Which one of the following is an example of a ve)qwgdd 5vc5i. :6t crector quantity?

  Which of the following operations will not change a veyfv .5v l2 7ug-h zu.dxbycfa/1v o62gctor?

  Which of the following is2. ssl52g lps:t 3snuyouts(. an accurate statement?

  The resultant of two vectors is the smalle mx8l r0a +ahq*io9v9est when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectivetme*xbn7r1eqvwdp91 l5 (w s 6ly. When these two ve(1wq*lx1vp6e 5e9d7smn w tbr ctors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the bl0fltdx +8l;following is a possible answ8ll;fxdl0t +b er for the magnitude of the resultant?

  Three forces, each having a m)8ymv w+/o8 wfxw e:6rek:y zuagnitude of 30 N, pull on an object in directions that aro wmrfx:u/) e:6k8 yzvy+8ewwe $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown ve s4 jo fvlv;j(8crl/px, 9x7bdctor is

  Ignoring air resistance, the horizontal ht 9;q,s8f wnacomponent of a projectile's velocity

  A ball is thrown witsz6s+kpa/cr vt+,t: ah a velocity 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:.iwgs m8s8 sxc67xl w horizontal component of a projectile's accelerationcss.gi s m8l876wx wx:

  A soccer ball is kicked with a96hzahsy 6gp2n*ljpl ;d 7klx0r.d-o 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 vector6 n0dgn6a5 sa8mo(bqn of an object is directed anti-parallel to the velocity veb8nman s0q(go665 andctor,

  If the acceleration of an object is always directed perpendicular to its vrxplc,fx pl r14 7 r/l+qo6r8eelocit,+r pqll71xr8 6xrrc4p/olefy,

  At what angle should a water+iyqx9*28 u; ee/ bvoj-igqf+j3xry, z ,osb k-gun be aimed in order for the water to land with the greatest horizo je bir qugisxx32kzfv+qoeb8*,y+o ;/9j y,-ntal range?

  An Olympic athlete throws a javelin at four differense5sngfo1z9em kw06p(s t- 6o t angles above the horizontal, each with the samees0 k-5e nw9 ozsg6(p1 6sftmo 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 your hand 6f1u z2)zj:s n:yeuoo with twice the velocy)j6: uuoo:nfz se12 zity 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 o/b 6inn7nmtl:zz .x:p2miwe 8f 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 re82,;uu k qqvbpaches its maximum height, how does its speed compare to 2bu upqv,8;qkits initial speed?

  A stone is thrown horizontally from the top of a tower at7 owln081*)j96 jtz pqaf70r nvopaw d the same instant a ball is dropped vertically. Which object is traveling faster when it hits the 7j6d79nr 1 )jvzfnoq plwawa *o008p tlevel ground below?

  A bullet is fired horizontallyaagto u)./xb -7mwmylpm+ +h)0ccx h 1, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compabx)0 1)-wma+c u7 h/ hamcy+o .gmpltxre the times of fall of the two bullets.

  A plane flying horizontally at a spee)uw4. p +xkllud of 118.2 m/s and at an elevation of 283 m drops a package. 7.8 seconds lat4x)pk+. ul wuler 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 one seconwislb 4m nr9/6niisi2fe5j5 6d later a second package is dropped. Neglecting air resistance, the dw f/4 js55iniei s9n2lr6m i6bistance between the falling packages will

  A pilot drops a bomb from atl je (:gyi:4tq ),sbx-6lpfi plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the grounlsti bgif4x:,q6l-p je)(:ty d the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixots cf jc8+p,;z6x yaf2-mip1th of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you wouldjc ipa+ 1spy czmo2xtf-f68;, on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level qa)03*nb yc9 gk9flx v sj.(vjroad and pass lkcsbxq9(ya j.gf *)j0n vv39a car traveling 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 s 1ar ws b -rin7cqlm2h78tyo)2trong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting o-qcrn2ta ywsb m 182 hi)l7r7point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. H6cdgi; *9jd iuow much time will it take you to move 12 km downstream, in a river flowing at 6.i9i6;djud* gc0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below tvhh*9h5 k+r slhe +x axis. The y com* kh hl5rvs+9hponent of A is

  If a ball is thrown with a velocity of 25 m/s at an a6 x 0b p0w)z*i.fvitgongle 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 directb +pjdjz( q0/jion north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have bp /jjz(+dq0 jyou walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vel bu20) jlu14oalmnh5/bp6s muocity is 8.)hnm0lsub2u4/1b5au o 6m j pl00 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a ir3 y6*c(tvtxi7ujlsk0v :v:600-m long shadow over a level ground. At what angle is thxu*yi v:rt(6 cj :ikl07tv3 sve Sun elevated above the horizon?

  Two vectors A and B have compozyjtq 2713gcgqgw6q 8nents (0, 1) and (-1, 3), respectively. What are the components of the sum of ggg2qw6q7qzc j13y8 tthese two vectors?

  Two vectors A and B have c65mc ,0bdj4 /o*nx(nl :c8 uxwv (c anhax9sldomponents (0, 1) and (-1, 3), respectively. What is 0n46nm:l *wavs ,c( 95oa(xbu /hx8dclxcdjnmagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vectm,pezroj+ yik1 .i//+j ictg9o/zxq1 or B = (3, 0). Vector C = A + B . What is the magnitude ofi z1 /tec,+./goo jjpqim x9/yz1+rik C ?

  A car travels 20 km Wes c u kurokrk27kw9(r8gd7+ y1ft, then 20 km South. What is the magnitude of its displacemen8(kk o2r fg79wk rkc+y du1u7rt?

  Three vectors, expressx + v)**v3i 9mmb k7tm ieayfzk*zjs:4ed in Cartesian 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, expreara,( a0o9qwnssed in Cartesian 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 tkv7j38ono 71 l 7tb :6c)abahfo+lvr= (+3.0, -8.0), what is the magnitude of veorhkl7nv1jtal : ab bf)367otc 7v+8octor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is thu v qu28sc(1cke displacement of the jogge8 kq(1cc2vsuu r?

  Two forces are acting ;9n3mg8nmz1c0xb) uch5 ejb v on an object as shown in Fig. below. What is the magnitude of the resultantj5me9c ;ngb)1u 3 nmhbz8vc0x force?

  Two forces are acting on an *57vbu k(zrsuobject as shown in Fig. below. What is the direction of the 5usk bz7(u*rv resultant force?

  Vector A is 5.3 cm long and points along tki f j2:hucq-0 bkw,syea s:;1he positive x axis. Vector B is 9.4 cm long and pa;ys1: e,-02bjsu qfwh kick: oints at $+26^{\circ}$ 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 71 cm lonv0xkqlcp;jyn zd; (;k2 29;6oyuhi rng and points at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 38 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 initihx +5u.ydsxae(-f/w gal speed of 22 m/s from the edge of a cliff. A stop watch measures the stonew.xf+aug -sdeh 5x/ y('s trajectory time from the top of the cliff to the bottom to be 4.7 s. What is the height of the cliff?

  A girl throws a rock horis.4f6 fs,hu cezontally, with a velocity of 12 m/s, from a bridge. It falls 14 m to the water below. H6.,cshfs fu4e ow far does the rock travel horizontally before striking the water?

  A ball thrown horizontawv gfbiaw -.s5ab/7c3iv5r 9illy from a point 27 m above the ground, strikes the ground after traveling horizif5/sa w7vr.39- 5wivbabc giontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speedts,a ,c.o; asc of 12 m/s at an angle t. ccss,,a;a oof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jb rz.o ;5lo(ss4g/mfjump goes into the jump with a speed of 10 m/s at an angle .f5/og;msszlr b4o j( of $33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 59.2 m/s at an angle of*k 6 akxsr auepr*(n7( $18.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 32.8 m/s at an angle of biu,/ jg :t1dbrv( h3v$19.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of . zsdmqc 9p)rvq+bkp(+51pf p$30^{\circ}$ 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 27.2jddt5 l,7d xx9 $m/s$ 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)thq7iz lp9egwk 3;.m 67.0 m/s at an angle zqmh7.kt pi; w eg93)lof $47.6^{\circ}$ 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.:5u1mqq (w:re oish 0e0 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 r:i qe:u1wq s5oe0m( hwould take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wind of u u7fk75dhj+h(6i rbh 50.0 m/s to the West. Theh i+5 ubhjfh(677ukd r plane's speed relative to the ground is

  A plane is flying due Sz (m2q2nffvxhaixxfg).1d- 3- wcwg9outh ($270^{\circ}$) 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/h is he(hgt-,s1.e 3lj0cxma 7 qq, / q(yh jowfdudl:aded $30.0^{\circ}$ 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 *3kb0tt ijx i8200 m/s horizontally fires a projectile with speed 50.0 m/s in a forward direction3kt0 i8xjtb *i $30.0^{\circ}$ 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, isg 2jh-1zgbsrg)46 tjs directed across a river with a current of 6.0 m/s. What is the speed of the boat as it cstj1h2g s gbr-)z6j4g rosses the river?

  The driver of a motorboat that can move at 11 m/s in still water wishe rp s8:85ybsyds to travel direct5d:sbs ypr y88ly across a river 1.3 km wide in which the current flows at 3.2 m/s. How long will it take to cross the river?

  The driver of a motorboat that can moverj+;mn cvx(z8 at 10 m/s in still water wishes to travel directly across a narrow strait in which the currenr(v;mj +8 zncxt 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 opw2al xu r+ya +dtyer,kf ,f8.5posite bank in 6 min 40 s. She is swept dowtaua52f+ rd+ey8f ,yxkr.lw,nstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the7q iy0py;uwhn(az1zq; fff1 ( opposite bank in 6 min 40 s. She is swept downstream 480 m. u w nq1(afzpi(y7z;q;1h y0 ff What is the speed of the current?

  A boat, whose speed in still water is 1.19 m/k:+c6d r+ .kulfh,pogs, must aim upstream at an angle ofcr kogdlpk6.++h uf:, $18.2^{\circ}$ (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)  $m/s$