Which one of the following is an example of a vn ,j ej)gk.ev;ector quantity?

  Which of the following oppp(ucj: p w;xhjhly4r9:cf 40erations will not change a vector?

  Which of the following is an accurat2lb dkndlt3 rh+kr568e statement?

  The resultant of two vectors is the smallest when the angle bpw b( uto*zv(c- e- in*xquga.sk: 1(jetween them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivelyp,/fcd guv 76m. When these two vectors are addm67upf ,v/ cdged, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are aduopcjmb(2 e 31ded. Which one of the following is a po1 p3eocujb 2m(ssible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an objp u.c1nr-5b cdect in directions that a1 pud.5 cbrc-nre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,ip3:u(kvbzve8pw4s r8.9 p ll the unknown vector is

  Ignoring air resistance, the horizontal compon3wk4 otxi4zs (o+im0ny dtl 23zr(b,e-9dyaj ent of a projectile's velocity

  A ball is thrown withpw6 x5q7gv6mv a velocity of 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, the hor +t4 jqh/w9oubizontal component of a projectile's accelerationw9 +hbo/jq ut4

  A soccer ball is kicked with a velocity of 2dq4s. . zrltn6)b3p vz5 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 vej7q h ag:0:sws059scbc r 6t( -ed;rlwuxl6mictor of an object is directed anti-parallel to the velocity vecto0s es sbm96lqh;:6cx t5l-uc d(jrw r0ag7iw:r,

  If the acceleration of an object is always directed perpen tmc* o+jx3x6rs:cypyagv ;3*dicular to its velocityj vcgxyc 3m p*x*s6atoy+:; 3r,

  At what angle should a water-gun be aimed in order for the water to land nc e; .fir/ppu9duc1ygih.bvb 78/o 5 with the greatb.ue9nricv/ bpcpif;/u od18y g7h.5 est horizontal range?

  An Olympic athlete throws a javelin at four different angles above tj81h0 hv.q6 l:om dbaet/7ada he horizontal, eacho80 d:m. h6q/v1a j bahdet7al 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. If the ball le 3bk:ww yz em5i:sr2itf.,um :aves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first sezbksf:mu2:.3 e w: wir my5,tirve) would be

  A ball is thrown at an original speed of 1h2 sbj3radb 7j t,y2c8.0 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 its maximum height, how 3ga c/fx v.8eddoes its speed compare 3c8age/ .xvf dto its initial speed?

  A stone is thrown horizon8f jf9y0ekrz1q dgx40 tally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level gy1z0 gjqfk0xdre 948f round below?

  A bullet is fired ho()fqw6l.sx0r pjx vl)z2( uetpehb1, rizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fal 0vluw61szeep,xhb(2rxj.( tqp )lf )l of the two bullets.

  A plane flying horizont86ys tg3tx;l rcr /zv jbnrul+64m+x5ally at a speed of 48.6 m/s and at an elevation of 175 m drops a package. 7.2 seconds later it drops a second package. How far apart will the two pargc45ntv;ty jxrx86 6 br /z+l ls3mu+ckages land on the ground?

  A package of supplies is dropped from a plane, and one second lateu-)oh fz9jwav/pm th3ni,6 x)r a second package is dropped. -9pov/hnw)t 6 mjha i3,zuf x) Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontall)dt5v mfewq0 p jnk;)*y at a constant speed. Neglecting air resistvw)e;tk d )p *0mn5qjfance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixths),f yalqhp3( mhrw(- of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed3wa y- lf(h)r(,smq hp and angle) 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 ro s5j1x+e+;gf0 wqy0cn 7w le grvie*h2ad ands gyr*q+lix2h g7v;0e+1fn ew jc0 e5w 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 ri3)x7zfllj lg+sa1 -h u5gq5bqver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shoulf x55 ulaz7jb3gg hlqls+-1)qd head your motorboat

  Your motorboat can move at 30 km/h in still water. n 9vym, jcp8ffv-( eqrl(*d (u How much time will it take you to moveu9p v c-*n,((v fqyj defr(l8m 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 below(vrjl044 8ze wmdlq-d the +x axis. The y component dev(4l-m4r8 l0zdjwq of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of 0v3z 0e6q ;z3hidu o lhzdb+3r$37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight lw7n 8 byp0zp.iine 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 walked0zy7pn8bwi. p ?

  A butterfly moves with a speed of 12.0 m/s. The x comp2 -zm:wdo hh8monent of its velocity is 8.00 m/s. hm od -w:zh8m2 The angle between the direction of its motion and the x axis must be

  A 400-m tall tower c6 b58 g9 orx3t;v4xffmdc4 fyeasts a 600-m long shadow over a level ground. At what angle is the Sun elevated above the ho3mvfd84xf y x5 fg9c;6t 4reborizon?

  Two vectors A and B have compkfs,88v t-llpn ;;gmjonents (0, 1) and (-1, 3), respectively. What are the components of the sum of thms8tj-ll p8vg fk;;,nese two vectors?

  Two vectors A and B have compi0b tor9*kh5u-mzud h* le z*)onents (0, 1) and (-1, 3), respectively. What is magnitude of the sum o9r*e) h id t-50o* lzuubkhm*zf these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Wlv c.* znt*k,w8 za+vthat is the magnitude ozzwatnv8*k lt,*.v +cf C ?

  A car travels 20 km Wes /uhvuq x(p0x9n57ii1vkh0 kr+ogf2x t, then 20 km South. What is the magnitude of its displaceme+iuuinqp57( gh/1hxx2f xk9 0o0 vvrknt?

  Three vectors, expressed6opo;.l zlszl0d:u*uc fi obh/b2 7y9 in Cartesian coordinates, 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 coorphwev*, .,:yf 9p/6r8bk(cjobmex s c dinates, 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, -8.01ccp*fqjxjz1lr9lw 78s tr)h 9h72ly ), what is the magnitude of vector C = A - B7ph1l fl9c zstx7 j21y8)j 9wr rh*lcq ?

  A runner runs halfway around a circular path of radius 10 m. What isb hfh:jj*6q6j the displacement of the jog6q*j:bj hfh j6ger?

  Two forces are acting on an object as shown in Fig. below. What is the maga/t f75a(dv jxnitude of the fvd7 a(ajt5x/resultant force?

  Two forces are acting on an0,2w:rt ,ysnvcy .bic object as shown in Fig. below. What is the direction of the resultant forcevyrb tcwy c20i ,,:n.s?

  Vector A is 3.1 cm long and points along the positive x axis. x.0edq.bzusw.h: d: w Vector B is 9.8 cm long and hwu db: w0:.s .ezxd.qpoints at $+29^{\circ}$ 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 68 cm lo v:alx8blkfw.7 7n:tjng and points at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 24 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 widx*+c srtw ;8tz 1z(iwth an initial speed of 13 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 thtwt 1;izr(z s cd*+8wxe cliff?

  A girl throws a rock horizontally, with a velocity of 6 m6vpj ukl jzh4 i-y7t+2/s, from a bridge. It falls 24 m to the water below. How far-kyhji +lpvt7j6z 24 u does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 msp85 yw)ft21 pj6dv; hn / pmsxs;aj7e above the ground, strikes the ground after traveling horizontally a distance of 19 m. With what s/n;m7s6 p5ed1)s2;pavy jf 8 txwhj pspeed was it thrown?

  A jumper in the long-jump goes into mk9n+t +t )r6s bhdsj*plc.s9the jump with a speed of 12 m/s at an angle of hm9tj.6kpc s+tlr*+n )s9dsb $20^{\circ}$ 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 j 6bhd+ 7ybfzh55zisg -ump with a speed of 13 m/s at an angle of hdz+h56g-fzyb i 5s7b$37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocityi1t3spt- tc x4ww0nc2 of 51.7 m/s at an angle of $24.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velj/m1 jc tka5sqq)4. h ad;,jcbocity of 59.5 m/s at an angle of $19.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an agt ,n (e8hvzc2ngle 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 19.64ett8v nvw 24or+ch/,l5zumi x+g7 r a $m/s$ from the roof of a building 34.6 $m$ 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 groun9cet*y afdxp (-8qj* od level with an initial speed of 54.9 m/s at an ang* -d(o x8 a*9petfjcyqle of $46.9^{\circ}$ 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 runomp;:- p99k ju a5swq4sus )fr a 1500-m race 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 it woo u w ;f)59a us4-msp:srjpk9quld take you to finish would be

  A plane has an air speed of 200 m/se8p q)s.xyqyzj:4*bl due North, and is in a wind of 50.0 m/s to the West. The plane'sy4*p:)8ejl b .qyx zsq speed relative to the ground is

  A plane is flying due South /,,gnb9wary3orm5 dlj r09bd ($270^{\circ}$) 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 spee2nwyh nxp en )e dokoz.+ 5.qj1l ((djz/8+mxdd 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 lx/ c76 kq7jl0skyli7a projectile with speed 50.0 m/s in a forward directlq0l ji y7ksc76 lxk/7ion $30.0^{\circ}$ 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 acrosjrxqsn im l 9kd23xo)ic17;p7 0j4tlms a river with a current of 6.0 m/s. What is the speed of the boat as it crosses r0mn4xtp7qio;ll jm)19i7cskdj32 xthe river?

  The driver of a motorbolkaq4-e3:zp*xu st6 f w,w5bzat that can move at 13 m/s in still water wishes to travel directly across a river 1.1 km wide in which the current flows at 3.4 m/s. Howq:34ku ,pls zzwfw tb6ae 5*-x long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to t9il iyejk -gl4-)ohs6ravel directly across a narrow strait in which the current flows at 5.0 m/s. At what anglh io igk)jy69e-l-l4se upstream should the driver head the boat?

  A swimmer heading directx6k l(y6ih4)n g q2 mo8lr.hably across a river 200 m wide reaches the opposite bank in 6 min 40 s. She im6rl4 g q)8h(kxnl2i 6ya.ohbs swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading dirknrt 3a*c:r ,sectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is snc: 3kta ,sr*rwept downstream 480 m. What is the speed of the current?

  A boat, whose speed in sti r1p 5lum - 9frznf18gkw490fapjn9n all water is 1.73 m/s, must aim upstream at an angle of n5n l4-r rw fp8g aum0n fak9991fpzj1$27.5^{\circ}$ (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)  $m/s$