Which one of the following kd luk +(i dhp uhzabd6zg4bi dl: .2ae0t+.+/is an example of a vector quantity?

  Which of the following operations4n u (v(b1oo /bw(4 qzwcy2qhl will not change a vector?

  Which of the following is an accurate statement? jly./ 4.gkvwoaaq 0jcum6c 0.

  The resultant of two vectors is the smallest when the aw)b/; ohezx0 fngle between them is

  Two displacement vectorsn*g se2)s8vn. rkq2h f have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitu*rsvs. 8nn22efh kq) gde of the sum

  Two vectors, of magnitudes stdzaj53weczt9 v603 20 and 50, are added. Which one of the following is a possible answer for the magnitudaz 9j3tzcs36w0vt5 ed e of the resultant?

  Three forces, each having a mu2. mfkzy5u 1hr;j l/uagnitude of 30 N, pull on an object in directions thf ulyk/ zu h5m;j12.urat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the un8(zuybh(tc. -8 r jietknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velobm0qo: bpxy) ,city

  A ball is thrown with a velocity of 20 m/s atbg +yy) *bsp/ rkg2zzwy po*10 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 pwj0y 8;q j,m )q5a+ athenj(urrojectile's acceleration8(yje w a5)0 qjaqm nrj,h+u;t

  A soccer ball is kicked w;)(nrb ulyld8ith 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 anti-parallel -)l8xjgqy uxz)hn4t. to the velocity vectoy)8)qug lnjxzt- 4h.x r,

  If the acceleration of an object is always directed we sk b, 5kzxnh h.;qc/pmhz qz4;c0t81s1z*zperpendicular to its velocitn 4 ,w* sz 1z.;s/qzcz pkhh081kbczqmhet5;xy,

  At what angle should a t.8ac 5ik*dvrwater-gun be aimed in order for the water to land with the greate rk.t58*viadcst horizontal range?

  An Olympic athlete throws a javelin at four different angles above the hori1-w1qac,l/ oeebegb*zontal, each with the same speede1-1lc babqo / ,*egwe: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 z+4 i: nkwwuzc )+u8tpyour hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serveitkpzwz+n)w u8u:+ c4) would be

  A ball is thrown at an original speed of 8.0 m/s at an ang+pzhr e ,f;nu4le 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 maxim -has* t, gjxt .yun+e )jd)w.r9oq/bnum height, how does its speed compare to its initial,eg9q nhs)r dn/owba- yjxu.j *t+ .)t speed?

  A stone is thrown horizontally 6;k1qgriq zvogj) kn ph- --1v2yj3dq from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling fas pg1);knqgq3zhq61v -io rvd-j- yk2 jter when it hits the level ground below?

  A bullet is fired horizontallyprq bh1* wbi /.jwp32p)vjeu: , and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the ti .p/ w j*1 3pqhbp:ejuvw2ib)rmes of fall of the two bullets.

  A plane flying horizontaiws;6 r,xf ,bc tng.piupp ,6+lly at a speed of 103.0 m/s and at an elevation of 241 m drops a ppcxb,p+,;pu6grsn. w tf6 ,iiackage. 5.8 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a planej+uujmxese eye4wz:: 6t8 f1;w1* yty, and one second later a second package is y1e;e:1w8:6t* mwsue j+yzte uyjf x4 dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane 65 czk1ii5uvh flying horizontally at a constant speed. Neglectin5z 5h 6i1uivkcg air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on y dj- e57abx0yj,ukv 7the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same jj7kyyu -dax5v7 eb0, 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 tav0p5 t,izg3ho a straight, level road and pass a car traveling at 45 mi/h. The relative veltgai5vph z3,0 ocity of your car to the other car is

  You are trying to cross a 9bcbk bl65g2 v jjlcv6)xay34river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach thvj34lb2b cay bv6k5clg 6x)j 9e west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still wate4gtbj4rmt/jyb)/ w/l 3 k,opdr. How much time will it take you to move 12 km downstretl mbjp/ oj4r,3tb)y k/4d g/wam, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 /j,jxbpywmd,g53ut f1 mn(z1 m at an angle of 30 degrees below the +x axis. The y component of A md( gwub ,51jmzjn/p1xtf3,yis

  If a ball is thrown with a velocity of 25 m/s jwo1 epy7dp; j8 (q0eg-ea/ imat 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 and you end u3 6j7.6k xd+njmpfx vwp 2.0jx wpmvkdx6n76+j.f 3 km north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The jf.)q2v20aehpd8 d1k8 ubgv c x component of its velocity is 8.00 pdfaved gu.8k22b8h0jcvq) 1 m/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts1up5d6qvjr 7i a 600-m long shadow over a level ground. At what angle isdu1pvrqi j65 7 the Sun elevated above the horizon?

  Two vectors A and B have componszf :qh6 p :b 7xrwtts.;6tcq*ents (0, 1) and (-1, 3), respectively. What are the components of the sum of these two vectorstb:zx;:*.qh7t c spq6fst r6w ?

  Two vectors A and B have components,-z -do ion+br (0, 1) and (-1, 3), respectively. What is magnitude of thz bdi, nor-o-+e sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector mc3k8:w(yoras 6k (de C = A + B . What is the magnitudeydk:6ar3m ec8 ( (woks of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of iih 01gm*e mrmt 0(,nbrts displacem rt010mgmim*,r(n b heent?

  Three vectors, expressed in Carte0 o* fk(w mjeteu3o,7zsian 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, expresse20-9ku/yz yiyx xk3 fod 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 = (+3.0, -8.0), what io yaf7n9;wag*s the magnitude of vector C = A - Bg ya;n*a9ofw 7 ?

  A runner runs halfway around a circular path of radius 10 m. What is the det5a6b vhgr79df b3y g-+t- h;ech.m tisplacement of375ah+ ebc9hm6b.v yt-g-etfh;rg d t the jogger?

  Two forces are acting on an object as shown in Fig. below. W4/jwtl,8sc gip;ze 8 bhat is the magnitude of the r 8ctps4z ew8;/lijg, besultant force?

  Two forces are acting on an object asc; dr:2o on-je shown in Fig. below. What is the direction of the resrnocj:-o2 e d;ultant force?

  Vector A is 3.2 cm long and points along the positivgrdxh9;-4 s/iaz.nufe x axis. Vector B is 7.8 cm long and points at hgnd-4u9f xar/z.; is$+50^{\circ}$ 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 62 cm long *48qi 8gkearu /b pj+hand points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 26 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 speedla8os/4/u.bylp kd2 b of 27 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from t.8kspla/o/ l 2dbb4y uhe top of the cliff to the bottom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock horizontally,;ga ofu kpeb/uu310r, -nd8fx with a velocity of 12 m/s, from a bridge. It falls 12 m to the water bel0ap-/1rgf ,be8kf uu ud ;nx3oow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, strikes the groun gb4et:e5e-mh9mtd9 ad after tr 9bh t9eed:m5-meta 4gaveling horizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes0:6(bufdfn nz) fso p: into the jump with a speed of 12 m/s at an angle o:6f0f:n fo sp u)b(ndzf $20^{\circ}$ 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 p ekukt,jlyz0j00; 7bzvz )1ja speed of 8 m/s at an angle ovjz7j1 t pkyz,bu000z)e lj k;f $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launcheh(j 1rho)c*yv d with an initial velocity of 42.8 m/s at an angle of $46.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launv6 /y7(r+0 utk lxhxsxdg8j aecx20+fched with an initial velocity of 59.3 m/s at an angle of $16.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angfulz3y6i6 ) cgle 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 atw .*h*u h158 hwo2n2fcddj.mx5zfcmr 22.9 $m/s$ from the roof of a building 48.9 $m$ 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 levean6;gpqp3(wx9wp+hj4 gp.mb b 6,twrl with an initial speed of 65.9 m/s at an angle of g6pgab43r9n xb h,(pqm.6 ;pwptj+ w w$46.5^{\circ}$ 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 wini)yp*n v / ;ic-2zbbxud), you can run 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 2b*-)unipzi/2;v b ycx .0 m/s, the time it would take you to finish would be

  A plane has an air speed of 20+xwo;s.. c pgwc *n.gn0 m/s due North, and is in a wind of 50.0 m/s to the West. The planecxcng*g.n. ;ww .p+os 's speed relative to the ground is

  A plane is flying due Soa -+ y2tp ub6c,rqupk.uth ($270^{\circ}$) 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 ynr9n*a o mfuu8h--/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 firespl.u g3 or*xdkuiv5j.e6b/pqka4 l( 0 a projectile with speed 50.0 m/s in a forwar. (dlq. e/ ilgpx54k3 uu0rak* opb6vjd 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 ak)gt4-i(o djzh su on1+z ;2kstill water is 8.0 m/s, is directed across a river with a curre4 +n-k1j(auigohk)s ;d zo2ztnt of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move ah *67:m(t 3xj1bse)psyzbcq eu9,tv kt 19 m/s in still water wishes to travel directly across a river 1.2 km wide in which the current flows at 3.7 m/s. How long will it tak:t m xy(b1qj h 3 u96e)esv7ztpc,bk*se to cross the river?

  The driver of a motorboat that cax cr1hr8a gd+lgi/eh 8/)hir)n move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angxcer1r l/ghai)g hri8)+ /8dhle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposidq9vf+x ll70 + 3uqcmbte bank in 6 min 40 s. +q dlb +3mq7vfxl 9u0cShe is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading dir8,t,p0ko ig zzectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is thigpt,zzk 8,0o e speed of the current?

  A boat, whose speed in still water is 1.04 m/s, must aim upstreamt gmqezy435f * at an angle of 5q4mftz *gy3e$12.6^{\circ}$ (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)  $m/s$