Which one of the following is an example of a vector quanti;y-5*zhpbvhx;a2juwa/o:p m / ttavr2m 8 yb5ty?

  Which of the following operations v.r mhkc*)3k swill not change a vector?

  Which of the following is an aew(r u*:v moig u)0h2rccurate statement?

  The resultant of two vectors is the smallest when the angle bei tld-hb,l 7wt vf2+n(tween them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, 0i4kgxirdda*6gt 7 4prespectively. When these two vectors are added, thtr4ag4 d*pi 06dx 7kgie magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whichmhxkf5hmcww ) c s+0gg))0d 8h one of the following is hgx8h) w0s5+)hcf0cm)gdw mka possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pm5nh, v3ei 0gbg,s cx1ull on an object in directions that arees35 1v ,0ig cb,nmghx $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vec(y09nl s3 ,dbs2s wqzrtor is

  Ignoring air resistance, the horizontal component t4pl qo3 +v5dhu6 xo/yof a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle of l*p,4)7ll:jv i r, xiey1ut, jly .sxw$60^{\circ}$ 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 projep )yj an5vz3vuhe(e co9y cs-7x v;y-.ctile's acceleration v -v 3juon e c-zx7aysv)(cy5yh;.p9e

  A soccer ball is kicked with a velocity of 25 m/s at an angle owez.w q2u8d) f4ks.rpf $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vector of umvy 2p.g. vd hjrd::vl49yj) an object is directed anti-parallel to the velocity vl pm9vyhvr2 dy..vjd:gu: )4j ector,

  If the acceleration of an object is always directed per.+ r,3 u.v.yajxc hnorpendicular to its velocitycox,y+n .uj.a.vrrh3,

  At what angle should a water-gun be aimed in order for the water to landt2gme d,nj. m6 2hk0fe with the greatest horiz .6tejnm2de g0 ,mk2hfontal range?

  An Olympic athlete throws a javelin at four different angles -xel 4/6ojl ivabove the horizontal, each with the saoe -vxijl4/l6me 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 lea6voqgl q4 n4+g;yhobq .gqs20ves your hand with twice the velocity it had on your first throw, its hoo;nqg sq+q4gy.42lov b06 ghqrizontal range R (compared to your first serve) would be

  A ball is thrown at an original sp4,tc/ xznwf1qszb/r , eed 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 heighf*h5i2ov ,pk- k nwm;ut, how does its speed compmi u*-nvko fh,k 52w;pare to its initial speed?

  A stone is thrown horijht) pu9 n)f)zzontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when ifhp)zn)tj9) ut hits the level ground below?

  A bullet is fired horizontally,asndrau,5, ; 1.m luza and at the same instant a second bullet is dropped from the same height. Ignore air resist51laz uu,,nd. rmaas ;ance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of uz6c)qwb 3v 5lqq(bl, 89.7 m/s and at an elevation of 267 m drops a package. 6.1 seconds later it drops a second package. How far apart will the two packagbbwqlz5(3 6) ulcvqq ,es land on the ground?

  A package of supplies is dropped msvx pwn-sx6-.7 4capbf;wn, from a plane, and one second later a second package is dropped. Neglecting air resistanw sms ;c,vap6nn7- xxp.-4bfwce, the distance between the falling packages will

  A pilot drops a bomb from a plane flyit-dn7uwlx j/1toq* y7z(qcxj z oe xr*1: po78ng horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the hori/pol8ot11yznoqcj *zx :ujexd x-w7t*(7 qr7 zontal location of the plane will

  The acceleration of gravity on the Mo-wj ph:in* 4uzmsqc2 2on 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 Eart ic2h:p-q2u w *mzjns4h, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight,t 4gnw4n6 eab8 level road and pass a car traveling 4 en4gban86tw 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 cur9) x +q(wp * bq:qa2;xfgn5u v6ckgdfkrent. You xkqf+;95 ba*uc2vq) ggwx6qp(nk :dfstart out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h y ,ngt,8(xncl q e,nw9in still water. How much time will it take you to move 12 km d yt8xnlcqw n,(eg,,n 9ownstream, in a river flowing at 6.0 km/h?

  Vector A has magnitudvds qok)7 hy)03kx 5ipe 8.0 m at an angle of 30 degrees below the +x axis. The y component vx) qksy70hp oi)k3d5of A is

  If a ball is thrown with a velocity of 25 m/s ay829ik o9 ral *wv,oxrt 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 yqcebnp.((az 9i6s r8 0-aouwxou end up 2.0 km north and several kilometers east. How many degrees north of east have you walkei -(r(o8 6zqbae0 .pc9nwx saud?

  A butterfly moves with a speed s qj2ks8c)enw3c* 7xse.4 zrw of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion a e*cs)swwqz. k3c j esxr78n42nd the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angl/kjiz1 x4wa aj3u ,ry8e is the Sun elevated above the horizoj wyaa x,3/4i8ujk1 rzn?

  Two vectors A and B have components (0, 1) and (-1, 3puft m-6 l/w4.jke.i s), respectively. What are the components of the sulfpis./ke .w-4tju6m m of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 8v/ ww.o1rr 6uwej-ac 3), respectively. What is magnitude of th/ erc8 ovraj-16.wwu we sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). 4qvx5tt zxjk- :t + 37j,aynz(uiee i3Vector C = A + B . What is the magnitude of3e 3tuq,ajnyttzj: x7ez- (xv5 k +4ii C ?

  A car travels 20 km West, then 20 kmc o+jnw.,b +xh South. What is the magnitude of its displa .n+bcwh,xj+ocement?

  Three vectors, expressed in Cartesian coordinatesi7m0 fqd 5 ;/*dnyyrlta )-nbc, 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 Cartesian coordinatec).yem(h 0 rpr-fi/k ss, 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),hgmpq)b+82 k f svc19m what is the magnitude of vector C = A - B)1mfc+8p gs9 hq2kb vm ?

  A runner runs halfway around a circular path of radius 10 b hu9q.-n d*kpm. What is the displacement of the jogge* bu.n-qphd9 kr?

  Two forces are acting on an obje *3akeeusqzuzds73o9v arkm s/ )*.6sct as shown in Fig. below. What is the magnitude of the resultant fo zs3rak)asoe6umv *3 zsusq97 e *.kd/rce?

  Two forces are acting on an object as sh)y+ : kj.hg7mfee :tyueyxu. 1own in Fig. below. What is the direction of the resmy+ e)yf:ehx.1y ue.7t:gju k ultant force?

  Vector A is 3.1 cm long and points along the positive x axis. Vector B is +d7l xxtdsl93)ev*ehg8dvo . 9.8 cm long l*+9dhdt)odl g7 evev xsx3.8and 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 81 cm long and pt 5+l d)m+jz *rmh2.byap ,scqoints at $30^{\circ}$ above the positive x axis. Vector B is 29 cm long
and points along the negative x axis. Vector C is 25 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 ih*f6(6yvij ks5z q+x speed of 24 m/s from 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 3.3 s. Whatz*+5shkf( vi6jyi xq 6 is the height of the cliff?

  A girl throws a rock horizontally, with a velocznj3; wd02 miyity of 15 m/s, from a bridge. It falls 23 m to the wanzw j3 yd;20miter below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 19 m above the grouq)(kutw o 9c*q6x 6cyvnd, strikes the ground after traveling horc*(ot6y)6 q wk 9quxcvizontally a distance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jumprwwc.-iph43uzk/ qe+fdch 7 9 with a speed of 12 m/s at an angle ofq+f-c k7 hu 9hdwze4i3p/w .cr $20^{\circ}$ 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 spedgdr ab-/2v 8fg7/wdfed of 12 m/s at an angle / g vd-8ga72d/brdfwfof $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial ve9aaqqvlp 72 *jlocity of 42.8 m/s at an angle of $36.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched withk1x+d a *k 1ornk;+k+ltks2dk an initial velocity of 39.0 m/s at an angle of $32.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fidr:/)bbmxdx x0*w/h; fs all5red at 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 horizontally at 16.3 irmkh56 fx5+j7 h-v;lku y*id $m/s$ from the roof of a building 33.9 $m$ 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 e zq,y(x9c*azq5)z.d; syrp n of 63.7 m/s at an angle of s,d9zaz.5ezqyn*c(p r;y x q) $44.1^{\circ}$ 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 p9oe.n;6)ck6y:tg6 k 7og 9zah skx ybof 4.0 m/s. If you ran the same 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 woul79yxky6o t;be6nz)ak o h ggp6c. s9:kd be

  A plane has an air speed of 200 m/s due North, and is in aux ,au,(j-gg6dv;hy l wind of 50.0 m/s to the West. The plane's speed relative to the xh;l- g( ugu ,jya6dv,ground is

  A plane is flying due Southw 44)ckcjaul:kq*dq 1 ($270^{\circ}$) 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 ud,ssg7 cm.nfp6q+ m2 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 un;-2qxkqbj 7fires a projectile with speed 50.0 m/s in a forwa 2jbqn-q;u kx7rd 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 a5y ie1q)c7yme (:u ca1ho7m hu4enk:xcross a river with a current of 6.0 1u me14k :o7 (7cy:h chaxyumnq5i)eem/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat th ey.kh+4 3vpkmat can move at 9 m/s in still water wishes to travel d.ykmv k3+ 4pehirectly across a river 1.6 km wide in which the current flows at 3.3 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wi g;uvs(c0+)(tvz rmf:hp:c dushes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the drsv0u( u;c rc:gd:h+( f)zmvptiver head the boat?

  A swimmer heading directly q-r9xsqn(ei7mnb7 v3across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 mn7 e q(m9r n-biq37vxs. How fast can she swim in still water?

  A swimmer heading directly across a river 2q v0+.3iq34pj u igzn kxt.a2p00 m wide reaches the opposite bank in 6 min 40 s.3pp.z3 q+i vuj4g2 ikqtax0.n She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0.85 m/s, must aim upst9wf 2b(8*mrunuanlr0e 0ws-)oigxd :ream at an angle ofrwe):nn(s ubdo0f-8i*2 m r g90lua wx $13.6^{\circ}$ (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)  $m/s$