Which one of the following i6lsor psv,gd7 m84q(g n(3.x :dqkmw gs an example of a vector quantity?

  Which of the following operations will not chang;+c ksad1tmt;d:6ji m9 nhxe, e a vector?

  Which of the following is an accurafa (1g df7u(obte statement?

  The resultant of two vectors is the smallest when thvlk-g7kb: * x,,iz3ji qmb3 exe angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, rr,q zhaun2gg 7-. 0j8 oxhnga+espectively. When these two vectors are added, the- + gq jaonu8rg hhzn,g7a2x.0 magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which*h +/u3o1v zf tejkr4u one of the following is a possiblevutk3 fr o*41z j+eh/u answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directionsqmws641mox,:fux ow3 that qm63mx:os f41,w xowu are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vect zch:96ld(gwkm+oqu 8or is

  Ignoring air resistance, the horizontal component of a projectile's veloci fe)4bsw275rshzuk m6c g.w3vty

  A ball is thrown with a velocity opr) bi ok) 9ter09b ngb2-1oxzf 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 horizoiiqn1a2t r +0vu pi)4dntal component of a projectile's acceleration 1dpi0a4 +t i)rn2iqvu

  A soccer ball is kicked with a velocity of 25 m/s at a0xyl ,g -jg)3 jpafu0cn 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 d,.r/bymvo c(uwui+7b irected anti-parallel to the velocity ve7 b mr/u ,v.y(+owbcuictor,

  If the acceleration of an object is always directed pex qbuj510f4hxrpendicular to its velocity4xj1 x0h5bq uf,

  At what angle should a watrecu ercl6 e0i15hz g,3o/ua2er-gun be aimed in order for the water to land with the greatest horizi /1cu2,c gar3560hre oele zuontal range?

  An Olympic athlete throws a javelin at four different angles abov1k8i i 8v1ec;msc5i oje the horizontal, each with thck;o veii1jm1i88 sc5e 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 leaves your hand with .zbu;cng, f1y esm:*atwice the velocity it had on your first throw, its horizontal range R (compared to your firs .bcufa1z,*m:s e;yng t serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle ofv4ju x8p kr:(m $35^{\circ}$ 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 ma c3mlobg4: h:nce+ xv4mhv x0;ximum height, how does itsmo: mhv4; +venlxxbhc 4 g0:3c speed compare to its initial speed?

  A stone is thrown horizontally from thnp xnkg lg)2, q5xy77xe top of a tower at the same instant a ball is dropped vertically. Which object is ggp xx xnynq )257,7lktraveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant akc a 7jv.4gtaw 7/o7ye second bullet is dropped from the same height. Ignoreyk7.co /g 4v77 aewtja air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 107.5 m/fmax 5k9zm5l/s and at an elevation of 232 m drops a package. 4.7 seconds later it drops a second package. How far apart will the two pax z k/lf95m5amckages land on the ground?

  A package of supplies is dropped from a plane, and one second bjzbag (6f r fqx.7t9 :h:afio c55cu0later a second package is dropped. Neglecting air resistance, the distance 5 ( xjuhg aat:b:.cqo05fz rc 7f9bi6fbetween the falling packages will

  A pilot drops a bomb from a plane flying hol .0uflj/hm uw..5obfv5 9opnrizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal l.9 lobh ojn0p/u5 wmv..5flf uocation of the plane will

  The acceleration of gravity on thq.exoqz0.f;rqu:i y. i f7+f ee Moon is only one-sixth of that on Earth. If you hit a baseball on the M0. ryfeq+f; .fxioe.:qi z 7uqoon with the same effort (and at the speed 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, leve1o l3gckgh(,gdsv /x:bk o3 7el road and pass a car traveling at 45 mio:vkeghb 1/73 do3(gcl ,xskg /h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due sou,wlbim9e nu5wtdc0t )xx87q4xnx b )4th with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank direqxe4mxx 4bxci bl9w7t,n5nd)0)8u twctly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stsw p(4sf (g-ynill water. How much time will it take you to move 12 km downstream, in a ri4gnwp (f-ss( yver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 de3 m )7dpu kako. fxdjy7zm4g8/grees below the +x axis. The y componentx. 7)kj akm godmu834y7zd/pf of A is

  If a ball is thrown with a velocity q0obhd/*x d;aof 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 noaul6:uis0z j. .*tcttrth of east and you end up 2.0 km north and several kilometers east. How jtu *tziac.s0ltu. :6many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x cob of y4+m6w xt) xvh8g4sy(mx6mponent of its velocity is 8.00 m/s. The angle between the direhxt)6m 8ygy4owb ( fxx+v 64msction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what df 1d ;2umadzdrw46:dangle is the Sun elevated abo62dddz4rwa:;mdf u1d ve the horizon?

  Two vectors A and B have components (0, 1) and (-1, fk3or3pb e14 b3), respectively. What are the componenf1rpk 3b43b oets of the sum of these two vectors?

  Two vectors A and B have components (0, 109oyfk1 lgm3g) and (-1, 3), respectively. What is magg 019mlgkyf3 onitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magn/ vkl+h4ro;iq itude of C4krol/ q;+h vi ?

  A car travels 20 km West, then 20 km South. What is twttty2h8 xj y-8cv* 2hw1gc,p*vt xi4 he magnitude of its displacemet y-yitcp8,g*tt 4h2xcwh* 1xv28vwjnt?

  Three vectors, express*n omu: r299qj/a h y(yxf//lpxrq+p wed 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, expreqt49 ty+cgs8 cssed 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 = (+3.0, -8.0), what is 5zlv/yjs):hb vr q; 3mmsp;6kthe magnitude of vectobs)s: vmjq6z3lm5yh k; vr ;/pr C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is t rog;2g6 .to+u czzs1qhe displacemen2.zz tgs 6u 1c+rq;ogot of the jogger?

  Two forces are acting on an object as shown in Fig. hty q hx (-j6*hiazb/zf.7x 3vbelow. What is the magnitude of the resultant forcez/h*z-(vxtbi xfjhh7 3.aqy 6?

  Two forces are acting on an object as shown in Fig. below. What is thx, u4kn t44 tz1uz3rbce directiout crt 3k144unz,4bxzn of the resultant force?

  Vector A is 5.8 cm long and points alonu:0 o,ei)7p a*ovj zewg the positive x axis. Vector B is 8.9 cm l ao:*eiopuv jz 7,0w)eong and points at $+27^{\circ}$ 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 73 cm long and x eaem6 u9mo2:jo h9q:points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 42 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 how . z3m/hpjit7j 8rv4erizontally with an initial speed of 11 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time pj7 h3mrvz. 4wi/ ej8tfrom the top of the cliff to the bottom to be 4.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 16 m/s, frogn 2snjf vs.*cn(2ad)++ w0j:mb kulim a bridge. It falls 11 m to the water below.2mswn(dkn+.+ vf2i :)l0b cgjau*jsn How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 26 m abobnl btdpvc,cselfd5-r1 p.0py3z/ 10 ve the ground, strikes the ground after travepbncv rcd 5-,b1sl30 l tpzdp0e 1yf./ling horizontally a distance of 14 m. With what speed was it thrown?

  A jumper in the long-jum0 6db6:syct a:-x4crr3yhlct p goes into the jump with a speed of 12 m/s at an angle 6ysr:6tc c3xa-b tyc40 lr hd:of $20^{\circ}$ 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 12 m/s at an anglsk68p,8pm gzve pz ,8m86 kgvpsof $18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launc 4bl1 hjm-to;fi vi-(shed with an initial velocity of 20.1 m/s at an angle of $15.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocitygu.lkw b 4o6/xti92 ga of 52.7 m/s at an angle of $13.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired x0wm01ih1ane mnn7v xy :u7-yat 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 horizontall7o:tm my4u/:eae 02tuv xk-yby at 25.9 $m/s$ from the roof of a building 62.7 $m$ 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 speed of 50.9 m/s at an yuh mb zl. bf/n4z-+m4w lph-*ang4y .-lf*np ubmhlb+w4 zmz h/-le of $40.2^{\circ}$ 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 ra5 ;d*2eyaaz9jteseue+/ av3 nce at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constantadsj5eu /e;+e enta v2zy9a3* headwind which slows 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 windkp0jsxg4 eo)ro e /9a* of 50.0 m/s to the West. The plane's speed r)gr jse4ooe*k/ ap0x9elative to the ground is

  A plane is flying due2b5h/(i xlmbnk -bifng 74 9nt 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 120 km/h is headedfl/,w2za mwi5 $30.0^{\circ}$ 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 horizotmjiij:/ ;3en ntally fires a projectile with speed 50.0 m/s in a forward directii; n/im jjet3:on $30.0^{\circ}$ 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. x/vv)xt.+j ix0 m/s, is directed across a river with a current of 6.0 m/s.+ vx.x)/ ixvtj What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 9 m/s in still water wishe7t.r)e;hslnv wf, 42 e biqdo(s to travel l7esvnwd ir4,q ;.f )bh2e(ot directly across a river 1.6 km wide in which the current flows at 4.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s:*:qub enib 38lfj+ :co ey1- dyju9j 55svafl in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver he:ebqfi:1o b5l8 sa vny*+cjy5 -j:j fu 3dul9ead the boat?

  A swimmer heading di ;nqs w3u,n6d65fdd he-nai8orectly across a river 200 m wide reaches the opposite bank in 6 miq5hus8d;6n 6wa3d-o,i nedfn n 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide*,bnu:l/nio v reaches the opposite bank in 6 min 40 s. She is swepl nnio*v /u:b,t downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.79 m/s, must aim upstream at an angle ozsdn fgw(74xza b,*h8 f g ,ax (8 dz*7fwhnsz4b$12.9^{\circ}$ (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)  $m/s$