Which one of the followi*)l:khqn p *3b *d* ;jfopjef)uxoq sucj 0b*3ng is an example of a vector quantity?

  Which of the following operations will not change a vectorfje. 5g0yevla8mgtwo2/,kl; n uvs8 3?

  Which of the following is an ac )jx4ih5 bs.t7v (cxrt6ma9h;gj oi /rcurate statement?

  The resultant of two vectors is the smallest when the angle between them is/yqx8pb d) f11zr lyg5/k;vf- og 5ra 4c)ivdm

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respecta csw.-er(.yk ively. When these two vectors are added, the magnitude of( sewr-c.k y.a the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the folloe9hcv q2o dw4nn5x,3qwing is a possible answer for the magnitude of th 39wqqeo,42vncnh 5 dxe resultant?

  Three forces, each having a magnitude of 3sqgjj* iwe kzkf a3;,l4.q7u/0 N, pull on an object in directions that are j. eukz/l aq7sjf*ki4;3qw,g $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectmd5-loy1: c i4de e+hmro9a 571 fouftor is

  Ignoring air resistance, thl( i i5zjxc32he horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an lcbtk1lxay( d3 z6 nsyj *0t2(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 kbjm v og/4,r4gpw87yof a projectile's acceleration 48 morybwpkg j,74gv/

  A soccer ball is kicked withlq-zbs yb)) i(g ;k7;mz(wqb.yrf/dm 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 0ovlfr 9is+g.of an object is directed anti-parallel to the velocity vec+rsvol igf.09 tor,

  If the acceleration of an object is always directed perpendicular to its veloc eqa7e*10f2kro4mp t city7tecf4e0 o 1a2rmk q*p,

  At what angle should a wat s4 hg;n:mp)dter-gun be aimed in order for the water to land with the gr4std)m;: ghp neatest horizontal range?

  An Olympic athlete throws a javelin at four different angles abovn/ca /kc x03lwe the horizontal, each wi/cnx klwa/ c03th 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 tb*u ) 2g)wskfy)e6cheh dm9.xime. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your f)ef xdwhs6b2 yc).mg )*9h kueirst serve) would be

  A ball is thrown at an original speed of 8.0 m/s at e,y*:yg3rq lorv(tvgq* 5ih ,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 fiellts*rp/(/y/2 ds drmrd goal attempt reaches its maximum height, how does its speed compare to its initial speed/s2/rr /p tlmsd( *yrd?

  A stone is thrown horizontally from the top of a tower atbj r-zbh .xk p4*r5d(8pxc8oy(knf : v the same instant a ball is dropped ver.kvdph4jr( xn*z 8 bxb8:pk( rc5f- yotically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at thl3j4b acm(bawik -5 f,e same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bul , maba lb5c4jf-i3k(wlets.

  A plane flying horizontally at a2hp)c4l 1oi th speed of 69.0 m/s and at an elevation of 191 m drops a package. 2.1 seconds later it drops a second packagco4th l)1ph i2e. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one v-:y99cic0 d-v) pybxeivo ub c2.k 4ssecond later a second package is dropped. Neglecting air resistance, te-)c-d b :yx.90b4c v9uoi2 pi cvsykvhe distance between the falling packages will

  A pilot drops a bomb from a ply) t8 at) )xqlxzla(6pane flying horizontally at a constant speed. Neglecting air resistance, whe86p)x) z lyqtxt )a(aln the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixt/z 7 za(h 4pbr:,tyq4vnvo7jv h of that on Earth. If you hi(tjn,q a/ozv:4br7y 7vzh 4vp t a baseball 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 rel g1k jhgs/xyxt0w5mgi247 .f /hgccz 7ative to a straight, level road and pass a car traveling at 45 mi/h. The relative fjxg7x1skwg4.y c c7i2tzg h/g5h/0m velocity of your car to the other car is

  You are trying to cross a river that flows due south with a s9v6jfyvfj . qjo 6i9)ltrong current. You start out in 9 f6qojij6vvyf9) j l.your motorboat on the 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 water. How md4qd:7e59r:u k lnxcw uch time will it take you to move 12 k :9x cd74erdunl:w5k qm downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axisj(*yh ot,io) s. The y component of Aot,j (s i*hy)o is

  If a ball is thrown with a veloctri;d, hy)z6 aity 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 of east*wcn,( s0rx8:v .1hofw ( q jekhttky( and you end up 2.0 km north and several kilometers east.y( the jq.:w*(nvs,t 1k 08wh crfkox( How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x componeu)bs, h 3id3-metnp; tnt of its velocity is 8.00 m/s. The angle between the direction ou;3-3 ,p dbis) tthnmef its motion and the x axis must be

  A 400-m tall tower casts a c,pr7vxw*em vvj 3d s922wz9 l600-m long shadow over a level ground. At what angle is the Sun elevated ab cmwlpe3j v*r9w2,dxz927s vvove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whao(i8t;n 7xvo l2qjyh.:p *ez* y0uucmt are the components of the sum of these two vecty0*olxteo:qnjm2pvz .u 8(hc*iyu 7;ors?

  Two vectors A and B have components (0, 1) and (- :n. 7) 4l8l6cx graxxw4ttjex1, 3), respectively. What is magnitude oglcjtnxxxwl4 8a6:.x 47r t)e f the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vectorxk)w2v+hddjz i3x1 3 m C = A + B . What is the magnituded )hzwxkj3i3m1 +2vx d of C ?

  A car travels 20 km West, then hcyq lbm8 w(;/20 km South. What is the magnitude of its displacemc(hm bl y;w/8qent?

  Three vectors, expressed in Cartesian14qeam6.3rbn e nfrc8j8k/bq 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 Cartesian co xcm1+4( i , c7obpekp.jngt0jordinates, 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), what is the magnitud1.jue cs9d/penl; e4fe of vectorce;/4l n.d1e ue pj9sf C = A - B ?

  A runner runs halfway around a circular path c -vuqd;dw7j: wlh:)wof radius 10 m. What is the displacement of the jogh : w)luqj;d-w:7dv cwger?

  Two forces are acting98f5loj u ;5 z 7s5)f pxxurjifjqf 3edtr0g0, on an object as shown in Fig. below. What is the magnitude of the resplf x5fjeu58qrfj0f9z) t,3x; 5 sojd 0 gu7riultant force?

  Two forces are acting on an object as shown in Fig.7qierl+h *mh6ok i:3, xyho5h below. What is the direction of the re, hx7e:k5i* 36 +omloqy rhhhisultant force?

  Vector A is 5.1 cm long and points along the positive x axis. Vector B is . anmy8tqly)z* ,de)u5.4 cm long an l) .8ay*dyt ,)zenmqud points at $+42^{\circ}$ 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 long s.*wtnx fd3.m and points at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 31 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 speed of 24 m/s fro 61 x6) jmsnu8pfjjqe)ra5t7vm the edge of a cliff. A stop watch measures the stone's trajectory time from the top m f68)a 1vp)jjutjensrq 76x5of the cliff to the bottom to be 3.7 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bridge. Ibt+-ez jqup;7 gcn2i/ t falls 29 m to the water below. How far does the rock travel horizontally before striking the iz-etjp qb/c+n gu72;water?

  A ball thrown horizontally from a point 21 m aboveqevpx8a1r7 y0us /0m q3z5 zua the ground, strikes the ground after travee1va05 3z7z8uam p0q sr xuqy/ling horizontally a distance of 22 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at nqu nh/;hcu)w;, tzp) an angle op,)q)nth zwh u;;u nc/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 the jump with a speed of 14 qwsu00d+ w1-78;ousm husrkn m/s at an angle m 1d; kwq8ss0our nwu-7su+0h of $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launc/n ))bko4fc krhed with an initial velocity of 30.1 m/s at an angle of $32.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity;d (l5/uezhzd of 35.4 m/s at an angle of $33.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firee6to m;x: g+.bt0izf yd 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 horizontally at 2q -vmev epgd089r4:t y6.0 $m/s$ from the roof of a building 53.0 $m$ 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 frod/2tkgpwsn h htd09.x 9q6o5am ground level with an initial speed of 48.7 m/s at an angle ofn/ gx5 69 .ktp0ohswqa29dhdt $39.0^{\circ}$ 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 bnc 53cb72hi m1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constabhi5m7 b cc3n2nt 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 speed of 200 m/s due North, and is in a wind of 50.0 m/smztvci(sw9f :- g *ut/ to the West. The plane's speed r* /t 9w t:ucvszgfm-i(elative to the ground is

  A plane is flying due South (/gie:qw6 *r81w ne bgr$270^{\circ}$) 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 heib2yl, 44ov9p yknk .maded $30.0^{\circ}$ 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 projectile with sx8q ,qg8pc -expeed 50.0 m/s in a forward dirxgqepc x8- q,8ection $30.0^{\circ}$ 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 dira2upi( y3) 3(lrh:xu 3qycltyected across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses aylrx(iyh y3 q3p2uc(3)lt:u the river?

  The driver of a motorboat that can move at 17 m/s in still water wishes to tamv1rx5mlg e61l *+ 9)vv lhrcravel directly across a river 1.1 km wide in which the current flo*la1cer61hv vgv9ml +5rlm )xws at 4.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to travbzx d .1(;fz4dl)yl sbyc u*(oel direct.z us1l4b * ; f(zdo)b(xdlcyyly across 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 wj0y7fvcq (l,k ide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still0(yjcf lq 7kv, water?

  A swimmer heading directly acrl4(f2 gmx z(.lt2allsoss a river 200 m wide reaches the opposite bank in f a2ls2zl(4 l.x(tglm6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still/9ph:np j6 j*sbt;kgx water is 1.06 m/s, must aim upstream at an angle of ;/sj gphkpnb: x69*tj $23.4^{\circ}$ (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)  $m/s$