Which one of the following is an example of a vector quantityag1v escdd( l)5r .id3?

  Which of the following operations will not/yxwpw1od+ 0z 1b(ow1tv - hdu change a vector?

  Which of the following is a3f5b9frkgk ep/w 2cbz3tg (0mn accurate statement?

  The resultant of two vectors is the smallest when the angle betwep/0nm tvqd .0lzof0(uyyph) , +bc4zjen them is

  Two displacement vectdunyi(-cya+. rrc9 .rors have magnitudes of 5.0 m and 7.0 m, respectively. When these twoyrir9.n.da rcyc(u +- vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 2-in(vuac9jny8z /6t a t-x6ba 0 and 50, are added. Which one of the following is a possible answer8x v -(n bc9a-6 ntaajiu6z/ty for the magnitude of the resultant?

  Three forces, each having 07s7gr g8p ptda magnitude of 30 N, pull on an object in directions that are pstg0gpd7r8 7$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thncjbs, b4.n2t e unknown vector is

  Ignoring air resistance, the horizontal component ofokb7 7euk3m k/ei/k/m a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an y-v,g).qyz: m izzv g0angle 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 projectile's ych/ lc*fa45bhkseuyl m592/ accelerationlb5fchlu/ye cakh 94/5 *y2m s

  A soccer ball is kickeduvwwe uj/ g,-7 with a velocity 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 is a.quuyfako m59fie3i6m1.) e directed anti-parallel to the velocity vectq 1 ..fi6em u)ma9oe3 kfuai5yor,

  If the acceleration of an object is alwaywpb3rv8jw1rlp/3wa ( iui8t7j)v v/is directed perpendicular to its velocity,7apj i/w8w3rw vj 1trib 83p)vui (/lv

  At what angle should a water-gun be aimed in order for the water to lanr (om1it0w7n;7lymw r d with the greatest horizonta( 17;lmi7 mwntrw0or yl range?

  An Olympic athlete throws a javelin at four dx7)x9ae l ,ovsifferent angles above the horizontal, each with the same speed:x)x79v,els oa $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 leaveso/cd-am1r6w dwz oq8+/ sy w;7v( xgty your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) w wz awyyo-+sdgx/otrcqd7vw/8 1m ;(6ould be

  A ball is thrown at an original speed+v/w szjdy6s/rd.f lw o86/id 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 ree1tj* b4bb6 gwaches its maximum height, how does its speg6*bte1wbb 4jed compare to its initial speed?

  A stone is thrown hor7tq *oamga f c,c/;nd:izontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it h ,*:7agc;fcod/qamt nits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bulle2jm d5uopu 7 f.s t0c/m85kwout is dropped from the same height. Ignore air resistancefsjtuo ckd 07ou8 /2.5 umw5pm. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 98.5 m/s and at an elevation of 21wrrqg0y6;uw/+p h8n l 2 m drops a package. 3.4 seconds later it drops a second package. How far apart will the two pacw/rg ;n qp6uy0 +lwr8hkages land on the ground?

  A package of supplies is dropped from a ;gsolm -ydxd1v + 1s8.lwv9ne plane, and one second later a second package is dropped. Neglecting air resistance, the distance betsd;x8e 9n+gyl.owv-dm1vl1s ween the falling packages will

  A pilot drops a bomb f.j +r. q 1pog:lckwvm9rom a plane flying horizontally at a constant speed. Neglecting air reo +gkpvclmr9..:q1wjsistance, 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 Ea*vw cr8e sp,wk 7qp/;irth. If you hit a baseball on the Moon with the same effort (and at the *;cwvrsi k8ep7,w q/pspeed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relati;yk ,;k osg+f9cxfm6 oml,wi+ak, m+uve to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car u;cg;,, fkmok9 f +o,xkywsa++ 6mi lmis

  You are trying to cross a river that flows due south with a strong current. Your 4cd rxw 0i)4 zb wq)untu1*/9hz9.nhhv/tjj 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 4)cd/wu./ 0zvqhrnu4*99h jit1hbzwxnjr )t motorboat

  Your motorboat can move at 30 km/h in still wi +7zc l/x5 +ssw3cdvheb7* ltater. How much time will it take you to move 12 ksb*elc dts+x7 v3lzi+w/c 57hm downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angg maq ccmw evu.5b0vo6 b0j/20l o:c;wle of 30 degrees below the +x axis. The y component of A i c.vgb ;ec0/mcaqo wl2b6:0um5 vw0ojs

  If a ball is thrown with a velocity ofajo oi14/ u-7cgost4x 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 north of east and r:.iu *f-iu3vxzx 4ywyou end up 2.0 kv x :w-uf iu*.r4ixz3ym north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x 1qp2m/ch * t0zljw5 o,)b/ jz8mhv ghhcomponent of its velocity is 8.00 m/s. The angle between the )o 1qvg 0w/pzzm2 lhh*m/bjjhh ,t c85direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. Atu rcs33q19qn r what angle is the Sun elevated above 19cqs rn3 qu3rthe horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respect8k5)(vsypvd2 ngrs3 q ively. What are td5(qynk83gsrp )vs 2v he components of the sum of these two vectors?

  Two vectors A and B have .7yl0pjrt;*ogu 6c iut+syf+3vsq +g2meg(u components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vec( 3rs+g+2umi 7lg;+6vfu qu*sy tpy0.tg jo ectors?

  Vector A = (1, 3). Vectorb wn8b*nc;eabx9 i35do qt)0j B = (3, 0). Vector C = A + B . What is the magnitudecb a 3win; d)j0*b nqto9e8x5b of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude o lmnklj92q*zz .x/ 5xlf its displack l5z 9xm2xnzql.*jl/ement?

  Three vectors, expressed in Cartesian coordinates, 2hq m c71pww:idj 5w.+dgm:lot-bsx 4 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, expresswh 8j)wss6p*i ed in Cartesian 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 = (v;s ,ukh)ny g7+3.0, -8.0), what is the magnitude of vectorhv gs,7)uk;yn C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. pg0:: ebtnq * zorhzu23i3wg -What is the displacement of the i2qg ue ozghtz0w*b-pr 33: :njogger?

  Two forces are acting on an p.qa mc t0m) +)qwdp;lobject as shown in Fig. below. What is the magnitude of the resuqtmadp w+ c.)l;0 m)qpltant force?

  Two forces are acting on an object as shown in Fig. e2:2pyh cy zw--8gr3zvhyua*7snmh5 below. What is the direction5*:hva2ye- hz3rny-szhyu cw 7p 2m8g of the resultant force?

  Vector A is 4.7 cm long and points along the+ ke7nnjqx/0d:iajis9) (7wqeww fu, positive x axis. Vector B is 5.1 cm long and po7n s j,feu j+/9q(niqe d akw)0xwiw:7ints at $+41^{\circ}$ 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 64 cm long and poin:2cee1g((l ilhyuw f2ts at $30^{\circ}$ above the positive x axis. Vector B is 24 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 horizontally 3g tm:xb2//cy gec:gswl64jlwith an initial speed of 19 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time frxm g:3/gtc6 yewcbs ljl4g2/ :om the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 8 m/s,t (o9b,7.1r nt ulpvqo75jc ep from a bridge. It falls 25 m to the water belot15o,tn bp. vq7oel (r9cuj7 pw. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally fro7lq3ggw ,5iq9hw mf)v m a point 29 m above the ground, strikes the ground after traveling horizontally a distance of 16 m. f whi93,mlgw7q5qg)vWith what speed was it thrown?

  A jumper in the long-jump goes into cj rla2y,hd :*;fwhx2the jump with a speed of 12 m/s at an angle o,;yrafch j:l2w *dh2xf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goesy f msa*gla 53hb71j7f into the jump with a speed of 13 m/s at an angle of jfh31y5 gfmaa7sb* l7$22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an igcy n(zi s9/pg-.a 3gqnitial velocity of 43.5 m/s at an angle of $18.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialep4u9g y k6o0-hxd6fq velocity of 55.2 m/s at an angle of $24.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired aaqeui 6+48kl0w2ncq.0 bijw w t 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 horizontally at m/spusnr6os cp1+ b9av5p+ed6/jmk ;23.3 $m/s$ from the roof of a building 65.4 $m$ 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 44.3 m/s atvd pnn. y7sr*tw7o s+;sv*3ux an a7nr*xd*7 wstv n3vy.p +us;osngle of $47.9^{\circ}$ 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/srp z+dl91hb6,ec.gjc;ou h8 f. If you ran the same race on a day when you had a constant headwind which slows your speed by 6,j 91;ecfh.phzgo8c bdl ur +2.0 m/s, the time it would take you to finish would be

  A plane has an air speed kr k,8u2trf. sof 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground t2rk.rs,uk 8fis

  A plane is flying due Solxrmpg)f(d .uxp) l/7 3zbgq:7tlom 9uth ($270^{\circ}$) 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 h u/i7cxgkkko m74 46ppeaded $30.0^{\circ}$ 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 speedie7t35,d/tk vf0 lj rc 50.0 m/s in a forwavi ctj l5,3defr 7kt/0rd 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 isu4td/at a5c vey1x4,xm -f (wv 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is ma a4(,vcuf4vx w/-5xy1te dtthe speed of the boat as it crosses the river?

  The driver of a motorboat that c5qi0v534*xoso nxa tdan move at 15 m/s in still water wishes to travel directox4nx d5t5sq0iv3 * oaly across a river 1.4 km wide in which the current flows at 6.4 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 water wijt-4qo n- 8exo5uuy n-shes to travel directly across a narrow strait in which the oqn 5y4-xu-no-8tej ucurrent 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 wide retu. .oyri5h vlo i;t58aches the opposite bank in 6 min 40 s. She is slr;.y.t5i v8uohi o5 twept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opb47: v7ifqxhiposite bank in 6 min 40 s. She is swept downstream 480 m. What is the :7fqh47i i vxbspeed of the current?

  A boat, whose speed in still water is 1.11 m/s, must aim upstream at an ant yc:z*z9igthx -*)4traby o,gle ofz)gb:cithy9*4a*z, y -xott r $15.3^{\circ}$ (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)  $m/s$