Which one of the following is an example of a vector qud, w(yf00fufry;3q5/qir0 w qqzf.o1bf2sj bantity?

  Which of the following operations wi v ;k)nk-3iwzdll not change a vector?

  Which of the following isk6r+coga32k8g7 icip pk9 5fja6rb7y an accurate statement?

  The resultant of two vectors is the smallest when the angleype 06m-a5 8-kgs cers between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivel b+va jb.mskzf*sq/yjd8.iw1 k65mu) y. When thes.s*)kq i+vjkmdbsy8faz5b 1 ju.6m/we two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following issd,rynw02 xc2p9p8 qjg 8 oq3s a possible answer for the magn2s s 20ywjo xrp8g,pq3 c9nq8ditude of the resultant?

  Three forces, each having a magnitude of-b-wa)k n uv(n 30 N, pull on an object in directions thbwk va)--(unnat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectsga +fd3k7ls8)q4:6qc1vb l )hltuocor is

  Ignoring air resistance, the horizontal component t4nvr3;s o *zyof a projectile's velocity

  A ball is thrown with a velocity of 20 m/s azwk fl7 +wnd q2rxzjm23*ye/x 4e7nd7t 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 projectileghm0w4r5kb9gqk+ + n b's accelerationkw kg5g9 bqm4 0nh+rb+

  A soccer ball is kicked witg + m)/c/ qsnh4h3 o24dwvoapnh 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 vector of an object is directed antork) uwmk, u-.l(tnx x,rnu(i18ir7 ni-parallel to the velocity ve x i xrn,un- (uun,o7tikkm) wr(r8.1lctor,

  If the acceleration of an2kcgordn v.+p7 5yy9 fd,qu-p object is always directed perpendicular to its velocit7uv. pgroqf 5pkc,d -9ny2d y+y,

  At what angle should a water-gun2lz14 trzncoze) )-l1eko) d i be aimed in order for the water to land with the greatest horizontal ztneodez 1)czli 2)r) 1 l-ko4range?

  An Olympic athlete throws a javelin at fou4o9jyq rm0qqi0o l-q6g*)x tar different angles above the horizontal, erliqo *j -q o00my9gaqx6q4t) ach 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 srb4w dxq.l.v 0econd time. If the ball leaves your hand with twice the velocity it had on yo4 .l v.wqr0dbxur first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 rfe9ph 9fnj0khs3gq -7o kr;ild0sgn71 r6j(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 height8/nnuffg .b4 m, how does its speed compare tmnbn8 uf.4 gf/o its initial speed?

  A stone is thrown horizontally from qtkwmvza dr;6y s0 );/the top of a tower at the same instant a ball is dropped vertically. Which object is traveltzy ks;;a/d6vq mr)w0ing faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a secovgv9 5y0 )yc jzcja6t 4wk6v1bnd bullet is dropped from the same height. Ignore air resist6vvb4cc )v0jgt5 9 wa y6jzk1yance. Compare the times of fall of the two bullets.

  A plane flying horiziw* :wm)k orh0ontally at a speed of 111.0 m/s and at an elevation of 191 m drops a package. 7.0 seconds later it drops a second package. How far apart will thew*w:i)mro 0 hk two packages land on the ground?

  A package of supplies is dropped froln 0xde;d (hoom7.wl ob j7;/4 awf6mem a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages wiwll7 /x emdb ;6oo47m(;nw eoj.ahfd0ll

  A pilot drops a bomb from a plane flying horizontally at ihc0xzd,+(mth 1y 4oaa constant speed. Neglecting air resistance, when the bomb hits 1hd,zm0 yxthca 4 o(+ithe ground the horizontal location of the plane will

  The acceleration of gravity vjvn g l2c 4ulg7x5,m/uomlt46zqe/ kny7.y;on the Moon is only one-sixth of that on Earth. If you hit a ba5m z44lv6 /l, 7yog7k.nc;mnxugyeqvjtu l/2seball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to (5j62n-x)i+v.hj ) tze v9nwt timjaca straight, level road an(h6cjv2)m+vi-).tzatjj in tn 95exwd pass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a rivern4 3paw4m,rnp-h1n wy that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the4n,ynhw-nwppr4 m13 a west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take y7 0 shdlbg h3*fema h6x0/m,jjou to move 12 km downstream, in a river flowing at 6.0 km/h h6 lsf jjh*7/mmhad,xbg030e?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis aa3xubfdhsm 4s,;4 5v. The y compon35 bvmua4d4as hxs,;f ent of A is

  If a ball is thrown wi*hu.jz u4(sfv3yzkg; th a velocity 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 cf8mf)3vttg/5 qs( hzi,kg.r a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many /.8qt 5)3g, fti cm( kfrhgzsvdegrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. T 5;bmro/ htmo,he x component of its velocity is 8.00 m/s. The angle between the direction of its motion and orm, mbo/h;5 tthe x axis must be

  A 400-m tall tower casts ruo lu +u0xu214 lft4la 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizon?20ofutuu 4lrx4 1l+lu

  Two vectors A and B have c8a 4cd/n3+/mitjr kt lomponents (0, 1) and (-1, 3), respectively. What are the compor jkmt4a8ltic/ /3+dnnents of the sum of these two vectors?

  Two vectors A and B have componentlz2 d*4) l zahwi5xsalm9y93 ms (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vecy9xm 2zsl)iwm9ldzlh*aa4 3 5tors?

  Vector A = (1, 3). Vector B = (3, 0).p h3+.7+jl9j.py mnps e gg4rt Vector C = A + B . What is the magnitude of C esgp+ rpj9h+.plj3yn.74t gm?

  A car travels 20 km West, then 20 km South. What is the m5zbh gb f4,l*kagnitude of its displacement,5kfg *lh4bbz?

  Three vectors, expressed in Cartesian coor 90ukz u38pxbh/knj z:dinates, 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 coordinates, (nxd8 /fspyk fbjotgnzz 2 .)sx9//*lare
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), what is the m27 ilhib0g +liagnitude of vector C = A i i0ig+ bhl2l7- B ?

  A runner runs halfway around a circular path of radius 10 m.)upt ,y7l4z mg What is the displacement of t zg )7m4ylp,uthe jogger?

  Two forces are acting on a-f,bvau eca-+tg (,r27o 3httv(a yyj rp1eb(n object as shown in Fig. below. What is the magnitude of the resulta eb(7je1(,-tth otg aar (3vyy,cpb arfv+u2 -nt force?

  Two forces are acting on an object as shown h 2;mswu,-vsjin Fig. below. What is the direction of the resultant fs ujhv,w;s2 -morce?

  Vector A is 5.2 cm long and points along the p2 lcv ba+g*g3mositive x axis. Vector B is 8.2 cm long and points atg2*mg+lv3c a b $+37^{\circ}$ 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 74 cm long and poizdwqcmnr +h ,3)41cjo nts 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 horizontallyqpftp;d57d*qgf 5.hw w p)jo9 with an initial speed of 21 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top.)5 7*ptwgjp pw o5hdf9qdfq; of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocitya3d8o/-/ w3nx,60w rcmthxse/ d e b0hv/jw wc of 6 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before striking the watew hn c,//d es0e6x/hw0c3tv-3jor8 dx awmbw/r?

  A ball thrown horizontally frrsff+l+6v:y rom a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 16 m. Wil ++frvr fys:6th what speed was it thrown?

  A jumper in the long-jump godd,t6 *ukgrw25+jd yk*4 vsches into the jump with a speed of 12 m/s at an angle ok62h kw,y5* gdtscdrd4j+u*v f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into 5q; ;ri:eop*tgn(aef)t fk,f the jump with a speed of 9 m/s at an angle of*gfaif(;f ee; knt o5)t:,qrp $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an i; i eze7tf 4.,f27tscsw0ostanitial velocity of 37.6 m/s at an angle of $49.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 41.28-6prqszhjbg 7hdf*ztwf/c 1x c) o)1 m/s at an angle of $47.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firmgp 1vnl*/l9c*2u3z x0pds d xed 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 eewg 5)e(v8s;knam.ef1g * m uhorizontally at 21.0 $m/s$ from the roof of a building 67.4 $m$ 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 ofwt(r vy*r6yp7bx v08 ;* pekrh 60.7 m/s at an angle *b8y (*y wktpr;hp ex6r0rv7v of $40.9^{\circ}$ 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 run a 1500-m race at a velocity of 4.0 m/ 55j4g icpb5 ck,d 3jpi-chi/*djnx(os. If you ran the samedccjjd35ipxnboi5 cg ,/h*-5pkj(4i 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 would be

  A plane has an air s -+k(87vxv* ozlewmfx peed of 200 m/s due North, and is in a wind of 50.0 m/s to the We*(k8 7mvw xfv+oz-l xest. The plane's speed relative to the ground is

  A plane is flying due5 o0c/8 uzvt wcci e4krce,q;( 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 spemc ; 6ickdch 2c6phem( *s64xled 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 horizonj2 z:x .d8kek*wufuc/tally fires a projectile with speed 50.0 m/s in a fou.udfkz /ej2 x*8wkc: rward 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 is8ldj78 6 hbiffcz b0ga+wi36n 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is t gnc ji8whfz36d6+af78 b0 bilhe speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s +ps7k;euif)w in still water wishes to travel directly +psf7ekui);w across a river 1.0 km wide in which the current flows at 4.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in sg/c-w)ier yj/w f0 y 6vu/:o1e+erpn btill water wishes to travel directly acreoc+ / 10e bf/uniwjr:rpwy6 g -y/ve)oss a narrow strait in which the current 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 th+zwre - yo54tpl;v45gm 1k chjkyu 9t(e opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wkyet4t1- jw ;uplohyr5v9k( +mc4g5zater?

  A swimmer heading directly acria e9g m6wig3(k4mq5.s9li lh h2(kwn oss a river 200 m wide reaches the opposite bank in 6 ma(326miiwge gk 5(hh4q.nl9l ik swm9in 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 0 *t (h6hysfywvuych7a-2v ,1h.99 m/s, must aim upstream at an angle ofu w2h176f( vhh y ,*asych-tvy $13.5^{\circ}$ (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)  $m/s$