Which one of the following is lb g59:s3 sxnzgy0(qxan example of a vector quantity?

  Which of the following operations will not change a v( (fnttil45.rn dld4nector?

  Which of the following is an accurate statement?;my-kve yp /wm f/9+eo

  The resultant of two vectors is the smallest when the angle between cum*7q,/ ,cbztp (v0 p fcjfh)them is

  Two displacement vectorz+ic5f;6 owg43qms yfs have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are addew34ziqo56f y ;+ cfsgmd, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50s,qaxz9c 9j ,b:m vx/pfakv10, are added. Which one of the following is a possible answer for ck:j/ 0f qa9z pv9bx,svxa1m, the magnitude of the resultant?

  Three forces, each having a mawk;u we:570tqnq38d6u ejb t xgnitude of 30 N, pull on an object in directions that aqqt30 ewun5 et8w7xjd:6; buk re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the;q ix94k-ke ar :au5ux unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velocida/fmdp;gc8xi) vpe1f7+*h ( ,z izvrty

  A ball is thrown with a velocitypzil hy9o(6l / 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 componej;6 6j k1.fpf lowqgq+nt of a projectile's acceleration; 6plf g+jkof61jqwq.

  A soccer ball is kickjz 8++/gv fbtked 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 vector of an object ixt 0s-,zhtpik iu):3.kude hj *97oxfs directed anti-parallel to the velocity vec)tihxkze, u h7 ofs d3p.t0-ik*9jx: utor,

  If the acceleration of an object is always directed perpendicular to its veloa(khusk -ei 9+cit- a(u9h ki+skey,

  At what angle should a water-gun beucepz j6:k)p6hn u/d9sanw a)8.n 4ax aimed in order for the water to land with the greatest48ch ae 6wu))/z n: dujka6p9.xspann horizontal range?

  An Olympic athlete throws a javelin at four different ang;xy- jlq0x j-iles above the horizontaqyjj-x0-l i; xl, each 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 second time. If th5r:mpf zyb*/gsazre0l w.y 5-e ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared t- p lbe55gwm:. arzsyy zrf/*0o your first serve) would be

  A ball is thrown at an0v) w0t9my3l) 5oznden+mjptvw+l x/ original speed of 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 reaches its maximum height, how do dzubt7pp(b9 wdy i5+9es its speed compare to its initbpyz(9wi tdp 5u7d 9+bial speed?

  A stone is thrown horizontally from the top of 04cjh-+zk:g l30 )cjaypss rna tower at the same instant a ball is dropped vertically. Which jr 0j p0kac+s-)y z4ln:sch3gobject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a se8r7 2ef5foe4 1pt9 yathjlq6econd bullet is dropped from tptf hej6ola2e9e14 t87yqf 5rhe same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a spenh;)q;na +m c)i t(o3o7wau sned of 91.3 m/s and at an elevation of 265 m drops a pau7a nwh an)m(sicq+) nt;o ;o3ckage. 5.2 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dro-l.i-kop boxi (h.6r; qh2xgepped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falliq-i xh;lr2 k.-i oxg (6bo.pehng packages will

  A pilot drops a bomb from a ucn87th/ds fv+/ +ngqb77 ktp plane flying horizontally at a constant speed. Neglecting air resist n7dv+hbqp g /7 +tus/fk78cntance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixtnc)s;, ekx 3 )vvcz7 hk93cualh of that on Earth. If you hit a baseball on the Moon with the sk c3h,vlcceuna7v zk x 3s;))9ame 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 a straight, level road a)/l6e-skz vefut 9gw 4nd pass a car traveling at 45 mi/h. The relative velocity of your car towe te9lgfkvz u)4/6 -s the other car is

  You are trying to cross a river that flows due south with a strong current;(kes c wt5pmedek2t3yx ;s(k c.0;lb. You start out in your motort.2(e k;lk3; t (pb ;ex5c ywscmes0kdboat 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 wateu(q6q.uj0g(54l78cl cwth c(w bebbvr. How much time will it take you to move 12 km downstream, in a river flo60 tuqejv(7c qchwb 5 4c(ul.g blb(8wwing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degfzdplbo.yjt)7tg8h s+p. 6 0f rees below the +x axis. The y component of A i06hz..f s ) y8gl opbt7ptfd+js

  If a ball is thrown with a velocity of 25 m/s at an anglj-1g qd2lyprh 4-pjm-kl 2fm6e 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 etp)rz7dc,q7/x ) sbt qnd up 2.0 km ndq x7p/s) tzcb t)qr,7orth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 0xma-6u5z q +3kwadar+xt8dj 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the directidd53x6x m+a u0rz atw kaq-+j8on of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long ohk0k *mwlihj v*z+9 8shadow over a level ground. At what angle is the khl9vw*k8jih+0m o*z Sun elevated above the horizon?

  Two vectors A and B have compotrrqov- 8k)0el,yoe 8 nents (0, 1) and (-1, 3), respectively. What are the components of the sum of these0ryr)q- voolke 8t8e, two vectors?

  Two vectors A and tti,f:cd5 xgeqmc:9 h+w ( 9igB have components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of theqxgh9,d9e:cctf 5m +ti(i:wgse two vectors?

  Vector A = (1, 3). Vector B = (3, 0). ;wmcfn48dx* fi gi2q(Vector C = A + B . What is the magnitude of Cwxgnf( qci i*dfm482; ?

  A car travels 20 km West, then 20 km South. What is the magu/eigxql3yw* 25 2swq2 rdrh (nitude of its displacementw2qulrs/x di2 h53 e*gw(yq 2r?

  Three vectors, expressed in Cartesia+823- 8zym 2cpxzr.80lnmmwsfwz ) q zipvg v,n 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 coordisa0tr8mw .vfd8 o3 g)rnates, 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 magnitude ofh70p de1q rd0vk f2fe4 71f4fep h k20dvr0 qdevector C = A - B ?

  A runner runs halfway around a circular paudg l)ixtv,4)8hknz 0om7sd* th of radius 10 m. What is the displacement of thzgo)vkd hsn*i07,4x8 uldt m)e jogger?

  Two forces are acting on an object as sho+okmpk3e0 ey5wn in Fig. below. What is the magnitude of ty0 k3 eemkop+5he resultant force?

  Two forces are acting on an object v g 9jtf+w6igbz9qg*8as shown in Fig. below. What is the directiongj6q8*tgz99f+bgiw v of the resultant force?

  Vector A is 6.0 cm long and point8.+9q/vjvz ez is 4xc) pr1/cfkifzl+ s along the positive x axis. Vector B is 6.3 cm long and points ale8+xq i4+ vc/fz. s1v/fcizrp kjz 9)t $+50^{\circ}$ 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 71 cm lon;t .y: p+kg pess+yel:g and points at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 30 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 speeywt), kk uc7s2hzd7um e qh,75d of 25 m/s from the edge of a cliff. A st,whqs5 7d ck2uz7)h kye,tm7u op watch measures the stone's trajectory time from the top of the cliff to the bottom to be 3.0 s. What is the height of the cliff?

  A girl throws a rock horizontalyv8twb2so ;51x qydr8 ly, with a velocity of 10 m/s, from a bridge. It falls 22 m to the water below. H5wrvqydx 28b oty1s8;ow far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 30 m above the ground, cz)s6tyk7kbr:7/l7 r gh;g x fstrikes the ground after travr6s/)fk; 7:7 ygkl7brxcg t hzeling horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a sp1. t s:r.qzdv khvei6+eed of 12 m/s at an angle okvqihz:.s1edv t6r.+ 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 13 m/s at g*bdrlmotnb0 v ayc*p)(56) san angle b 0g )yv56b ldaonst*p (m*)rcof $36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initiahp nvr-de )bgnd;0(p7l velocity of 21.8 m/s at an angle of $28.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 36.3 m/s at an angle o5gns0ujpj -q2f $46.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle sgiba0 18dc :tof $30^{\circ}$ 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 27.4 dl5cht0i7qv+b qrd tiw*:/n3prfx.-$m/s$ from the roof of a building 45.1 $m$ 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 s r iy)ifv;0x2g+vqc 9ypeed of 39.5 m/s at an an+yxrqvvi2f0;i c 9 )yggle of $38.5^{\circ}$ 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 wil /kd.e-gz- w6mbrxw2ejr: m:t -wyp +nd), 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 whirdmz/p-.6j: ty 2ge-x- lrm: ww+bewkch 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, ;)mhyy4q( zfg and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grounhgfy(qy4)zm ;d is

  A plane is flying du1gljyraq)dhfi5 u;m)nk/wcc;j9- j -e 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 speed of 120gv6/gk) 0 tbbacg :f3n73vtll 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/:n6:bzk po)2 gp uuva 200 m/s horizontally fires a projectile with speed 50.0 m/s in a fvz/gpon::uba 2p u6)korward 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 is 8.0 m/s, is direct9sxwt ;;e6 95fxu w k7m:ad rnoix7)hzed across a river with a curre 7f;au: 65wwkxxx; sh m)tr9 znid97eont 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 at 1h) tj7bm:*r er0 m/s in still water wishes to travel dire h :j7)*tmrrbectly across a river 0.6 km wide in which the current flows at 7.9 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 1 q ;hje.uw7jfwishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle eq; 7.jhfuw1j upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank ick 9e) fgce971ok-v9k uptaz3 3)e tocka-f9kcz eku7vgp199n 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reach4sx2dbg* /sq fes the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of 4s/g*xdq f bs2the current?

  A boat, whose speed in still water is 0.94 m/s, must aim upstream a8d gcleud; b b i(q4q09h9h;cpgb;si8t an angle ofbc4;hgu0d9ihbql; qdci 8b; sp89eg( $22.6^{\circ}$ (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)  $m/s$