Which one of the followingd/:c+0 + +wvtcjz3bv exbzhg( is an example of a vector quantity?

  Which of the following operations willg+ sikmwt en+uz;26v 8 not change a vector?

  Which of the following is q2w4exrw7 12nl;x1 a z1viml x)*zmkran accurate statement?

  The resultant of two vectors is the smallest when the angle betg5gqoksn1 )qe)a yn 1 o921 he2pr)mnqqg i7;tween them is

  Two displacement vectors have magnitudes ofk6;u:gxg5k m7i. lcwe-d w7ej 5.0 m and 7.0 m, respectively. When these two vectors are added, thee x76m e;cdkwi-7kj:ulg.wg 5 magnitude of the sum

  Two vectors, of magnik0l1 w9l-spkqv a- 4 upc9,n sb9-nizdtudes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the ip 9s-4 sqdna0vlzn w kupc-,bl91-9kresultant?

  Three forces, each having a mag2zg.g:7(cj x.zn+itkldfy r *nitude of 30 N, pull on an object in directions that are n gz *x:c2rd(ft .7 j+zky.gil$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unf9to7sphgi 8p 5(g,wfp m gxk5:x)n.v z,qp0fknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velocity nj6fbjhn3sxk4(n//e

  A ball is thrown with a velocity of 20 m/s5kqy +7k9bw5j gq2veu 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 compkf,b4r;ae j/ tonent of a projectile's acceleration/bk jf, aret4;

  A soccer ball is kicked with a velocityh (41fnybmy(l 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 obj ijf2i8s w*pj.fm7u i)ect is directed anti-parallel to the velocity vector,2u)m.8ipwfjs*i f7j i

  If the acceleration of an object is always directed perpendicular to its vew(:x7rmyp romfizr 6y9;6v4olocity6rof :xvpz; i(m ym7o9rw4r6y,

  At what angle should a water-gun be aimed in order for the water to lkgr i/ h,4gt60o6d krxand with the greatest k4r6d o0rkghx/it,6 ghorizontal range?

  An Olympic athlete throws a javelin at four different angles above th-w + : h.tpdrbkf2zjp5d.cv0z e horizontal, each with the same sp prd5d..bkw0:vtz-z+h jcf2peed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 your hand wits- 1nx,bd4tt qh twice the velocity it had on your first throw, its horizontal range R (compared to your fir1qbst,x4n d-t st serve) would be

  A ball is thrown at an origin jx*uqt2 ct.lcn98hhk2* q1jnal 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 nt0o vjc;czx3j.:gr ; its maximum height, how does its speed compare to its initial;zrvjccjont 0 x3:g .; speed?

  A stone is thrown horizontally from the top of a toww,+x fndy);+wk u;ma fer at the same instant a ball is dropped vertically. Which object is travex )wyk ,wam;+ ;n+dfufling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet hgl / v-bj z*ozc,ua98is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bullets.8jgl u bvo9z*z,c-ha/

  A plane flying horizontally at a speed of 95.8 m/s and at an elevation of/) uew5 mtv5kod 21nqg 274 m drops a package. u 5k5mvwen/go d1 )tq27.9 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dro7s n 5d8d.jdsyrjk.iu rh*8 i1pped from a plane, and one second later a second package is d 881jysidu ki*.sr.hr dn jd57ropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at rs/,i)4 pg gqva constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locatp4i v)gg/s ,rqion of the plane will

  The acceleration of graviyo,dlk r3s4 6xn+ wa)sg4gg2vty on the Moon is only one-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 wo3w4gkg+vsyl6 2nd ,xoga )rs4uld land

  You are traveling at 55 mi/h in the +x (o;vq+p+* aejv xsvqu66k:axaxis relative to a straight, level road and pass a car traveling at 45 mi/h.xp+av66:;oxqvk+e( qu * vs aj The relative velocity of your car to the other car is

  You are trying to cross i ,ny(cu yrbx .45jhr3a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank y i3.,ycj ur4rh( bx5ndirectly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How6sy) cc6:lw db much time will it take you to move 12 km downstream, blcy)66w:s dc in a river flowing at 6.0 km/h?

  Vector A has magnitus vp87ta ehrnv 6r:m:;de 8.0 m at an angle of 30 degrees below the +x axis. The y component of Aar7:p6 r8ns;vevtm :h is

  If a ball is thrown with a velocity of 25 m/s at an angle 83ipq*t nw(heof $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a stra3.5 uc f9e,vrzls,ocuight 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 hav3lscu ,v .ezu,f cr95oe you walked?

  A butterfly moves with a speed of 12.0 m/s. The x s hfez07plsd1 1d u.p2component of its velocity is 8.00 m/s. The angle between the direction of its motu edd10spp2hz 7fls.1 ion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what vr gupxn,5(*yangle is the Sun elevated above the 5,uy( pvr*gn xhorizon?

  Two vectors A and B have components (0:*( fgsocb(ene*ku l w yj:90m, 1) and (-1, 3), respectively. What are the components of:mbunc e gk *w eol(j:0*(9fsy the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), uivesyp q n wti)6+)6 dsl77s)respectively. What isn7q 6yi6s7evd p)s))st +iwu l magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Ww8dgbtx *6r( dhat is the magnitude ofdxt d6(rw*bg8 C ?

  A car travels 20 km West, then 20 km Sou3czar: k4cy* nth. What is the magnitude of its displacemrkyc n43:c *zaent?

  Three vectors, expressed in Cartesian coordinates, ares1em,0 h0f-e 4xldlor
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 C gwx7 cj:)bry-artesian 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 = (+3.0, -8.0), what is the m4n apr01oqw1 1jhuy(iht+sy;vn/r(pagnitude of vopy0nwrj;h ((4nu p +yvs aqt111r /hiector C = A - B ?

  A runner runs halfway around a circular path of .6 p8c ooyrn4 -hyf4slradius 10 m. What is the displacement of the j lorchoy6np8s.-44fy ogger?

  Two forces are acting on an object as shown in Figi :,syc97zjju1 2gldk. below. What is the magnitude97:ucyj2z,j lk i s1dg of the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the di2d( iyo;x0zso rection izy(o0;xo s2d of the resultant force?

  Vector A is 5.9 cm long and points alobfbf j:h,/h;upiy 1,u7b8a nx ng the positive x axis. Vector B is 6.8 cm long and points x8i,ba,:nb1jh /7; hpyuub ffat $+58^{\circ}$ 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 86 cm lon o b: adcxheeg,yaa6w4y p- 8*zk7j-m8g 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 27 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 ho8nlz8nr t sm2x2nww29 rizontally with an initial speed of 21 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 4.8 s. What is the height of the cnnwwr 8t29msxn822lz liff?

  A girl throws a rock horizonp l)xjln sw7 k(aum.( 0xt42yy(ky 5zitally, with a velocity of 7 m/s, from a bridge. It falls 22 m l4()5y0njku .a7 2zxlx yistpy(m(wk to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the ground, oth wv; 7e/nxg9ju1/ sstrikes the ground after trastn1/ ou7;9gx wehj/vveling horizontally a distance of 13 m. With what speed was it thrown?

  A jumper in the long-jump goes3zwpu fw+p1a8*mtl2+nlv3 7jo,r vah into the jump with a speed of 12 m/s at an angle ofuznl+fow7+t8r13j, m*vhavp lp 32w a $20^{\circ}$ 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 of 14 m/s at an angle sah5zx4g t 7h;y*3jjj;gh j*7jjs4yzx5t 3ahof $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with )gdbh.hnui4:an initial velocity of 53.1 m/s at an angle of $10.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial :d:pjq5jv xg2/ x*kgtvelocity of 59.3 m/s at an angle of $47.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of:y9onff/ifq5 fw, qb;xf 6p7r $30^{\circ}$ 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 horizoiu3( pdz4n* hcc:r xb3+;pspwntally at 25.0 $m/s$ from the roof of a building 47.7 $m$ 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 spee40 , mvm42 .rfn2oinawit2/dsi tr p4ld of 48.0 m/s at an angle ai4l t2d rf mi,4/n2ro0m4s n.ip2wvtof $43.8^{\circ}$ 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 velocity of 4.0 m/s)rd7 k7afzq5hhk/l(wy,v. q9jzpah2. If you ran the same race on a day when you had a constant headwind which slo2,.(f)9 wzaklk 5q/yv hhzh q r7p7ajdws 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 oj a.q f8h/*afsvyk1;kf 50.0 m/s to the West. The plane's speed rajy;ka s hf1.*/fq 8vkelative to the ground is

  A plane is flying duehp;vj (s3fb4. zor n 3og2mj/t 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 kx/hmw0,r6 wzkf9;.vd9cqa s120 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 w*sffsc:p i;516dop7saq - p hlvs06xprojectile with speed 50.0 m/s in a forward direc56;x ca0qs vpl6:fdp17oh* i wsfss p-tion $30.0^{\circ}$ 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 ag;:2 zv)t-t/unhvr8f qer h:d cross a river with a current of 6.0gr:t-;zhtnfr ed2:qhvv)/ 8 u m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that cahk2scmt-j) zx:wr11 s n move at 8 m/s in still water wishes to travel directly across a river 0.9 km wide i-jm)wzxk :2s c1t1s rhn which the current flows at 4.4 m/s. How long will it take to cross the river?

  The driver of a moto1jix7 xc rh/ :y+i+enmbh;uvc+tg )k7rboat that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at cjbkimyt+/)h 7+i vhe 1x7+x:ug ncr;5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide re9s:8gx ygfh y,x kep)) rsvp*d 9ll9.zaches the opposite bank in 6 min 40 s. She hx*89p ,x9fys z.p gvsy e) :lrd9)lkgis swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bannqdg:o6y .6zrf.;xm ik in 6 min 40 s. She is swexdrz;.o iy:n.fg6m6q pt downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.82 m/s, must aim upstream ;qg-o vo 7peg+at an angle of+ -;pog 7ovqge $31.5^{\circ}$ (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)  $m/s$