p i)osr 2r gb86yd/svlay,

  At what angle should a water-gun be aimed in order for the water to land with jafbf8o ak8xjq(ika* d3, a:t );3mym the greateamyk8x () fi: kb3ajaoat,*dqm; j83fst horizontal range?

  An Olympic athlete throws a javelin at four different anq9qdkcq* n6/pgles above the horizontadkq cpn 6*9/qql, each 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. It vz:g4vp5ua zn. :mm7f the ball leaves your hand with twice the velocity it had on your first throw, its ho m:vpv.zm 57gtan:u4zrizontal range R (compared to your first serve) would be

  A ball is thrown at an orilel;hf+e; tlq.*m - ,*zsqs uxginal 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 attef, 8ncutvxaggx19z5 nhn 5x +1mpt reaches its maximum height, how does its speed compare to its inix u+ 1 n 5agvnch95nt8zgxf1,xtial speed?

  A stone is thrown horizontally from the top of 4i 3hbcddk(4c9l fyw4 a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the le4( 4 bdy idw3fkc4c9lhvel ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is n eux:/-zn0rpdropped from the same height. Ignore air resistance. Compare thenpen0rx/: -zu times of fall of the two bullets.

  A plane flying horizontally at a speed of 56.0dfy1() yqh0fk-kz v+l( srv1 cxh7cd4 m/s and at an elevation of 131 m drops a package.yk0qc)z s dfch7vh v-f x+k4(y1 (lrd1 2.9 seconds 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 secondo8bx6 qwm9d.6wc kaen59u:qo later a second package is dropped. Negq om9dc u9:q8b6 ow .5n6ewxkalecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a planfqeo*nlxmi(( (qnl 4co/ u-lwmok)- / e flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal /-qel/4olonkcn )*-x m (woful((qim location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of t 8 fflr2jpl/lv ekc+9 j2ms;,hhat on Earth. If you hit a baseball on the Moon with 2+ p/8c,srhjf9m2l ;fklve lj the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 0sxermc s+p n:a 8 e.a-kl4-h.mbowx*mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative ve nw e0mmxs+lcs8- xpark.a -4.:ehbo *locity of your car to the other car is

  You are trying to cross a river that flows due south with a strong current. pywwbv7 o-w/*j5x ofp +bb3 ;x You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting po;y*b+w3 bp/ jo5bwxow-p7xv fint. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time wr+rebj7.b :0 pc,mmrkxt2u z6 ill it take you to move 12 km downstream, in a river flowing a 7m6+.xbjp0 et,zbc 2 ruk:rmrt 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degmyi5j ua0( wyir *to;qad4876lc hia5rees below the +x axis. The y component d75;qi8(tj6 y4 iyo iaa lrcu*a50hmw of A is

  If a ball is thrown with a velocity of 25 m/0 jygh1 f+n+has 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 line7ah+ by/qm w0f in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have yom7y+qh/ bfa w0u walked?

  A butterfly moves with a speed of 12.0 m/sfb 1hrumr- erj0* + ;fw-smq0y5wh;dp. The x component of its velocity is 8.00 m/s syhh0 -1*rfrbf ;we mdr;w0 jq+m-p5u. The angle between 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 ..mu d:i7 2vq:ya pamoground. At what angle is the Sun elevated above the horizuaa:2mopv7y.iqm: .d on?

  Two vectors A and B have comp85s zlwxy:wchjf8 *b 8onents (0, 1) and (-1, 3), respectively. What are 8 bl5*w8 zjwh8f csx:ythe components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1.xd 1 srhew*t-g., goj, 3), respectively. What is magertdggsox1 -*..jw , hnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3(cz )v ,paccmo6d4u8dfq(nr 6 , 0). Vector C = A + B . What is the magnitude a,rodd8 46 pf6nccm((c qzu) vof C ?

  A car travels 20 km West, then 20 km South. What is the magnitude ofczqk93o7pz cr) b)f 5c its displaz)c qz ock7p3bf5c)r 9cement?

  Three vectors, expressed in Cartesian coormv*fy:kt4 k(rug lh.2q.f r w9 ar8m9ldinates, 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 coord8f: qm2zo;ih gc4upx-inates, 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.f*-dbk2wh6ypca /pte hl, h-10) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - Bwhb6h-ep/,p -cltkd1 hayf2* ?

  A runner runs halfway aro0b:.noxcs ;aj und a circular path of radius 10 m. What is the displacement n .;0:xj cosbaof the jogger?

  Two forces are acting on an object as show2me(1u 6jlo2fc + wwccn in Fig. below. What is the magnitude of the resultw2(l mc6j e+cfo2ucw1 ant force?

  Two forces are acting on an objec7xte,, :o ebzvt as shown in Fig. below. What is the direction of the resultav ,,x7b :tzeoent force?

  Vector A is 5.5 cm long and points along the positc9buybz )kn6+ive x axis. Vector B is 7.4 cm long and points at u c)kyb zb9n6+$+37^{\circ}$ 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 61 cm loun/ca4fjyk*p /i34)y k ut 7hqng and points at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 38 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 initimm5.a6lhgbd zim-b9a5k nb7i,d1 i r7al speed of 15 m/s from the edge of a cliff. A stop watch measures rmb.97k6l-dznb hb51i5ia da img, m7the stone's trajectory time from the top of the cliff to the bottom to be 2.3 s. What is the height of the cliff?

  A girl throws a rockw tsm4oa ;w(go4 00whx(or1caz6il.v horizontally, with a velocity of 16 m/s, from a bridge. It falls 13 m to the water below. How sx44 (vwmgaw. 0l;1i trowc ooh6(0zafar does the rock travel horizontally before striking the water?

  A ball thrown horizontally fro:0ut8(o6uh bo8iaa h om a point 26 m above the ground, strikes the ground after traveling horiz0h a8 o68buaoit(h: uoontally a distance of 15 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed o22h -wjoy r)lw y7e:s;ny9y otf 12 m/s at an angle o -t w9)je;lyyy :yrnho2s2 7wof $20^{\circ}$ 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 a speed :8 mpemi3:: zpp efb-ypsw9l6of 10 m/s at an angle of :3p m8lbppfp: : e6w-ezsmi9 y$33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched withejox-zevj0; 38w f1fjc4d6e h an initial velocity of 55.5 m/s at an angle of $26.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 49.2 m/s at an anglh cg1smdte 18mas8mp/-u l91we of $16.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an armblu,g/z5 ko1 v:f /zngle 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 horizontally + vlj6m/d-amrrm 5u/ dat 20.7 $m/s$ from the roof of a building 40.3 $m$ 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 65.0 asu 0d*7: oof -j6rli g6x6eupe7x5 qvm/s at an 6 jsf 6i* e5gq-xlarpuo60e:d7 ox7vuangle of $41.6^{\circ}$ 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-m race at a veloci5erqpg+m+u,nv 3 )opcty of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed by 2.0 m/s, the time it would take y5v n g+ 3,mqepop+ruc)ou to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of 50/-;xrl kft6,/st xr gw.0 m/s to the West. Th-x fr/w;kgl/stx6tr,e plane's speed relative to the ground is

  A plane is flying due South q sa 9(hc /y,kv-zvvt.($270^{\circ}$) 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 spku; 9jdpck *dr ,e6-sheed of 120 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 projectile2 -dh np0ep1ay with speed 50.0 m/s y2n 0a-heppd1 in a 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 4n,k9(9flqa.gh nwxn* fapq9water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of thef,hqnkqf.9l49 *pa anwn9g( x boat as it crosses the river?

  The driver of a motorboat that can move at 18 m/s ime,bwf/; t0pqn still water wishes to travel directly across a river 0.7 km wide in which the current flows at 3.6 m/s. How long will it take to cross,feb tm p/wq0; the river?

  The driver of a motorboat that ca17f5 a0hy btjin move at 10 m/s in still water wishes to travel directly across a0 t7fijb1ay h5 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 wigigm+: //n dcod f.e,vde reaches the opposite bank in 6 min 40 s. She im d,fd:ni. / /+cegogvs swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across aeja ebvzq0u6a/ )sl9 2 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 current?)ea2 v96ze jlu/q0a sb

  A boat, whose speed in still water is 06v6uq1 u u(jjm.97 m/s, must aim upstream at an angle of uqjj(6uv1mu6$16.1^{\circ}$ (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)  $m/s$