Which one of the followie,d+cazs; yzwa 7 fn5m 8g:jf4ng is an example of a vector quantity?

  Which of the following operations will not change a vector?2w)v ip0vp:fra(jj l* 68fpaw 2qd1 rb

  Which of the following is an accurate sta6b y9; qy*ablytement?

  The resultant of two vectors is the8o06+8soevz;ir vm fe smallest when the angle between them is

  Two displacement vectors havevbk f/0ra8ej . magnitudes of 5.0 m and 7.0 m, respectively. When thekb8 v.jr 0af/ese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following2 ) imuo*.qedbb9a0s-9bw*rnjj wur3 is a possible answe0wqu-2br j)b 9wo3ibn .m**jae 9rsd ur for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in diruu ow677qzhj8g 6kwb-ections that aw786uj uhkg-qzo7bw 6 re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkvoit,jsj )kz -q* 9re-po(d 1cnown vector is

  Ignoring air resistance, the horizontayrks0 ,.(,uln: ung xb(nvzw9l component of a projectile's velocity

  A ball is thrown with a velocity aomp;c,,2 31h5khw, tit 85ar olj .w7ddwiwlof 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, theayv*9)vkei ooe1t .gy. o0ko5 horizontal component of a projectile's accelerationv*.yoy9o g o1kek e v).tioa05

  A soccer ball is kicked with a velocity of 25 m1z0rp snx u,g,* h t2,2hvpykx/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 anll :h1i 9pm3 *ncju4kqel,ii 7ti-parallel to the velocity vectoi3km9*,l l7iinj lce: 4uh1pqr,

  If the acceleration of an object is always directed perpendicul7+p 1k zbhha4ecte8v, .h zg.rar to its velocity, 7hhab41kr.ez+,ehcg 8v.ztp

  At what angle should l+-n d-lnrg;mv;*sg qa water-gun be aimed in order for the water to land with the grer-gg v;n* nl-d; +lsmqatest horizontal range?

  An Olympic athlete throws a javelin at four different angles abov ;9fn*npdu60apizd4ita; 7sf e the horizontal, each with thezpi;tdd0sf*ip97auf;n 6 na 4 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. j+l9tvn+wu 8z If the ball leaves your hand with twicw 89j +tunlvz+e 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 speez d-up xim;c svoil* -sa42+k/d 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 reacj y60;0vt e1oavz:c mhhes its maximum height, how does its spee0a oyt6j 0v1;mhcve:z d compare to its initial speed?

  A stone is thrown horizontally from the top of a tower atz0czl w6ul :ul hh1gd- (zv;3u the same instant a ball is0: vlw63u(;lhuzg zuhdcl 1z- dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired hooc9 /kbr)d-q jqgjnen y-:v8tyqg.t.m7 j :.urizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resjvq.g::dq8bg-eok) rjy t. j97m-uctnnq y/.istance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 69.7 ai/ns8ax9bq 0*euu4 h m/s and at an elevation of 251 m drops a package. 6.0 s /4iabs *8qnxu0auhe9 econds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is ddc/csz3; razw/8u5b3jm t .pyropped from a plane, and one second later a second package is dropped. Neglecting airb/ 5/ 8 zu3apsmdw.t;zjycrc3 resistance, the distance between the falling packages will

  A pilot drops a bomb from q*1 2ctu a(sbq;v(wvs a plane flying horizontally at a constant speed. Neglecting air resistbt(w *;ssqvq1 c av(u2ance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. I/;j p9zhqe. r(tauc ks+di2z3 f you hit a baseball on the Moon with the same effort (and at the speed and ank(/ea9z2+rs; qzctp.d i j3 uhgle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road f+p/gzrok tbh3da.(1 and pass a car trave(p/.gtofkz 1hrb+ 3d aling 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 8i)to(d;h cc vjx*r1e:9is7cjjg d6 qwith a strong current. You start out in your motorboat on thee*hx(9r vjodid gcs;81 jc7)cqj6it: 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 in still w;zr(+(ea/3he tzsz6q8 yhplnh o/b0vater. How much time will it take you to move 12 km downstream, in a h lheb/ zh(zt0ns ;erazy+86qp/3(o vriver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle6ro.6tx orxe5p++fr 6zs9 see of 30 degrees below the +x axis. The ytr +e+p osesf56ox 6rx.9rze6 component of A is

  If a ball is thrown with a velocity of 25 m/s at an angle ,aiuhfesd j w /p*r+::of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a s v /efsw:(y ,3we)fucntraight line 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 you walked?w3u n,e)csfe/v:wyf (

  A butterfly moves with a sped8h azq/;y ox1+ 7lb4r7mx 8xc( brhaeed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the directi478bhdha7bqrx ( +1a x/m lxzo eyc8r;on of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground.h /3 2-uirauiom )d44aktnh-y At what angle is the Sun elevated above the haimia )hn4k rou4- udh/3-2ty orizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whz9):a6p vqzvgat are the components of the a 9z:z6)vgvpq sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respec.trr7t0/yv uw kb k.yo w(y:8li6jr+ ttively. What is magnituvlwyw7j.ktr/y+ t 0ioy86rkb r.:tu ( de of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mafxh;uq.s 80ed1p eq7d gnitudsqdx .h d87q0e;p fe1ue of C ?

  A car travels 20 km West, thensa09ub u- g a6;f9lcqfb:yn 5i 20 km South. What is the magnitude of its displacafb5 -09 ;si6ayf g9uu ncqb:lement?

  Three vectors, expressed in Cartesian coov3/ m.j 6 dccaq.qqct6rdinates, 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,xcn8 o 6cm,9dado5 o53fjqbw (vv( xv, 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 = (+3.0, -8.0), what is the magnitude ofc s;v2 ou1*l)vbv k/t ljg/5uk ve/k1* v)5u /vskcog vutjbll;2ctor C = A - B ?

  A runner runs halfway 3l(u0)fdmo(iv -tz v7( d wrtparound a circular path of radius 10 m. What is the displact)wltd7p- (3 o(mzf dv0ir(uvement of the jogger?

  Two forces are acting on an object as shown in Fig* skb.k) imo:q5 f2xti. below. What is the magnitude of the resultan.o :)ii2st5 qk*fxkmb t force?

  Two forces are acting on an obg*nfh u m5mhq k071x)mject as shown in Fig. below. What is the direction of t 1qmhu7hg0m5k f n)*xmhe resultant force?

  Vector A is 4.9 cm long and points alo )e.8zkk t43mhtm3hgh ng the positive x axis. Vector B is 8.9 cm long and 4h3g 8h tkektm m)h.3zpoints at $+25^{\circ}$ 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 83 cm lox(wmd4id)*r nng and points at $30^{\circ}$ above the positive x axis. Vector B is 23 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 horizontar(bu+ jkz/ ..p8tyj gwlf3k,;r,bgon lly with an initial speed of 19 m/s from 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 4.5 s. What is the heibjgyl8.pf rjkk3 +wgn/;obtz,ru . (,ght of the cliff?

  A girl throws a rock horizontally, withjb(zwxn fbv)wr: v ;;uxj 95;e a velocity of 6 m/s, from a bridge. It falls 23 m to the water below. How far does the rock travel horizon;xr;xv;(jzuf b9)wvnw:j 5be tally before striking the water?

  A ball thrown horizontally from a point 24 m above the gj,52z*,q;bq svimob6j 4 d gfground, strikes the ground after 2imjq5b o j,;v 4bgfdzg*q ,s6traveling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes intou5gjg c8c;sy9 the jump with a speed of 12 m/s at an angle gcs yjgc8;u59of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jhcf qt2kcg78pvdu + 50-yso3w ntd, d;ump goes into the jump with a speed of 11 m/s at an angle of +gd8scw0 k7 qy,p-tod3t5h fd;vu2cn$29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 59.0 m/s at an anglv nl 3vpm2c+i6e of $11.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an inibs4mct bt:o .7h+7 jzztial velocity of 56.8 m/s at an angle of $49.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglef1s;9 wf.bl/llp oud+ 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 atnbs //v6b;on v 21.3 $m/s$ from the roof of a building 47.8 $m$ 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 ofwak vze ik8/. p,/l91d xenjz4 43.7 m/s at an a zzija /ep.4 x8dk,evwln/91kngle of $44.2^{\circ}$ 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 ra dezy e247f-lg2pdil3rdv 4w *ce at a velocity 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 d e2 yfl4 *v47ped-lz3wgird2it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind jo r.ba f(-)mhof 50.0 m/s to the West. The plane's speed relative to )a.m- hjro( bfthe ground is

  A plane is flying due Sout ks7-: f;len29 gyjqlth ($270^{\circ}$) 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 heck.3 ,b4.8gv msev +o:rwx hdvaded $30.0^{\circ}$ 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 pr(f5htug17e gc)s n7s mojectile with speed 50.0 m/s if(77u e)st mg5s1gc hnn 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 watwml)4dom2/: fuxa f b;er is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the river?;f4f)b2: da/lmx wmu o

  The driver of a motorboat thaumcz1c m7xwyj3s.t z7kt/65ea8 bv6l7xt at8t can move at 14 m/s in still water wishes to travel directly across a river 0.9 km wide in which the current8a1ztmct7x/8k 6e73ctlx .sbum7zwt5v6 jay flows at 3.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stxu g/jal0h(5will water wishes to travel dgwh5j(u /0xal irectly across 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 across9v8smccbiiw y o-h(,) a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast sy - c)bcv8oim(h9, iwcan she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppositob zgz(ty* /4*j rf-qde bank in 6 min 40 s. She is swept downsrto/(gzj*qfb* - dy4 ztream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.13 m/s, must aim upstream at an z f3.yd6t4fuah8m-url rcv8, angle of 6 u-hf.f4vc 8 md,a ur8tylrz3$24.0^{\circ}$ (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)  $m/s$