Which one of the following is an example of a v* rlcuxw4x2) r.dt 2l45wclw bfv0ih-ector quantity?

  Which of the following operations will not cl.x2ak nes-kk) - s *hkld6bi3hange a vector?

  Which of the following is an accur+mvnj (lca) -fdlt lx)-zn,w /ate statement?

  The resultant of two v/m03vjdu3 zcq ectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, rehuu u+c4mf.w (t 8t;xdspectively. When t wfu( t+d;u4tx8.uhc mhese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which onec mo boftzn4;jnq01u+umx c3 ;y.rd.2 of the following is a possible answer for the magnid.mqfmxjoz 0nt32b cu + 1uor 4y.;;cntude of the resultant?

  Three forces, each having a magnitude of 33zump8zy3ubmb i*x . ,0 N, pull on an object in directions thzyz8piuuxbmb*3., 3m at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoc i a5kk8 ,pynq b3wmdz+s6qm*s0 2vi6wn vector is

  Ignoring air resistance, the horizontal component of j+lmv30jv mzbd g,vl.;o +m2m a projectile's velocity

  A ball is thrown with a veloci3p sc 7 xahekog2tc*041fxu t5ty 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 horizontal component of a projectile's accelc1 ;fon- d y6ijpern5*eration5 yj1c* rn oid-6;penf

  A soccer ball is kicked wit+g8vxrm/*lwd fw8h 9ptubta2q) 54;zluvui 9h 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 directey7zg m7,pw/o;2xsm nvd anti-parallel to the velocity y;vgwmpm /7snx2o,7 zvector,

  If the acceleration of an object is always directed perpendicular to its9a 9tu9euxhg u:1mqe3xjfi 2 h09u vn/ velocity,192/ 09taeqh:j9uhu9 ufgiuv mxexn 3

  At what angle should a water-gun -to;n.fb r5v6v zycb* be aimed in order for the water to land with the greatest hortzcn *6v-y obfv5r.b; izontal range?

  An Olympic athlete throws a javelin at four different xkc)kbruy)*pdi) h,- angles above the horizontal, each with the same speedx)* ,khkyc))b uip -dr: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for tl:r+awfe8 .6gy8 hx xdl+u*o9/sugn che second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (fsou.r98cg++y:xahudl/*wnxg l 8e6compared to your first serve) would be

  A ball is thrown at an original sp xu:9iqsj. j ebhfk;e;ms ,0-seed 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 maximqv+k ai44d ;/o7lm/ is4klvtjzf e)t2um height, how does its speed compar;4st7m otez+d2) ljlkii qvk/fa44v/ e to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a bswd(/r u4zy an1bi6l /all is dropped vertically. Which object is trsw ri 6/zba1u(n4l dy/aveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instantxpx4v iw8d; 7 .t upwh1cynif-:+b 1tphquv( 1 a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of tw8 wp;xqi :h hp1bx 4uc(dt1uv.p -nfv71iy t+he two bullets.

  A plane flying horizontally at a speed of 108.2w h.q8 *cdu9pb m/s and at an elevation of 131 m drops a package. 3.0 seconds later it drops a second package. How far apart w.* cupd8hqb9will the two packages land on the ground?

  A package of supplies is dropped from a planea y5 ccd wb,v1f 81z2il/lzz4v, and one second later a second package is dropped. Neglecting air resistance, the distance between the /5wz14vvzlzdb1c8,aiy l 2 fc falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Nbh:71rh ) asz,.v 1zmtgs/yvxeglecting air resistance, when the bomb hits the ground the h1x zhrs: 7zavm)g vh,tb.ys1/orizontal location of the plane will

  The acceleration of gravil ty(a+q+lojqrsr6/ /ty on the Moon is only one-sixth of that on Earth. If you hit a basebaqqjryl(s+ o6a l r//t+ll on the Moon 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, level road a,t g(/ c2g;w.feu0e ftce jju4nd pass a car traveling4,e /2 0t tcf(ceef. g;ujwugj 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 stro :fl8r5yz0xbpng current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your0xb:58yr plz f starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How x bte)++:cvwmhm4ls : much time will it take you to wx+ 4m)s:vt +c l:bemhmove 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 zrrpndf(i 9* a)hlu ,h3zmgrtk)( +c- m at an angle of 30 degrees below the +x axis. The y hd)zz9 (lr+ hu (*imrgk)3 ,c prt-afncomponent of A is

  If a ball is thrown with a veloci6 y,0hcmc 6rgg s5cmi,ty of 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 dirbhrg1no n pp8v217 i7mection north of east and you end up 2.0og8hv12n7b1pp rmi7 n km 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 component of its veo s)mt(sl:lap y 7-,sllocity is 8.00 m/s. The angle between the direction of its motion tl) (ap mosss:-,y ll7and the x axis must be

  A 400-m tall tower caszeyu yh fnqb9c01 9 /n.6vusr+rut2s6ts a 600-m long shadow over a level ground. At what angle is the Sucze f92y96uu +s ry.n0 rhu/qb tvn16sn elevated above the horizon?

  Two vectors A and B h )gg0 72d0ycslk4ycgmave components (0, 1) and (-1, 3), respectively. What are )c04g 7c0m dlkgyg sy2the components of the sum of these two vectors?

  Two vectors A and B hbmyc*uj1me/- 3zq 3of ave components (0, 1) and (-1, 3), respectively. What is magnitude of the sum3qu/1 czmjef3*bo y-m of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitdit(643gjlt-xl cmv p;d72 dwudex 3 7(itplg6 m42lvtd-ddc w;j of C ?

  A car travels 20 km West, then 20 km South. What is thmci67mx m/z hnde38/ de magnitude of its displacememmdc6/7h x3ize/8dnmnt?

  Three vectors, expressed inmbyxxwzb4 ki dew+ -f*r3 .q/5 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, expres cnh4oj 0,,fbcw/gwg5sed 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 = (+3.07 ; 7gw:znvs(i8 s- 9d c8iclapnbykp1, -8.0), what is the magnitude of vector C =gpk-(b8vi9czadcwlyin n 8;1 ps:s7 7 A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the diz5i3zvftnfmq 60)h-uspla v0f zuzhnq) m-5t6fi3cement of the jogger?

  Two forces are acting on an object54lvnir c d9ukn ;bn1- as shown in Fig. below. What is the magnitude of the resultadknv;-c 41 blr5i9nunnt force?

  Two forces are acting on an object as shown in Fig. below. What is y0/0d7g3j1 dlzlz2 oix/ vzupthe direction of the7xzzizdlu/y0pg 0v /2 o31jl d resultant force?

  Vector A is 3.3 cm long and points along the positive x axis. Vector B is 8.5 -24afqjkt;ml( mno9 pt vilb/*3ha - jcm long and po fl3jlm hq-pn-(2amj* ;t9/tbvik o4 aints at $+23^{\circ}$ 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 81 cm long andmo06d52c0ikl d tewb ( 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 35 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 initial speed of 24 m/s from tn d,y+:k4 dncyhe edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the4ckdnn+y d: ,y bottom to be 3.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 8 m/s, frl0fh+tc7i*k j s:rz urg l z.7(w4r4suom a bridge. It falls 26 m to the water below. Ho(* hjr+ls4 i 4f ckrusztuz gwr:0.77lw far does the rock travel horizontally before striking the water?

  A ball thrown horizontallbi ()xur6 v1zo,j0cgvy from a point 20 m above the ground, strikes the ground after traveling horizontally a distance of 14 m. With j, uxv)(obgr1z6vic0what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed oupr13/ rgk+ls f 12 m/s at an angle oulrsg3 rk/+1 pf $20^{\circ}$ 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 wtt :6vvj 3h7mpith a speed of 10 m/s at an angle mj : v63thptv7of $30^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initou2)kj 8xhza/*wy tj.ial velocity of 21.5 m/s at an angle of $15.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial ao/c(*hav,gn l*a; kivelocity of 43.3 m/s at an angle of $23.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angvuwqvk- n;3+apf4 z9 d 6.:kktid+/s ixx+pgo le 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 ho 7u9 ;nnapy+.yex2pz3p zj6o brizontally at 22.8 $m/s$ from the roof of a building 35.5 $m$ 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 l((pgj6jtq3b k evel with an initial speed of 60.2 m/s at an angle ofpt(q (kbgj3j 6 $40.9^{\circ}$ 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 ve klsen;(f-h3clocity of 4.0 m/s. If you ran the same race on a day when you had a constant3l;fsceh-n( k 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 dr,liu3 1yb j(jue North, and is in a wind of 50.0 m/s to the West. The plane's spy(i3 jul jr1,beed relative to the ground is

  A plane is flying due So d9(/3pbtklgeuth ($270^{\circ}$) 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 1we*fz6k9ve baahbz5jqf;r 0 * ,4ioir7dc9 5s20 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 projectile withh;1 8hah-u6 l2kiozvd speed 50.0 m/s in a fo u2zh6i ;k-h81hv odalrward 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 wa-j jt4;v 7smowter is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crossso- jjm7t4vw ;es the river?

  The driver of a motorboat that can move at 20 m/s in stil)dqtgx (*kcf d:k3 kse+6e1 wll water wishes to travel directly across a rive+ 1q: k(wlcgdkfd3)e sketx6*r 0.7 km wide in which the current flows at 4.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 ez qvw 29+ggp7u6 r7 ker vh+6uu3yt0om/s in still water wishes to travel directly across a narrow strait in which the current flows 7rq7 h2y pr90ueuvk6tzgg+w3eo6u+ v at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 2 )8svr fsdah;t)ghs)/ 00 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast sasr8d)tv h )sf;gh /)can she swim in still water?

  A swimmer heading directly across a river 200 4.sa wt0:oeet m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480ate tw04.e o:s m. What is the speed of the current?

  A boat, whose speed in still water is 1.47 m/s, must aim up c(q:fbcyu: -/xwqke3stream at an angle ofcwu:kqyb:xq3 /f(e- c $16.3^{\circ}$ (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)  $m/s$