Which one of the following is an example of a vector quantiks m:.umb 1bntaj(+7 2ogi* eaty?

  Which of the following operations will not change8m3x l6pxbv b6q* /uav+g-cr rv44w,ye-u a dq a vector?

  Which of the following is7gp) hrvhlo2m65k lntv)-4 nd an accurate statement?

  The resultant of two vectors is the smallest when the angle betwrd yf19yk 02ibeen them is

  Two displacement vectors havee5/zzfs7kc rovw6gx 3-c 2,yo magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the mac3fsz5,7co gzv r2-w /xo6yek gnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followe;,heqcf xjswwf0;-*4ezs 9r ing is a possible answer for the magnitw9hrjesx-es fe0,f; wcq*4; z ude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions tvy5 ushckc zx*;pz: :;hat cxhz y;c*szuk :5p :;vare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,k*5qtj / i6c+ dzs3opy )ukgf6 the unknown vector is

  Ignoring air resistance, the horizontal component of a pq16q jz-pd)s5s kbnbw- owu 09rojectile's velocity

  A ball is thrown with a vef*cr ty 6gdnj:z6n;6ilocity 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 hoq z)d vcyh343prizontal component of a projectile's accelerationz cv3q3yp4h )d

  A soccer ball is kicked with a velockwlj+n g7r m0-c:) y s1xqug/dity 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 a;p;vcsc6aom p lw+e-4 nti-parallel to the velocity a c-cp w;p6o4+el;sv mvector,

  If the acceleration of g:2xldnph 8rn; 1v0bban object is always directed perpendicular to its velocityg80:n pv; r2xbn 1ldbh,

  At what angle should a water-gun be aimed in order for the water to land with t2f4yv;k v3uw yfkoksk09* j6n he0; knsv* yk uky6v2w jff43o9k greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the z k5djfyh(xy3qi; xaar;f;8-f 8 orb)4gy0 qg horizontal, each with the samebof848r;hd;(ygj3 axfkx qfrq;gy -a z y)05i 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 timp67m/u g -8vqnuv zu7oe. If the ball leaves your hand with twice the velocity it had on your first throw, its hu-m6uv pn vo/7z7ug8qorizontal range R (compared to your first serve) would be

  A ball is thrown at an oq.dux 9gabb6nfa+,* m riginal 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 field goal 5lh; x txxv)k bbwvze.-+b/e)attempt reaches its maximum height, how does its speed compare to its initiaezwh;xv )v+xeb b k)-/blx .5tl speed?

  A stone is thrown horizontally from the top ofx m*dz v+(sq+l a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level gr ++x mvz*lds(qound below?

  A bullet is fired horizontally, and at the same instant a second bulletlnm4vtn5 .ghz 3dp85w is dropped from the same height. Ignore air resistance. Compare the times of5 h wmndvz38g5t.l4 np fall of the two bullets.

  A plane flying horizontally at a speed of 96.3 m/s and at an elevatih q .uf5fpsgkw1c*5 7vy(9jqhon of 233 m drops a package. 5.6 seconds later it drops a second package. How far apart will the vu(yjg k*h5 7fqfs591h . pwqctwo packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second h. 9brzsuq t;a6 :9i311:re* ahqlhvyat -rpypackage is dropped. Neglecting air resistance, the distance between the 9r6rybh ilhusq :;1p h9rt-.z:q*a eat3y av1falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constazkvt6tg uc5y7f p8 b-1nt speed. Neglecting air resistance, when the bomb -6zf 8k1tgpy bct75 uvhits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is kl *wues :tc7(qy5hj,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 Earth, the ball wou:t s*j,qyeuch wl5k7(ld land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road a uswa0cxlh.; +nd pass a car traveling at 45 mi/wshla+uc x 0.;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 current. 31sdajdyi7c2 You start out in your motorboat on tcd7 j3dy ia12she 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 in still kc-uq,ajsx cmz gh14(;);d ru water. How much time will it take you to move 12 km d 4c(hq-d,;zmra sujc g1) xk;uownstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 de 8u1pz i6f1zez 3uabc27dnx0pgrees below the +x axis. The y component of a 3z07epdipb 8fcx12znuu6z1 A is

  If a ball is thrown with a velocitynsa3( +;rglk,w pa;wf ;2 cskm 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 direction north ,d:a1 dz q/,rcl6yz2ljae*sx of east and you end up 2.0 km north and several kilometers east. How many degrees north ocl2yseq*,ax/: rj, dadz16 zlf east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x ko8ddp (u9/ ehcomponent of its velocity is 8.00 m/s. The angle between the directiondude/8h(9k o p 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 what angle yk 5p8qtz5mqav 23oy 1dzy5j2 isk1 j55o 3yyqa58vp 22zzyqmdt the Sun elevated above the horizon?

  Two vectors A and B have components (0, 2e v 7zc23wefv1) and (-1, 3), respectively. What are the components of the sum 2ce ef3 72vzwvof these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), resp:p f9;c2kxq+1coyvm wuj nl)9 ectively. What is magnitude of thl9 +n x9 pq:u2;1ycwjfocm k)ve sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magd ;daq9d2r8t8wehs 0j nitude 0r 9ddw;28ateh jqs8dof C ?

  A car travels 20 km West, then 20 km Southls.gt),: cwbw. What is the magnitude of its displaclb st:wg).w, cement?

  Three vectors, expressed in Cac3 wgfyl 1qw)o,a3k /zrtesian 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, expressed in Carte + (s-po, oa3gwnfq +hp(uo(sjsian 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), whpo4n p9pyyx65at is the magnitude of vector ppp5 ny69yx o4C = A - B ?

  A runner runs halfway a s8pm);5 l* zvv.,nv2agpi3hvfn .yu iround a circular path of radius 10 m. What is the displacementnm2unv;f gl5v).y.pva3i,v zp i*hs8 of the jogger?

  Two forces are acting on an object as shown in Fig.eu, rew/tgtaz6x8t ,1 below. What is the magnitude of the resultant rt1,/uaw g te, xe8zt6force?

  Two forces are acting on an object as shown in Fig. below. What is the dirercuawa bllj;uujpcf(/ d5h b6, 0,0d- ction of the resultant forc0j 5ld, (d-,u/bfa6wrhu;p ucb 0l cjae?

  Vector A is 4.5 cm long and points alongdr.7bhztr 79r the positive x axis. Vector B is 6.1 cm long an dh7r7trb9r. zd 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 56 cm long and points at -hur.a7cus nmd *m xz5i *8lq7$30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 36 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 spez,ecp + wz621vnzdhaz (e2d1ded of 30 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 bottomzz2hap ndz2+e,wcz d1(ve16d to be 3.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 17 .y g8k;gfj7yy/g5 cvb m/s, from a bridge. It falls 25 m to the water below. How fag8ycbgjvy5.k;7 /gyf r does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 2dhi n8j9s8lgjk 4;8,d 5oeejx4 m above the ground, strikes the ground after traveling horizontally a distance of 24 m. With whl8 ndk95je jh, os;i8x4d 8ejgat speed was it thrown?

  A jumper in the long-jump goes into the jump with a speedf*zbcv+z) r; v of 12 m/s at an angle ;bfr +vcz)vz*of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-j7v hk/oxi57f xump goes into the jump with a speed of 9 m/s at an angle oxf5i /v 7k7xhof $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 25.a72stx0t )lws2 m/s at an angle of $15.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial;w emoq21j6hc velocity of 40.4 m/s at an angle of $21.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at +xf9yo ln :bv2f/o0ypan 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 shotm9 /1up(un sax horizontally at 18.4 $m/s$ from the roof of a building 54.3 $m$ 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 ix)egsk-g2c9 p3ku1kvgb 12 l2 k9 hjzynitial speed of 41.5 m/s at an anpu1b2 g2-xy gkz k3)cvl9keg 9h2jks1 gle of $41.0^{\circ}$ 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 ayme(swx64o*y6eln s z/ol3.velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows youo l/zs wny3e*e(4o66.yxla smr speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of bd 4v:vbgaa:3y) w5pf200 m/s due North, and is in a wind of 50.0 m/s to the West. The pl g:dapb)y3bf :vv4wa5ane's speed relative to the ground is

  A plane is flying due Soutac9q0xsrf 06(:pj07lrb vq25k bj t evh ($270^{\circ}$) 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 cg +od. er/p5hd2,uks120 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 movif( y6y 0pqkwu7 jxe/z5ng 200 m/s horizontally fires a projectile with speed 50.0 m/s i( 5pz7xqjy yfk6ew/0 un 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 wi mm *dh; wwy/)c08frnater 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 th )i/mh fdcwmy *;rwn80e river?

  The driver of a motorboat that can move cgf 1h+s(hmbq4- o2n lat 14 m/s in still water wishes to travel directly across a river 1.9 km wide in which the current flows at 4.7 m/s. How long willsl1g2c omh h-(q4nfb+ it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wis+obji +ba5 /ashes to travel directly across a narrow strait in which the curren5j /+asio b+bat flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches thb5+/5(j mgpn(wcur wm2v mu1 te opposite bank in 6 min 40 s. She is swept downstream 480 m(m +wu2p1t(bvm5/ruwg cm j5n . How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposlv7 (z/)hmwxt vk0e5site bank in 6 min 40 s. She is slz5(tw 0xh)mv 7/ek vswept downstream 480 m. What is the speed of the current?

  A boat, whose speed in stil*;d rd xqdd(tl::e ) t,s9bvlrl water is 1.77 m/s, must aim upstream at an angle of ;ldl, d(*t e drtxq bdsv:9)r:$14.9^{\circ}$ (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)  $m/s$