Which one of the following is an example of a k6+if z2xjp:u cc (v(avector quantity?

  Which of the following operations will not change a ve jamwgt;5s/hrf d22p*ctor?

  Which of the following is an accurqj//s*cu: 3jzn dpz+od9:u rfate statement?

  The resultant of two vectors ;k6dlde7zn-5 x+yd q4sn pv1iis the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. W jg3pzd;l4(-f1avp tmeo3jxd,2i;-y t0g oi q hen these two vectors ar-, ; fadl gt-o3evpoiqigdtyj1m3x 4z; 2p(j0e added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50:vbza8wn0 d,oe n0/f 8mft2da. s8axh, are added. Which one of the following is a possible answer for the magnitude of the rwb/8hfa0.xdm8 2o,at8:v zafnse 0dn esultant?

  Three forces, each having a magnitude bkuyrg8n8 g(ef4:+g - rywj8wof 30 N, pull on an object in directions th: g8ek(8fw 4n 8ry-rjwybug+ gat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the un ,gbnn 3hgh0m0known vector is

  Ignoring air resistance, the horizontal component of a pr ,zx su)t+ r09rhcnmg8ojectile's velocity

  A ball is thrown with a velocitycp up0 qj)q3l.v ruh1, 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 projectinscg-i/:+8rvn ld u sv8 nyr-;le's acceleration/n8ns c;grnu--r+:vy v8sl id

  A soccer ball is kicked w u29nrn ct6q,3kx8cfar*id+p ith 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 vectopjr l./s 9 lb*jrgj)6sr of an object is directed anti-parallel to the velocity .g6jr9jjsslbr)/ p*l vector,

  If the acceleration of an object is always directed pe /4;v22.btg,l2h oepvkplddt rpendicular to its velocitgd 2t,ll/b.;phtk2o4 2 depvv y,

  At what angle should a water-gun be aimed in order for the wa+fo41nq .b)uf3d2 xib g9qb qcter to land with the greatest horizontal range? 4c1gdbu3bb +n.ofq)q92xfq i

  An Olympic athlete throws a ja/cz.mvlp 3 ;bivelin at four different angles above the horizontal, eac plzb/c .;imv3h 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 leaves youro-lj qzm3o/- c hand with twic3cq/m--zjloo e the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/;vh euc:x;k5v cyg-9 es 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 doesgmcu+) qhr) a 5s7lph2 its speed compare to its in+u)a75scq plr2) h hmgitial speed?

  A stone is thrown horizontally from the top of a tower at the same instanj 7yazlhxnphk)1t;b rfp 13/0o*wju8t a ball is dropped ve71 tp1jxa;n*30uprkz bj)8o/hyfw h lrtically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizodz6cwor 8*q3 ,p3 glahntally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bullczl8*3o whrdpag ,3 q6ets.

  A plane flying horizontally at a speed of 9tq yce4s52 l9ifhp s4h2at.m45.4 m/s and at an elevation of 239 m drops a package. 4.0 seconsqf5y.iha 92 sh4mp2tl44et cds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and /,mmw .wlfdw6one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages wimm d6,ww.fwl/ll

  A pilot drops a bomb from a plane fl9 .8y/o lm s7rdzgjb6. xw(fu8h4kw sxying horizontally at a constant speed. Neglecting b4/f9ys7lo(r.dsm6jk. 8ux zwg hw8xair resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon i7v pi8l0a riih0( xk+cs only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and ankl xcr0 +pii(8a0v7 higle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis *042if xw(oh sz6kx r4t 4g3k-gneovc relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity n42z3gic(oxr60kkv 4xt-4we g f hos* of your car to the other car is

  You are trying to cross a river that flows due south with a strong currmg -wn3:dz p c6yb ofw2t9x41kent. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starmpt9yx2ow k:3b4ng -f 1wd6c zting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still watery p49i0y v5clm;qr i;d. How much time will it take you to move 12 km downstrea;lmcv9pyq5; 0dy ii4rm, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 d.5 ow zthv44bqejme 1t+j;, qregrees below the +x axis. The y comp,btw5rmqq4jtv. +je; 1ezh4oonent of A is

  If a ball is thrown with a velocity of 25 m4wk:tjl da3i/+uc *ag/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+y+9 ss;dmdmmh n /09achf9k2j b ,tda direction north of east and you end up 2.0 km north and several kilometers east. How many degrej+,amcn d90/m9;hk hdsf9t2 +yab m sdes north of east have you walked?

  A butterfly moves with a spee3px)1cvz8d k e-ge0bn d of 12.0 m/s. The x component of its velocity is 8.0d0 8pevcg-1xz3b)ke n 0 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At wh xk6o dm/b.;bpat angle is the Sun elevated mxo db6k/p ;.babove the horizon?

  Two vectors A and B have components (0, 1) and (-1y c9gu3i3s0 0bd. dzky, 3), respectively. What are the components of the sum of these two vectorsyd 30kcy 0.dubs gz3i9?

  Two vectors A and B have components (0, 1) an5 mi iz:z7m:hsd (-1, 3), respectively. What is magnitude of the sum of the:hmziis: 5mz 7se two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnit2bbdbqpi5k em64 / png9r9 zr1ude z 1 2p49k/mr5qe dbbni9g6prb of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of pf5qir s8v)g7mw a12eits displacementme)vsg1fp8q wr7 5a2i ?

  Three vectors, expressed in Cartesian coordinates lhj 22ydv 9m06wn8kcr, 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 ;6 *4jt3 ,l0ytbq;orml wtrseCartesian 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 = h m1m+4eixq5,k/ smv e(+3.0, -8.0), what is the magnitude of vector C = q/sv5h,i xk4emm+ 1em A - B ?

  A runner runs halfway aro9f f:x jxuno);und a circular path of radius 10 m. What is the displacof)n9;ux:x jf ement of the jogger?

  Two forces are acting on an object as shown e-)3i gay4rhq in Fig. below. What is the magnitude h -ria)ey3qg4of the resultant force?

  Two forces are acting on an object as s) c g;u.ppw:+7ij2d j1 dkrbnlhown in Fig. below. What is the direction of jbn+uw i.jpdlkc;12d p7g:r ) the resultant force?

  Vector A is 3.5 cm long and points along the pfex(u7rkk/:rju4g 9tl/w2mz7)w wo zositive x axis. Vector B is 6.8 cm long and poiluz:g7 )wkjwo2rru9etzm /wfkx( /7 4nts at $+53^{\circ}$ 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 60 cm lon21 jjmseuw6;ujer( 5zg and points at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 46 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 horizonta) 0z rjggz;zx8 zs(dfjc0v3-ally with an initial speed of 29 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the tofsc0dgx z ;0 r3vgz aj)zz(j-8p of the cliff to the bottom to be 3.2 s. What is the height of the cliff?

  A girl throws a rock h q9e +1x:g/d xjael flrs)ad7(orizontally, with a velocity of 15 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before striking the waedrdex/jaf9)la1 x: +(q slg7ter?

  A ball thrown horizontally from a point 27 m above the ground, stri 7og8tcrqye9 szk:e5+kes the ground after traveling horizontally a distance ore 7:qk+z 59o8yt ecsgf 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump wit1 upgf 5 ndf./v6o yikk2vl6;zh a speed of 12 m/s at an angle offvfz/yko5 d6gk lvi;p2n.1u 6 $20^{\circ}$ 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 d.h y1bo o3xk)8 m/s at an angle of 3.kyoxh1b od) $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 33.7 m/s at an angle ofu*i kl2a lvw)6 $38.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with anv/ gf. dmo+f.s initial velocity of 36.6 m/s at an angle of $39.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anygcob8(g)6 )jt6tl zogle 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 20.3ed7e,7ln1r mg4ck m /o $m/s$ from the roof of a building 43.3 $m$ 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 levs4coe/i r4y jed9w9j) el with an initial speed of 58.7 m/s at an angle os 94 joyeic 4/9e)wrjdf $43.6^{\circ}$ 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 /5e/)wl0sph vn.kld sm/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 wo0v)d/l e. kslwp/nh5suld take you to finish would be

  A plane has an air speed of 200 m/sn.o+-so rnr8 s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relati-.or r o+s8snnve to the ground is

  A plane is flying due 3oju5/ud 6n+cxp+4roj +zp mjSouth ($270^{\circ}$) 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/ ,0xfd3py5 t fbt62akl :mw7cnh 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 projlx4)v+( qv(o;bve.jzlu(j uj n 1 km8hectile with speed 50.0 m/s i(ojv h lm4(8lj;)1q k euunjvx +.vz(bn 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 ss,qqmes 0+)u atill 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 crossuq,) m+qsas0ees the river?

  The driver of a motorboatbcii4w jy7+ z:n*1tok it;ws; that can move at 19 m/s in still water wishes to travel directly across a river 1.1 km wide in w1 owz;;:iynjk 4s it* bc+7twihich the current flows at 4.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that c:jirk 7y mj/rwhv,5 e.an move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boajh i.w/:r7jk5,y vm ret?

  A swimmer heading directly across avc/ egt 9z+zxb;kd76 d river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can t+z vdx; z6kg97/dcbe she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite b:;q9k )y y1dwmdz bck-ank in 6 min 40 s. She is swept d91y cwbmzyd ; :)-dkkqownstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is r-tut exqv1;va l8* 6c1.35 m/s, must aim upstream at an angle of-u 6tr8t* axvecv; l1q $28.6^{\circ}$ (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)  $m/s$