Which one of the following is an 1rfhi;olyw8, p*1-oi ib 3nc nexample of a vector quantity?

  Which of the following operations wywp d--y5 pd*yill not change a vector?

  Which of the following is an acxo: h /bzg0ks5curate statement?

  The resultant of two vectors is the smallest whencl2q 3tm0nby8 the angle between them is

  Two displacement vectors have magnitudes qlak:g uck,:-i b4s:x5 n.jt; cq+t1z n8ut beof 5.0 m and 7.0 m, respectively. When these two vectors are added, the magcul t+ c e1ksbk,uq5t 4;z-ji.t:ba8:ngnx:qnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the fehfnw/mm --gxlw,wa x75r 4 mf,s,q+uollowing is a possiblge75ufx- s /hx,,rqmmwa w nfm-,4wl +e answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in ss58+w-mdmi q directions tha +w- iqs8msmd5t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector islpc8aco0 y9/2h,s e uk* po8sa

  Ignoring air resistance bf7;h+xs*gws, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an ang7fy 9cujss i k31v(mmsz:/i7kle 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 accd)/l,,eqw(hs 3hrs)l7f bjpf - n5wcrelerationf5wsh pb)r /nd hq,lw3-e ,7(fsjl)cr

  A soccer ball is kicked with a velocity of 25/uv61+ p, pmphblrfu 7 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 directed an/dlac2wsz 7pg uuc-2gd86p 1eti-parallel to the velocity vectsg2cc17gpd uu w2z 6/8d-paelor,

  If the acceleration of an object is 8nnzuk) ku+fu k0djn20-u,o0c6 zjk qalways directed perpendicular to its velocity,2zkzj8 + 6n0 j- kcuq u0,ukdukf)no0n

  At what angle should a w.l (*kbjcmig ,z ;kym,,ue+ deater-gun be aimed in order for the water to land with the greatest horizok yg.k,ezi,,ju mb(c+ld m;* ental range?

  An Olympic athlete throws a javelin a bfi8mb u(8d.ht four different angles above the horizontal, each with the same sped m8fub 8hb.i(ed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 +: yo3,q +zyfgk c)yefball leaves your hand with twice the velocity it had on your first throw, its horizontal range Rky+ogqfze: )3,cfy +y (compared to your first serve) would be

  A ball is thrown at an original spee*r 00s dzlvbgy3y zd 9d5/x9ljd 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 its maximum height, how doeb; bk snce,fvi6.57kdfz3z7 js its speed 7;b v3bjzzkdef s.i nf76c5k ,compare to its initial speed?

  A stone is thrown horhd i(uveww7dr.)-lgt a/f3y . izontally 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 ut . -ehw3d vl7/.drgwy(afi)ground below?

  A bullet is fired horizontally, and at the same instant a secoi kds -wn;4n.knd bullet is dropped from the same height. Ignore air resistancek4in dsn-;.kw. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 101.pc.y3/pa oue0ywtm 5n f7et:58 m/s and at an elevation of 293 m drops a package. 2.5 seconds later it drops a second package. How far apart will the two packages land opm/ e0ny3 75at.efuytcpw:5on the ground?

  A package of supplies is dropped from a plane, and one sec krf v8p8mfw: bf/yt;91i1t ziond later a second package is dropped. Neglecting air resistance, the distance between the falling packages wy1/pf8fzi1v ;tt k:wr9 8 imbfill

  A pilot drops a bomb from a plane flying horizontally at a constant speed.kw:o-teoo+ng 1q jp76 vwq z3- Neglecting air resistance, when the:gokqp t3 -oo6+1qnww7-vjze bomb hits the ground the horizontal location of the plane will

  The acceleration of gravit 3, *8ordc y(ywsv /b(-umptt3ikh cj8y 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 E/((t dou* pycjkrwi- 3 chvy ms8t,b83arth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straigcl nvzondb+iot w w+1,-o- )bkbq3w-6ht, level road and pass a+-w,zdoo+b-)k13bno6lww i- n bq tc v car traveling 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 with a strong current)5-2kd .d gf cwwyip1r. You 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 motorbow52-1 drwy )dc g.kpfiat

  Your motorboat can move at 30 km/h in stilif1.jp6 n tjgu:x)t 8vui1nn:9 i)jn rl water. How much time will it take you to move 12 km downstream, in a riv6ign1fin jx1n) :8u: rt )ji .u9jvntper flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thezyepu5l m k4 dkd*j,-8 rwce 8vck.x8, +x axis. The y component of Amjc5x,ce p-k *k evwkyd.z8rud 8l8,4 is

  If a ball is thrown with a velocity of 2tlm : psgi68e35 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 rb:0c6/7fms .gk uhj 9 bfzjv3line in a direction north of east and you end up 2.0 km nort jb3hvjg:f7s0 rzb m9f.ck u/6h and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/v1v4g 7.c+z) msfa8t8 pvi nprs. The x component of its velocity is 8.00 m/s. The angle between t71itsrzv 8 pp fvn8v4m.)gca+he direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level gr wz 7:qq1sdbmj) ;trd.ound. At what angle is the Sun elevated above the horizd7m.dsr b;1:qjt w q)zon?

  Two vectors A and B have components (0, 1) and (-1, 3), respecv ib+sdn q2r,o, q8mv; ha9w0ntively. What are the +; bnonw2r ,vhsi9m0vqaq8,d components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and ( s7/egsmw,d )o-1, 3), respectively. What is magnitude of the sum of these twowes/)7osdm,g vectors?

  Vector A = (1, 3). Vector B :r ewsb7**i6rf8 zp,kut.exh = (3, 0). Vector C = A + B . What is the magnitude of uet, f*eh: r76*b xzrsi.wpk8C ?

  A car travels 20 km West, then 20 km Srmgr nmg988l *outh. What is the magnitude of its displacemernmrm8gg 89*lnt?

  Three vectors, expressed in Cartesian coordinate un7t,uh4fr( ts, 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 Cartesi 3zlvj) *gtx2oan 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 rq6n hp7. 4l( fnhcy;burgn5 :magnitude of vector C = f(g6l unn4;cn.r 7h :yr5bqhpA - B ?

  A runner runs halfway around a circulziz*svkkwh + kc;1,i uo;1 0ctar path of radius 10 m. What is the displacement ofk1 vkszi,zoc ;u;t*+0i khwc 1 the jogger?

  Two forces are acting on an object as shown in Fig. bel*ktksc*:e 1mjow. What is the magnitude of the rest:**msej 1kc kultant force?

  Two forces are acting on an object as shown jno pb8o 6cb;/in Fig. below. What is the direction of the resultant force? jbop oc86/;bn

  Vector A is 5.2 cm long and points along the positive x axis. Vector B is v,zk az jl u7eytpta- u7zgz486h./-r 8.5 cm zp l z7jza4uhyt8.zgr ekv-ta-76/ ,ulong and points at $+47^{\circ}$ 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 70 cm lone.f0s0(isk c bg and points at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 21 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 with an ;sg eu2nq 0v(/n6 u rbjly3zk4initial speed of 15 m/s from the edge of a cliff. A stop watch measures the stone's njkq;gz/b(6y 2rl4 vu s0n3e utrajectory time from the top of the cliff to the bottom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity ofi)r0f2 wuq8e g 13 m/s, from a bridge. It falls 29 m to the water below. How far does the rock travel horizontally befoe2iwug 8 )f0qrre striking the water?

  A ball thrown horizontally from a point 19 m abn 3eh2qgm4m3hcrmg:9( iq wj1ove the ground, strikes the ground after traveling horizontamrh wimq2nhjeg(41 :g3qc 9m3lly a distance of 13 m. With what speed was it thrown?

  A jumper in the long-jump goes into the 6sds gcs0, opho, pcg1 :uq2y8j9bu)v jump with a speed of 12 m/s at an angle ofc1 pgbhsdp j:yc q80,2o ,osu69s gv)u $20^{\circ}$ 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 juov sxdq*i23icy 34m;kmp with a speed of 14 m/s at an angle of ds3ii 2k*3yvmc4; oq x$16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 47.4 m/s at an anglenl:1p.2kb wqe of $40.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 41.*sx 9 *v7ot24si qn0svdvlr7- ei9dsl7 m/s at an angle of $22.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle o6z2ns2jw rbv :f $30^{\circ}$ 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 horizontats d6u)d,(cx e)rg:p cdu3-cuf7kn1glly at 19.0 $m/s$ from the roof of a building 40.1 $m$ 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 63.6 m/s at axn38f dxqk+j 3n a3f d+3kx8jxqnngle of $40.5^{\circ}$ 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 mq bu dx he9ymi,y+p,03/s. If you ran the same race on a day when you had a cy 3 dyqup,h+e ,xim9b0onstant 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 wind of 50.0 m/s to th)/tu1ocz ; ju yp*w/jn;6mjxhe West. The plane's speed relative to the groundx o/)hym j;;c *njp/w61uuzjt is

  A plane is flying dur7e 5 uuie7 e2bu7qm pn1u1r4re 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 heade4 kwiugwxjjs+ (*3e0hy4o 3 mhd $30.0^{\circ}$ 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 i;ym1m9e t):rf b: nizspeed 50.0 m/s in a f)m y;fn:t mr iz9:1ibeorward 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 is 8.0 m/s, is directed a/.j m*)g 0ekzgm*8wbbrnkf7d cross a river with a current of 6.0 m/s. What is the speed of the boat as it crossegw/.z*bk e*nm8b 7d)rm0fgj ks the river?

  The driver of a motorboat that can move at 19 m/ vtv6m s v(rzu 6tghc.viu774.s in still water wishes to travel directly across a river 1.6 km wide in which the current flows at 5.5 m/s. How long will it take to cross theuh6tivvs4rv.g 6(v zmc 7tu7 . river?

  The driver of a motorboat that can move e)n-fo cb4,h/fohhijf cu. fon1u ,.3at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at ,uhoc41f3hiceo nfj ,u o.f)bf/nh .-5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches * njo4 x1ngn2ethe opposite bank in*ejgx 2onn41n 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a 11/y1q w+w b:jmakone river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is thq1e b1:w1jy nk/+owmae speed of the current?

  A boat, whose speed in still water is 1.42 m/s, must aim uphnax l +c*+tl7(qd n+mstream at an angle of nx+ (q+m7 t dl+h*acnl$24.5^{\circ}$ (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)  $m/s$