Which one of the following is an example of a/ mw5 *ka j0xl3d:vqfc vector quantity?

  Which of the following operations will not change a vectorp 7 lwu.z61rea?

  Which of the following is an accurate shg:yjj/ xbn2; i* vnttbf16bol8)n : mvi c(y/tatement?

  The resultant of two vecto mc .q2+sp4;,plnpxzky2;ab /z9 enhlrs is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respective8wkya9hw tf pg2pt93u 5d9d 8mfrkj7(ly. When these two vectors are added, the magnitude of the s jpd8dm75ph23 ykgu9 t9(ff tkw8r9awum

  Two vectors, of magnitudes 20 r; + app7 o.xtwl4h osmpg4i 1,30hjrdand 50, are added. Which one of the following is a possible answer for the ; x43hp, .d4mso1optg wa lrj0 7+prihmagnitude of the resultant?

  Three forces, each havi7.c+qy y pq/. jekbdq5ng a magnitude of 30 N, pull on an object in directions thajpcy.7qbk5yeq .q +d/t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec:5(h1()dw 6j fznc is5ijp m; o+wktsrtor is

  Ignoring air resistance, the ho*s.er t;uu ucva,an6w rk, 71os9db5b ik2og )rizontal component of a projectile's velocity

  A ball is thrown with a velocity of/owvg;y9d3j ezj )vewwt k8/+sl4 1vf 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 j3bdno 60n0h mix- .li)3f uyoprojectile's accelerationh.n3od j- xbio fm0y 6nl3)i0u

  A soccer ball is kicked with a velo6gid3z 4f8m g qki-l)fvh rh*:city 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 directed anti-parallel to the e3 zz)zrfv y1)7ez-,9b kaa4sxsl7z hvelocity vectorz77ayb4 -rh xkz s1 esazzl9,fve)3z),

  If the acceleration of an object is always directed pe1ayk0m,*odn t+mx g ,arpendicular to its velocity,a,n0 m d,tym*a+k1 xog

  At what angle should a water-gun be y; jrxe 9w/ro(aimed in order for the water to land with the greatestroryx e;9w(j/ horizontal range?

  An Olympic athlete throws a javelin at four different anglesyyd )ji 8a)c t,acg18rp3u0ab above the horizontal, each with the same speedy8g tauy1r0,pd3ca) c )jb 8ai: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the second time. bam/hxem*:x)-dkz ccbqx484b 0qn r 7 If the ball leaves your hand with takxemx r0b-8:hbqm74 dqz4b *cc)nx/wice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at l1:kcutwu s bm3+g0g:0e+e t wan original speed 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 fielfldyhmr ,9e2 h1m: l l95yd)xpd goal attempt reaches its maximum height, how does its speed compare to its initial spledy5fhdlm 1:99y2h xp ml r,)eed?

  A stone is thrown horizontally fro u:*v 2nqgpkjd;m+:e7ww )e pdm the top of a tower at the same instant a ball is dropped vedwn) e27ug+ wvm;*qjd :kpp :ertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet ish zm9z21ez)hjjc/f :j dropped from the same jcz 1j:j)9h2 ez/zhfmheight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 96.2 mf n0mz du )tt)en2ot26gqx9g;/s and at an elevation of 130 m dr ;mz xut 0d9of)2 nn6ttgge2q)ops a package. 4.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is droppepa ;kme7jbv,+ d from a plane, and one second later a second package is dropped. Nae kbj;p,v7 +meglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a pl*drfenrp k: 59ane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal :rn59k*erf dplocation of the plane will

  The acceleration of gravity on the Mkkuwd7,5 q7ul z6+pfc oon is only one-sixth of that on Earth. If you hit a baseball o7k czu ,+f 7kqd5wl6pun 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 roadxjpuu 04 9ds-uen;zm 1 and pas mu- 1jes0 x;pnz4uu9ds a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a riverhfh((2b jp o pjl.5l4r 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 stah.5(h o jpprb f(4llj2rting point. You should head your motorboat

  Your motorboat can move at 7*bu n9c npxtik ,ziy*j zo)1:30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing )i*zu1ixcyz79 p,j*nb ko : tnat 6.0 km/h?

  Vector A has magnitudi d 6f(agee-;l2ovs)ekyna6/e 8.0 m at an angle of 30 degrees below the +x axis. The y component of A g-)niksa6;oe( 2vl6 fdea/ ey is

  If a ball is thrown with a velocity of 25 m/s at an angwlp*r3: a2 pf6 r;khc;gr /rxa5ab ;sfle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight lcqlcf.e w,e1k/um c :q* .uqz(ine in a direction north of east and you end up 2.0 km north and se/ q* f:k.,uq( 1ce cucmq.lzewveral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The de51o)ep3ggt x component of its velocity is 8.00 m/s. The angle between the dir)gpeoe3 t5g 1dection of its motion and the x axis must be

  A 400-m tall tower casts a eov b/nw: o0)x600-m long shadow over a level ground. At what angle is the Sun elevated above the howbo v0/n):xo erizon?

  Two vectors A and B have components (0, 1) and (-1, 3), rv x:vy:d )tm4x3htj (yespectively. What are the components of the:dx( 4hvt )vyjxy tm:3 sum of these two vectors?

  Two vectors A and B have compon:t, +y5lzwae bents (0, 1) and (-1, 3), respectively. What is magnitudetz by5+,al we: of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0).1a: y5o46h;5p eue ycwje;jjq Vector C = A + B . What is the magnitude ofwc;e4q5pyjh eu5:;aj6o 1y ej C ?

  A car travels 20 km West, then 20 km South. What g 8h/7pvy(dnyq)vo2 ais the magnitude of its displace apyy78(vn/2q hvdog )ment?

  Three vectors, expressed in Cartesian coordinat hiv)qs) (sno4es, 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 Cartesiah+yymjr)9lx/aaxy6 + b s1wq *n 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 t3m5bzhlr(f j9he magnitude of vector C = A -blzj rm593(fh B ?

  A runner runs halfway around a circular path of radius 10 m. What is the db5+o9y)d *td sp tje(xisplacyj x)ts pb9dde+5o *(tement of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitud) wbtd74;hborzb/ +4u kvr m4se of theu)hwmkd47b/rs; r4 +b4tbv oz resultant force?

  Two forces are actin4cu2 v3zkrry -,8zan ut9d ,ixy- rc*kg on an object as shown in Fig. below. What is the direction of the resultant kazc cd, tk,u-ryn23-x4rzrv*uyi 9 8force?

  Vector A is 3.7 cm long and points along the positive x axis. Vector B is 10.0 cnoan:v7y.k +cakyn:7+n.oc v m long and points at $+28^{\circ}$ 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 53 cm long -(z/voqud p7dyxsay9;db /d) and points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 39 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 sle,3(587a euol, n f;oxd tafqpeed of 10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from u5e 378a;lqf, otex( adol,f nthe top of the cliff to the bottom to be 4.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a brid, ybqf 89tnd2t56tfoe0;hv f xge. It falls 14 m to the water below. How far does the f6fox50;q92b8ytt ,defnth vrock travel horizontally before striking the water?

  A ball thrown horizontall3; o4( sfevt-egnl pk+y from a point 28 m above the ground, strikes the ground after travelinv3 pgs+ kle;onf -4(etg horizontally a distance of 24 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed o8.o+n,oix5 +gf jh83 rlsxhtt f 12 m/s at an angle ogi nh.l38,5oh++r8 x sxjtft 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 spe)fhv.0m;xsvh p bg+s7ed of 14 m/s at an angle mxv.ss0)7 b hf;vph+gof $30^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched fb,orknrl r) d)+s/ oi/rhg;1/ziee- with an initial velocity of 52.4 m/s at an angle of $27.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 54.9 m/s at an xk4m3q ; +w xhmr*r.npangle of $35.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angler. b)fuxqc,0ro . *5lk,zit tqy9d(hu 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 kjwk5).a 3bf 2z3pg4uk dsw-vu i2kk +at 24.3 $m/s$ from the roof of a building 61.3 $m$ 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 45.8 m/ b7wln/n* ncv8s at an acn8nvl /nb7*wngle of $39.3^{\circ}$ 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 racjb h.gh,dfd4.e88z q8bgg 55 6yqp aike at a velocity of 4.0 m/s. If you ran the sabe5.g k88q8g dp46hjq5.h,dfz y agibme race on a day when you had a constant 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 ailt tk wjw bo23m ei4-tfhgv()g,.7)a wind of 50.0 m/s to the West. The plane's speed relativ ) tf3gk2(4g wmjola7)h. itt,be-wive to the ground is

  A plane is flying due South (jv, gj qr8la;e4fotqt9osi zr3; oo29ae79l9$270^{\circ}$) 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 ofo .u4pjun- (yp 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 3gtebf;yot:0n l07 gj)eu x,lrkzu, 5m/s horizontally fires a projectile with speed 50.0 mlf,nrjb l;0e 0zy7u,gtt 5x3uokg e:)/s in a forward 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 across a river witeqhjd6 3pxbl9c f16x.h a current of 6.0 m/s. What is the speed of the boat as it cc6.9 jx3x 6b dfelp1hqrosses the river?

  The driver of a motorboat that can move at 16 m/s in still water wishes toeut 27 jojl;5r travel directly across a river 1.6 km wide in which the current flows at 4.3 m/s. How long w5tjoju7l2e; rill it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wish+ pch6vi5e8hpes to travel directly across a narrow svhp+e86c 5phitrait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 2 p9y iim)dw j3)0nybo.00 m wide reaches the opposite bank in 6 min 40 s. She is swept dow)m n3j .0dw ypbii9yo)nstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reacheb7mx) .me4- enmi :o; wef6ozf owyx59s the opposite bank in 6 min 40 s. )fb. y6mwoz5oxo m;ee4ex:-fn7 i9w mShe is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.80 m/s, mk5(zxttg* +g ;zqjz)p ust aim upstream at an angle of k )x5 (+tgqzzjg*pt;z $18.7^{\circ}$ (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)  $m/s$