Which one of the following is an example of a *21 s8vbvtp8:wrve kyvector quantity?

  Which of the following operations wds) k31oab5wdill not change a vector?

  Which of the following+e+vdnf4b).e:i vlx b is an accurate statement?

  The resultant of two vectors is the smallest when the angle between ykk) ip*qn.:3zg, bjf them is

  Two displacement vectors y4 8ckjasaz( d()z,kp have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of(pz8kj4k z)(sa, ayd c the sum

  Two vectors, of magnitud ph2by c1be*en/1+ux2wir+ hedps(f ,es 20 and 50, are added. Which one of the following is a possible answer for the m,e+* i2 h +x /pewfen1yrp1cdu2bhs b(agnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in d1fqd( ysp :5z ,ymkx,tirections thayd ,z1, xsyk:5mp(t qft are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknoripffg3)9 3 x4xz8y ;acj5 5npro:iey wn vector is

  Ignoring air resistance, the horl oh*nrv(doms d*n1)v;d f 6(rizontal component of a projectile's velocity

  A ball is thrown with a velocity ognc vjo*( d8x1nc;/8weo eo3 nf 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 cb09. cat bg gyob1w e,j:()nalomponent of a projectile's acceleration90nwbobb c(:tg y, ael 1.)gja

  A soccer ball is kicked with a d 6 drn.ajdsjre;:s*/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 vectoc lbe;y z m.(o8c.lmk6r of an object is directed anti-parallel to the velocity vy8c bolk ;mlz6(.emc.ector,

  If the acceleration of an objz6.rio rea s73ho9,v .5nxcv1kcx*ty ect is always directed perpendicular to its velocitx95.*k7n . t,r chci 1zvraov s3o6exyy,

  At what angle should a wagosz )5wu 3v6tter-gun be aimed in order for the water to land with the greatest horizontal range6uz53o) tgvws ?

  An Olympic athlete throws a javelin at fousy* pwuntrb/i4te7 /.r different angles above the horizontal, /wne tr*putiby.47/ s each 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 leaves7w* 8w6hg, q)xjxhn:gl ne kz)v-c1gz your hand with twice the velocity it had on your first throw)kzvg nh7* )6:gjn ,lwchzxxw-e 8qg 1, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an azg*by/ly:;k1uzv 6mb ngle 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 heigh)c y :jlo7m(g ls9e9hrt, how does its speed compare toe7 glr9mj9(lsc :yho) its initial speed?

  A stone is thrown horiz mu)0 c/pnalij3u8r6,yt nlcbi :(;xmontally from the top of a tower at the same instant a ball is dropped vertically. Which objrpml;c0 nxu,lu)y6i:3 a m/t ib8nc(ject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullewoe.uxom.b)8 ) p-p)0axe jzki 4b8m ft is dropped from the same height. Ignor.0u io8f p)p4b)x-e 8z.aomxej)bkwm e air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of .i aax nub :i:o3oml0;c p5l1i94.2 m/s and at an elevation of 154 m drops a:1i5l:p u nxcam.;l0obi ao3i 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 dropped frow pn+8f*cok jz(e 6sn:m a plane, and one second later a second package is dropp6jzo *encks(:np 8f+wed. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horiii8(wuzv0e7xgj84ql zontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locatioi8xvj8 ue( q0gwli47zn of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Eg60c4 )vcp(5nfbo (xv 6 xiz/v(ujsum arth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you woi)om cvb(u f(vc4v50xsuxjz/gp( 6n6uld on Earth, the ball would land

  You are traveling at 55 mi/h in thr;9ir ye4 1i,*ddqx vle +x axis relative to a straight, level road and pass a car travelqxlvidi,y4* re1 rd9; ing 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 soc 2b 2,mvzjpgl3/1apmuth 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 b cap ,21/plmvj2z3mgshould head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take yde2izyp)fe6 zu0 4 n*oou to move 12 km downstream, in a river flowing at 6.0 km/heyo20d pz nfe6z4i )u*?

  Vector A has magnitude c8:2vzih+uqy8.0 m at an angle of 30 degrees below the +x axis. The y c2:i8czv+ huq yomponent of A is

  If a ball is thrown with a velocity of. 05fxcfz/vcz.0 qboe 9,glqr 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 north of east and you end u j4xa +8xj dxnn06rnf*p 2.0 km north and several kilometers east. How many degrnjrxx4*86ja n+fxdn0 ees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x co+;ho6qnk i rt7mponent of its velocity is 8.00 m/s. The angle between the direction of itsiohk+r 6t7 nq; motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level gri; itmlk :;;9udfnjdj zc(h*/ound. At what angle is the S*h:dl(c;zm;tj/ id ;fj9nkuiun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respe(oxit rwtd)458kre:ewp i 6 (v)zyeb9ctively. What ar :e 6b e(wz8i9pyd)wv)etx5ro4 ikt(re the components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respective(ab j49lyy+lily. What is magnitude of tl (y4ibly 9j+ahe sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, v y+c6 fphcx 53ycv g/8zb+/vi0). Vector C = A + B . What is the magnitude by 6vpvf x / v+iy8c/z+cgh3c5of C ?

  A car travels 20 km West, ep++ q4p;ny*m 5yfwjs gb+u,ethen 20 km South. What is the magnitude of its displacem b+5y,my;pgueen4qf p+*ws+ jent?

  Three vectors, expressed its*lrelav4vub /gl.q4 *2 u 2un 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, expressed1)squ4 3e3uacfxb0lj 6v (jidhdf)sv2t 6 -uw 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, -823jb6uay4 w6 ih0 +hi8 -sh8gprsyetj.0), what is the magnitude of vec4r-sh60 6tgjh iw8j2+a8h3y pu esbyitor C = A - B ?

  A runner runs halfway around a circular path of radiu4s2wae ou73ugg f4 r+4qudb a3s 10 m. What is the displacemebaoqsf 4guu2uw 4ed37gr+3a4 nt of the jogger?

  Two forces are acting on an object as shown in Fig. below. Whmv+5emxf-7s q at is the magnitude of the resultant fxsf v75+mq e-morce?

  Two forces are acting on an object as shown in Fig. below,26s5 ojv9rsz y bidn9. What is the direction of the resultant fo9zjsb5yv6n2 , sidr9orce?

  Vector A is 4.2 cm long and points along the positiveegnr l+4 zjm+-dm-3ki x axis. Vector B is 7.2 cm l-id++g m-k ljmrze3n4 ong and points at $+34^{\circ}$ 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 84 cm long anpqzof: 0xc 99*h/tsqx,1,a 7wyao zuw d points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 49 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 10 m/s froq oel6 npvd3;filoh*o oh)30(w2p o q.m 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 2.3 s. What is th2)h6qnw o*p3 d.l0 evhp 3lo(;ooiqof e height of the cliff?

  A girl throws a rock horizontally, with a velocity of 6 m/s, from a bridge. I4 nfi vbq3g4.fv) s(mm k*j:oyt falls 22 m to the water below. How far does the rock t b*4:i34msmkjy .v)qov fg(fnravel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes t o-p i/k*ywlx3he ground after traveling horizontally a distakw-i3 xly*op/ nce of 16 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/sc uvzv ig/3ecu4 8lc7pr+ibaip59m- 8 at an angle ofi/9iml zuc v37 i+8ec a4gbp58r pv-uc $20^{\circ}$ 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 13 m/- e:zw7 jsql jj.wk24o8.9xdf.las r ws at an angle se2.-.qaj j 7:w9zjl8.rfwlo x 4kswdof $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initia5m t0gkpc,l-s l velocity of 26.5 m/s at an angle of $25.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched withmmk: :8iwd e)y2clm9 u tpsv;-wy0)ru an initial velocity of 58.6 m/s at an angle of $18.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an amjq; sl8 xm;p2ngle 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 horizontallyp x ej*dbt ((.vuhb;veo14f-f at 21.5 $m/s$ from the roof of a building 47.6 $m$ 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 ground level witt52 3c)ukor,uvbcum w2z.3tcyb +;jth an initial speed of 38.8 m/s at an angltz+c u,crcwmb)2ot2vtuk;u b5 j.33 ye of $46.3^{\circ}$ 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 race at a vel; gqgp e25 ldxic6*2gmocity of 4.0 m/s. If you ran the same race ox p2lgg c 2i;mqd5*6egn 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 Nor.lw7 /gnmwe5r; ey1vtth, and is in a wind of 50.0 m/s to the West. The plan7lnm rwe wtv/1e;5g y.e's speed relative to the ground is

  A plane is flying duet :mtb0/o nc5b 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 s+c3vjlfe/)dg *gxn21 ssc sglv qn**6peed 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 a projekz an6f6kd7i:zxm c t ))()plaw85wfwctile with speed 50.0 mw lzk6k57f (x:n)f)za 8pw6tic)dawm/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 wx dpho2h.-/lz(-pft still water 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 crosses w2d pt(ph. loh-xzf/- the river?

  The driver of a motorboat that can move at 11 m/s in still water wishemj/ (bss1c /oecg.nx-am*u( ns to travel directly across a river 1.5 km wide in which the current flows at 6.4 m/s. How long will it j*1( /ngc.ms/uaxscm - onb(e take to cross the river?

  The driver of a motorboat that can move at 10 m/s in siuf7n dqnaux/(;6jur(w (tf75n1ebe till water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At whaxfi7u5; n76 ae(bud qju(1/wef(nntr t angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches th j gpe* g+z7kn8ryu3-qe opposite bank in 6 min 40*q pr83 gg+e nz7yukj- 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 rknw91x1h wn( teaches the opposite bank in 6 min 40 s. She is swept downstream(h1tn9knxw1w 480 m. What is the speed of the current?

  A boat, whose speed 8tuqe6xh g j:-in still water is 0.97 m/s, must aim upstream at an angle ofx:eg q68tju-h $29.8^{\circ}$ (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)  $m/s$