Which one of the following is an example of ah l3h-1-/y kl9f iqghe vector quantity?

  Which of the following operations s9 ).9lbeea ipwill not change a vector?

  Which of the following is an accurate statement?0idht2w/a 8vc) zgf2e16jhf j+ wvgu :

  The resultant of two vectors is the smallest whui;ag mkqc8/ywt 30 /qen the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. i.zbc,+.rp rh When these tw.,h rcbp.z ri+o vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 abg u;*em 3*x,pzdx)xc nd 50, are added. Which one of the following is a possible answer for the magnitp3* bx;gxzmxu ec*)d, ude of the resultant?

  Three forces, each having a magnitude of 30 *5 m5c qa nu9wp0ap*tcN, pull on an object in directions that are 9*p muaw0cp5n* tqc5a$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkno1ix9x1p3wm(moidui; ysg, yuaf0/b *wn vector is

  Ignoring air resistance, the hor)q74a)cxcb u9ku yt1k izontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s atrzdk9dw10.7/oodk p6 7nw ull+z9lm k 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 componenk5 iwv4i5) qoot of a projectile's acceleration wv4i5k5 ooi)q

  A soccer ball is kicked with a7ds ;+v(d pp61*gs0pjr,6kvmy h sqme 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 vector of an object is directed anti-parayrh*k vu 97g+:*qb g:dwkw 9ghllel to the velocity vgkbgd w9* v y* :wrh:+uk97qhgector,

  If the acceleration of an object is always directed perpendicular to ii cyzd(re7, s4ts velocit4dc7ze,( ysri y,

  At what angle should a water-gun be aimed4xfhxk9p.x 4n c l6t+x in order for the water to land with the greatest horizontal rangpc+49 x6xtln4xk. fhxe?

  An Olympic athlete throws a javelin at four dt 6s;hxht7 -hlfj/ o6tifferent angles above the horizontal, each with the same speed:t -l7/t sthx6jo6;hhf $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a b;bf2.ku m5wx3hhwy ar 95ha ft;h:s2zall for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serveh9rkw;y; asfwmhhfat2 uh235xb5. z :) would be

  A ball is thrown at an original nk28mwa6z b a: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 attempt reaches its ma hhcl2jhe 3q,(pj( mmbt9d5w )ximum height, how does its spe 2t e,bhh pql(cwjd593 )(mjhmed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a +e hh s./qcn 6ujnksz/1;kgr)ball is dropped vertically. Which object is traveling faste1 hq +zh gk)6;urk/sn/ .cjsner when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second,c l+lr j/x *dypvbgq+ye: v6. bullet is dropped from the sly6pvq.x+vrey* ,:g+ cb/j dlame height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 117.9 m/s and aybcn5m.1:a m co. 3pgzt an elevation of 286 m drops a package. 2.3 seconds later it drops a second package. How far apart will the two packam 1cac.bogn3z.5ymp: ges land on the ground?

  A package of supplies is dropped from a plane, and one second laterebq+do .d,x8;8 xal*rg7g2 jg unxt-u a second package is dropped. Neglecting air resistance, the distance between the falling pa7*x;rng u-bdu +qxe8xtgdag j .o2,l8ckages will

  A pilot drops a bomb from a plane fcn vic.k 2d5q5 u5glv/lying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane /ku vc55dn5g2vqcil. will

  The acceleration of gravity on thuhhe. p+rfr- +j tviz) 9fg3+ue Moon 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) 3p9t-i hjf+r+u.zhve u+rgf angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the ofz66w:ln f 963bzhr6 qrchp;+x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the ot6 6o9:fln 3rqwhf zph ;c66zrbher car is

  You are trying to cross a lke(sg-tsbq2l 3e4c1 86y rauriver 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 starting point. You should head 1 elsc3l8ub se(r 4kyg-62 tqayour motorboat

  Your motorboat can move zjssvs2vg.;/ at 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6..2vv;sssz /j g0 km/h?

  Vector A has magnitude 8.0 m at an angle of l4u k+ *hzoj+2ow- xot30 degrees below the +x axis. The y component okhox w o4+jz+-t2 olu*f A is

  If a ball is thrown with a veloc 5zg8psdy6+o. dyic9m ity 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 iq)qub; eyg,p 3q.qpby4g.g7 en a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How mae3 pqgq4 )ypy .g,qgebub7.;qny degrees north of east have you walked?

  A butterfly moves with a speed of 12-8nwnj k,j h,/ 3kioxn.0 m/s. The x component of its velocity is 8.00 m/,noi/jxk nk8 3h- j,wns. 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. A6 mj jmw3h1h7pt what angle is the Sun elevated above the h1m j7h hp6wj3morizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatj x4xu/nw.t 4 o5-6fbqkg-vxucx 1 x7l are the componen x. / vnxulcx7q-w1to j645fx 4xu-bgkts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and ( +;wnfw)2r+k enatw /f-1, 3), respectively. What isw);e2+fwr nt+ /wafnk magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A +vyjgn 7j9sk34 u42r wi B . What is the magnitude of C ?4urjvi3k wgs74ny9 j2

  A car travels 20 km West, then 20 km South. What is the magnitude of its displa*3 twdky yf (:ypebpj:md.5d7cemenw 73ypkj5b* yd(dptmfe y:d:.t?

  Three vectors, expressed in Cartesian coordivii*7 nwlm-rckl 491noe(*z qnates, 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 c x8vd5 )7xbhkcoordinates, 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)(a0mpqni--hy8 k z1xxb *yp :yn:i;ow and vector B = (+3.0, -8.0), what is the magnitude of vector C = A b yo8mq(0iwa : nxinpzh-pyx-:y1;*k - B ?

  A runner runs halfway around a circular path of radius 10 m. Wh u s4g8t;:l o0 xft):zrolq-wxat is the displacement of zo-sox :0l8 ;qw4tftrug:x l) the jogger?

  Two forces are acting on an object as shown in Fig. below. What is q8kl. q1:t 5n g,mmqnkthe magnitude of the resultagqq1 :.,nmm kt5kn8 qlnt force?

  Two forces are acting on an object as shown in Fig. belo2gu/4(:jg- :j cdptu v qpj 6yb,(jxxrw. What is the direction of thrq,2 ybp- u4d txjj6jv::j gx(c/p (gue resultant force?

  Vector A is 3.9 cm long and points along the positive x axis. Vector B is 8n zjs(g7wzad18l-jo-.1 cm long anazldz-7 j 8w-josg( 1nd points at $+21^{\circ}$ 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 54 cm long and pointse 1jr5z 32v 9sd (uugfjhzf38h at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 47 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;xs *jdb/wcd 8 with an initial speed of 13 m/s from the edge of a cliff. A stop watch measures the stone's tras;d8wc * x/bjdjectory time from the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 9 m/s, from a bridge.hu.r vv br+)se 0qvx42e1bx j, It falls 12 m to the water below. How far does the rock travel horizontally 2vru q,v0 .sjvhrxb1eb+ ) x4ebefore striking the water?

  A ball thrown horizontally from a point 2p.ac r oax3rbrq5 ef95lz6* 31rdo1we7 m above the ground, strikes the ground after traveling horizontally a distance of 216q or .9br*3prd f1zal3e55wearc o x1 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed .7m7bhfenz up b8fy30of 12 m/s at an angle ofeb7f 0pun b3.87 yfhmz $20^{\circ}$ 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 12 m/s at an anglh-ssj8:iv9 t ir.k-qm e - q9s8:kvs- rthij im.of $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial vle ,nphr ls-k)y7/. i jl)igi6elocity of 57.2 m/s at an angle of $14.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 40.9 m/s at a /-1(ewbw1f z,nqwb6sbg, w vp:p2erin angle of $39.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle e,)6 iqhnh i4yn plg2c rt4*q*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 horizo+ vg )w)a+lqzyntally at 24.0 $m/s$ from the roof of a building 65.6 $m$ 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 with an initial speed of 56.3 )brinpux:,c0ffoi3*u , e -hkm/s at an angou xh)n:3 e*i f ,cifr0,-pkuble of $47.9^{\circ}$ 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 rj up2/il6pqh3 3pvjm vffoo .-+g-lj 9un a 1500-m race at a velocity of 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, jigo2o 6v9p+-l.v uqf3l/jpm-p3j f hthe time it would take you to finish would be

  A plane has an air speed of 200 m/s due North, and jt bw-hfa ao68--bu:c is in a wind of 50.0 m/s to the West. The plane's speed relative to the g6fbata wo-8-ubc -h j:round is

  A plane is flying due Sou(fpe xy2+eb)-h:h5w vvxfes 0/irsr+th ($270^{\circ}$) 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 k v-6zefd9al n74l3y okm/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 o,dgf vb*,o95tgh5bwa projectile with speed 50.0 m/s in a forw5bfg,5tv*go d hwo,b9 ard 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 ch;v;s)/gjqo4 v 0ve gwith a current of 6.0 m/s. What is the speed of the boat as it cros)v;o4 /vhc0q g;vsge jses the river?

  The driver of a motorboat that can move at 14 m/s in still wqo- apk+ 7hn( fuc-6iuater wishes to travel directly acrosohai6cnk- pq uf7u+-(s a river 0.5 km wide in which the current flows at 7.2 m/s. How long will it take to cross the river?

  The driver of a motorboat that can mhv)xgxo8hgz- 7z 2mv4ove at 10 m/s in still water wishes to travel directly across a narrow strait in which the curzo )vvgm8-g z47x2hh xrent 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 the opposite banke y87-lzf s9zw in 6 min 40 s. She is swept downstream 480 m. How fastszyf 9zwl8e- 7 can she swim in still water?

  A swimmer heading directlt))ri4,0xl kdwws8oo y across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m.l4)wwdx ) st0 ki,8roo What is the speed of the current?

  A boat, whose speed in still water is 1.24 m/s, mus pha 05aeuc53a7qdsec1p dv.7t aim upstream at an angle of uvps a7hp ad7deaqc e530.c51$26.2^{\circ}$ (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)  $m/s$