Which one of the following is an exampbp8ih5fe0 uw+k3aoq ,tq)sk 1 le of a vector quantity?

  Which of the following operalc easbxix *w(h)sh 2o:k).-ltions will not change a vector?

  Which of the following is an ac fq+rp-3w 3esscurate statement?

  The resultant of two vectors is t sr;o+z(2gdns*e3laohe smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7 l78.n1m6 sjce/qtsrg1 awv1i.0 m, respectively. When these two vectors are jms /gs617wql118aitnev r.c added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one ofm6k7p0grqvr- 1rr;zbqj,i0 f the following is a possible answer for the magnitude of the resulr0;r, -mqg670iqpkfr vr bj1ztant?

  Three forces, each having a magnitu.+, mfxwrzh-usb2gg ,h 6b5hmde of 30 N, pull on an object in directions thath, bs6 gm25hxbhu, zg-wm+f. r are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unk .oya7w v-d6 uzn29cv fgj.m*rnown vector is

  Ignoring air resistance, the horizontal componenwg2f tn3ovew02 8 6alwt of a projectile's velocity

  A ball is thrown with a velflvnrjed.fl/e e0ju)+ kgeoxm9 z ,8u9c2,4vocity 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 horizontal component of a projectile's accep(q1k2vn5p0b zy yp5blerationbq pp(15kyn2 5pbyv0z

  A soccer ball is kicks70es x1l nfg .1ztsh2-(kr zbed with 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 vefa/8rtb 4dqt;w .wks *ctor of an object is directed anti-parallel to the velocity f r4kb;a8dq t*.st/ wwvector,

  If the acceleration of an object is always direcy tz-je),b7cwt r6h7v n8ikn f/n (hc;ted perpendicular to its velocity h67 7-(ykwtit /,benc8hz)nr fj;nvc,

  At what angle should a water-gun be aimed in order for yfyzor0j)ef (, l2l)hthe water to land with the greatest horizont) 2zfoy) l(fr0 hlyej,al range?

  An Olympic athlete throws a javelin at four different angles above the horizouqps((z 0(2vfsa vjj+i-v:rm ntal, each with the sa2 u(:s(ma 0vv- q(jrvji +szfpme 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. a ,6ne oop-ou*n)3t u yyg*,glIf the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) wouldp3,u on,-yg ua)n*lgtey *oo6 be

  A ball is thrown at an original speed o(vok2 ce ,uy6zf 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 reaw+j5:b zasr p*ches its maximum height, how does its speed compapjz*a5bsw+r : re to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant a b a/+v/v1c8+wo wkrygzall is dropped vertically. Which object is traveling faster when it hits th8++w krwyva1/o/czvg e level ground below?

  A bullet is fired horizontally, and at the same instant a secooq.bawuag0p.i: .m- end bullet is dropped from the same ew-.qpia bg.:auo.0 mheight. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 109.4 m/s and at an elevation of li:5q hgy k5x7g4m*ie,s) fcy215 m drops a packah i:5,ye 7kfcyqg)*il5gm s4xge. 4.0 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped fh6vrjqgh98 9*re;eeo6m p 0pdrom a plane, and one second later a second package is dropped. Neglecting aire;re hv6 069ppg9oj*mer qh8 d resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying w t,1gw2 qm+3 (ikkej o:prbh9horizontally at a constant speed. Neglecting air resistance, when the bokog 9mp,b : k(3t21h+r iwqwjemb hits the ground the horizontal location of the plane will

  The acceleration of gravity bjhjhlp4h *k:w5h liu0vsw uk1(i/b;80x sm+ on the 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 angle) that you would on Earth, tihb sl5(w/ :ul48;u0 mpv0khh *+jwjbsh1k xihe ball would land

  You are traveling at 55 mi/h in the +x axis relative to a strwqkdl)zef8m6 z;wr6:h;:. o gzcyl6n aight, level road and pass a car traveling at 456kzmelfn qo) yglrw.6d h8;w;zz :6c: mi/h. The relative velocity of your car to the other car is

  You are trying to crob-;a te f6m9xdss a river that flows due south with a strong current. You start out in your motorboat on t-b6xma f t;9dehe 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 u u3o;kcc6ms- much time will it take you to move 12 km downstream, in a river flowing at 6.6; 3-uksmoccu0 km/h?

  Vector A has magnitude 8.0 m at an 3 .+pgs- p/ 9evqk;qxfzrufw9angle of 30 degrees below the +x axis. The y comppqse.u3 pfwrqx-9+;v k z f/g9onent of A is

  If a ball is thrown with a veloos5i j 9riih 4i)8ti0icity 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 o5xc 2ek(z(prof east and you end up 2.0 km (eor5z2c (xkpnorth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves wity 4xir+qi0 t6 dh.t9czh a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the directionr 0itdxz.6 y9h+qtc i4 of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At8i a3y )9bxc)v p9:pwc(ewjrof1w,vg what angle is the Sun elevated above the hoabwj9 rv 1),i f9(pwpc )8wc y3:xeogvrizon?

  Two vectors A and B :5ot 4ca9+n2f.zikk tbxwn8ehave components (0, 1) and (-1, 3), respectively. What are the componebekt.+onx 9 tfk2 :wza58cni4nts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whatcc2/ v)v m4p4 d1dz :q6gsuaxzb*wpm 0 is magnitude of4 /z*aup46v m2xcc d:p zdgm)s1wbv0q the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vectb/h -c9mr9 ijsor C = A + B . What is the magnitude 9shcij9 b/rm -of C ?

  A car travels 20 km West, th.m 1:/epjke;l*k ry 9 zcunk-7 yob pq2:eetg8en 20 km South. What is the magnitude of its displacementoye eq7;y:b/pktpj1kml-2ezngkc:r 9 u8*. e?

  Three vectors, expressed inmdtmh f.1rb5r idqhc:-+0 1f d 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, expressed in Cartesian cooafd ba2.08sn crdinates, 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), wht:r8j/ /uujom at is the magnitude of 8/mujjt/ :ru ovector C = A - B ?

  A runner runs halfway around a circulaex/a9p yq sjrs1f45d- r path of radius 10 m. What is the displacement of the/fx 45dp -qsryaj9s1e jogger?

  Two forces are acting on an object as*p5/qh+ he iqj shown in Fig. below. What is the magnitude of th/*qq hpj+5ih ee resultant force?

  Two forces are actinujyqkrq ,5 )xt2:yz2rg on an object as shown in Fig. below. What is the direction of the rtx,5 qjqku:z2y2)ryresultant force?

  Vector A is 3.7 cm long and points along the positive x axis. Vq1u+vx+9 y uzzector B is 5.0 cm long x+yzz+qu1uv 9and points at $+52^{\circ}$ 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 50 cm long and pono(u2ikpc0n.lai 4 b :ints at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 37 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 ocs2zg/ q2-de sf 28 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the tqsz -g/s22cde op of the cliff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a b9-oieh2 g wr sy0tkn /8:lvq9velocity of 11 m/s, from a bridge. It falls 17 m to the water below. Hov-bkr9es o/qgt :hl 9y8w2n 0iw far does the rock travel horizontally before striking the water?

  A ball thrown horizonc ro9f 1ky:hd,+e3gxktally from a point 23 m above the ground, strikes the ground after traveling horizontally a distance of 23 m. :1 fxehg +k9 o,dcryk3With what speed was it thrown?

  A jumper in the long-jump goe62 db 7knuhh6r5y/;mf imce ct7: d3was into the jump with a speed of 12 m/s at an angle o7b6kamcdh2tycmu: n;3w7d re6 fh5 /i 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 10 m/s at an anglzbhn,5:lpqg) s*h 0fc h/8zqne bp,/*g)h0fnq5n h lz z8h :csqof $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launchedi:v.j:g-0i mk+sff c i2 jt2dk with an initial velocity of 35.9 m/s at an angle of $25.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 20.0 m/s at a2 i sn862*e+agkrycqdn angle of $33.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle 9 :0u/9gx( lq qmsnxxlof $30^{\circ}$ 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 ho6mkri/7:d cba t 4sez)*sl-udrizontally at 26.2 $m/s$ from the roof of a building 44.0 $m$ 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 from ground level with an in.w 7+v/jvvunoitial speed of 48.0 m/s at an angvj/v+v . un7owle of $38.1^{\circ}$ 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/sy;ztz gtd tc5)nxd8. ,. If you ran the same race on a day when you had a constant headwind.)y d5,zn ctt8tgx; zd 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 20oxavp:a - a;1vvir:4lj1 uep. 0 m/s due North, and is in a wind of 50.0 m/s to th;j p:1aul. i1xvaao: -e v4rpve West. The plane's speed relative to the ground is

  A plane is flying due South p;568j rhfv rb($270^{\circ}$) 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 q k6r/9c/ tjwm21 rm08pnjkcpheaded $30.0^{\circ}$ 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 horizo xew.(2oysqt ;t .vqk+ntally fires a projectile with speed 50.0 m/s in a (2k.owx yvqt.t ;sqe+ forward 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 stf 69k))kfb*c no:0)fsyj sm) 4d ochhcill water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the rivm49sh hc) 0okjy:f* bfsn)kc))f6cdo er?

  The driver of a motorboat that can move at 20 m/s in still wat5sa5l r1*dq7n edj7jker wishes to travel directly across a river 1.8 km wide in which the current flows at 6.2 m/s. How long will it tak ed1q7*k rdlj57asjn5e to cross the river?

  The driver of a motorja5jytr:i5 3i ; yyy(eboat that can move at 10 m/s in still water wishes to travel directly acroryj yaiy it:y3;(5e 5jss 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 the oppr8kfe x( 3y4z5ik1t coosite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim infr(c53txy kkz 8e1 o4i still water?

  A swimmer heading directly across a river 200 m wide reaches the oppositi/ 6vjxq6oxrf uqke-* de812o12o q cze bank in 6 min 40 s. She is swept downstream 480 m. What is t6- xj 1z8qf *qx oooveq k2u6cer1i/d2he speed of the current?

  A boat, whose speed in still water is 1.10 m/s, must aim uw9 6 g2*kj3d k8ezdjhspstream at an angle of *6 9e jw2zsdk h83kjgd$12.0^{\circ}$ (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)  $m/s$