Which one of the following is an example of a vector qua9etd,p1ej-b.e5f4:lv o k y rontity?

  Which of the following operations will not /z5nkd ,yof /lchange a vector?

  Which of the following is an accurate statemqebrn,r+:om ;wkflk/kn3g /7f9 joz+ ent?

  The resultant of two vectors is the smallest whe ze v(2a3+n 2at5xezbimoan2:9o9c aqn the angle between them is

  Two displacement vectors have ma0ff0 -)caon+ kggy-z eb.qqm+gnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of+ymefc o-ak-q+g0 f.0bz q)n g the sum

  Two vectors, of magnitu6kpcpb0d ;t;sdes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultpd ;cs;tbp0k 6ant?

  Three forces, each having a magnitude of 30 N, pull b+*j3kxtx ez 7*sjhl8 on an object in directions th*jx+ 87skj3hebl txz*at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown tvwk8hl9ldj1 :7-2v zjf9eh:k)xeiey )cp)jvector is

  Ignoring air resistance, the horizontal component xjzk)q;y)caq/99x j2bsv9cxyqz* -bof a projectile's velocity

  A ball is thrown with a v, c hs()sow+hkelocity 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 znc+i.(a1 lgc y505eqp kc4 d1 6kvtszacceleration s+cyc. lgketka(z0dzc5i115p n4v 6q

  A soccer ball is kicked with a velocity of 25 m/s at an angle of paf zeo )v:gfmbly8+ :yki(9ik*y,2s$45^{\circ}$ 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-par,f.svp t2)t r, yrb/tvallel to the velocity vector2pbtrtv)vys. ,, tf/r,

  If the acceleration of an object is always directed perpendicular t 8le,+iimygc0 o its velocity,iyl i m+g,c08e

  At what angle should a water-gun be aimed in order for the water to lando,0*0zm( 1ydz0qzbbqh t-*5r8 7fifyvs wjnp with the greatest horizontal ra0opjv0bqz 5(d7yn z y** 0ffri-zm hs1w,q8tb nge?

  An Olympic athlete throws a javeand5 q7 fpu;t4pl8hoi3c3 n5h lin at four different angles above the horizontal, each with the saoi4pn5 d;35fpln tq3c hha87 ume 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 handizyl5: r q6f(b with twice the zylfirq6 b5 (:velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original spexs n9*zua1/hhj *i 4oved 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 db u+ mtp. :+m:qkgrk/vkg.)ws u k3xw9oes its speed compare to its iktkskquuwx/k.g bv9):m+g + .p m3rw: nitial speed?

  A stone is thrown horizontally ruk:)5lsbmo ls eqv25j i8;br +h.il:from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the leveli5 j)hrs;:8rsq.llk5e volm: ub+i2b ground below?

  A bullet is fired horizontallylm :3 edei/eex2bqa:-, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the twe:e aee/-x:bdml i3 2qo bullets.

  A plane flying horizonta+w6imswa1 d1dn* (u billy at a speed of 113.5 m/s and at an elevation of 278 m drops a paw6db( 1i1w *+un daismckage. 6.4 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped yd2x g(4(buhd from a plane, and one second later a second package is dropped. Neglecting 4(uhgdd y(2xb air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying h(t m n6 bhdo 2:4gkqpv9yk5ny(vq c33rorizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locationk q:5ot3ny rcy9 62hpkqg 4v3v (bm(nd of the plane will

  The acceleration of gravity on the Moon is only one-so;ah 46qdhyz mm(:e4sixth 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, the ball :hmosh6a44(; e zdymqwould land

  You are traveling at 55 mi/h in vexv(q 9ab. z5v+qe)k the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car i)zq.v(be v9qkx va+e5 s

  You are trying to cross a rivmtp6av,b 2iv +er that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. Yo+ia 6v,vbtm2 pu should head your motorboat

  Your motorboat can move at 30 km/h in st3a/(ensma +nnc5 0y4 bmpwqy )ill water. How much time will it take you to move 12 km downstreae+n/ 4cbysnaw a0ymnmpq 35) (m, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below thed2 3)wcm( vsat7av 8my +x axis. The y component of A )wc7 ya8ms(dv2v ta3mis

  If a ball is thrown with a velocmi m5ip+lzp/zd +)k, *qvns.nity 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 2vp9cadu 7 n5vin a direction north of east and you end up 2.0 km north and9vd upnc72v 5a several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocityvti9 up9.ptn* is 8.00 m/s. The angle between tt i vn9p*u9tp.he direction of its motion and the x axis must be

  A 400-m tall tower casts 2 u7o6 qsadh-xp(ndv1a 600-m long shadow over a level ground. At what angle is the7dad1 vpn-uh 6s (o2qx Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-m7 pdjvqb;o :01, 3), respectively. What are the components of the sum of thedjvm7o; :bq0 pse two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What y) y(cagah )w kpx*aff8v6dn e4g97d1is magnitude of the suwf7na9ycgp e8agf4 hkd 1 yx(*a)v6 d)m of these two vectors?

  Vector A = (1, 3). Vector B =b g;e94gtzkl 2 (3, 0). Vector C = A + B . What is the magnitude of C g9ble;4kgt z2?

  A car travels 20 km West, then 20 km South. What is the magnit zlq *od.j:z:bf3b-x(gy.q ik;i dxz* ude of its displaceme;gk o -d:izq*bq*z .xl .dxf(ib3 :zjynt?

  Three vectors, expressed in Cartesian coordinates, arznjn)u :opf5 5e
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 crv o6xe, 7h5puoordinates, 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 magnitudex o( th05n05x 9blqnxbim5.n t of vector C = A - B ?nt50xl o5bi(x.m0bx5t q nhn9

  A runner runs halfway around a circular path of radius 10 m. What is the d+gt pmda yq(lnx*.bd d,5;y6misplacement of tmbl5p(.dgd 6y;m,qtdynx+ *a he jogger?

  Two forces are acting on an object as shown ah6 0gsy,xscnn5;,egin Fig. below. What is the magnitude of the resultant forcey0 gs6he,; x, nas5ngc?

  Two forces are acting on an object as shown i 1)gud9czoic10mgc3c 7 zgsm 8n Fig. below. What is the direction of the resultant force?g0zcd g1m9mi3g zuc7oc8)1c s

  Vector A is 5.0 cm long and pd*j 2pm-g4onvkcs p.d: ( s2rfz+0n-xw yl oe*oints along the positive x axis. Vector B is 8.4 cm long and pomncol0d4n-ywzose ( 2p-* v* srd.xk:gf2 + jpints at $+57^{\circ}$ 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 84 cm long and px-/(j. lmz;t 4euzjf 8fcxop6oints at $30^{\circ}$ above the positive x axis. Vector B is 15 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 20 m/s frelx9m4 y7w+e0 o*sx2w m6nhskom the edge of a cliff. A stop watch measures the stone's traje7n4hmexs9es6+o0l kw2ym xw *ctory 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 horizontally, i3lxh:9mgx2a8t,u3ag ue s y3with a velocity of 6 m/s, from a bridge. It falls 19 m to the water below. How far does y8ltm: aagi 2933,suhxuxge3 the rock travel horizontally before striking the water?

  A ball thrown horizon gth9jn0: 2esrtally from a point 28 m above the ground, strikes the ground after traveling horizontally a distance of 15 m. Wits2t :9e0n hrjgh what speed was it thrown?

  A jumper in the long-jump goeie4fq 1/f3 bxjktq(8ls into the jump with a speed of 12 m/s at an angle f4qlkf q3x/i1e t(j b8of $20^{\circ}$ 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 speedeb :u*l tvqr. pxb)07e(fay,xo.wne6 of 14 m/s at an angle of r,.by 0 qu)l*epe(f6oavxbw: nxte 7. $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched withtq1+ 70lu3p6 iwftksm an initial velocity of 56.2 m/s at an angle of $18.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an inicm/s e++ 2oc :2*hwgaukf:qvytial velocity of 51.4 m/s at an angle of $42.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired iex/nsex6vz 8 -.+ qdxat 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 ho o3jbacw- zc.z*50ua -lqknu*rizontally at 16.2 $m/s$ from the roof of a building 37.0 $m$ 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 groh qi;8nt8 p4wcund level with an initial speed of 60.0 m/s at an angle q;h8p4icn8w t of $42.0^{\circ}$ 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 c(vx09x:pau i van run a 1500-m race at a velocity of 4.0 m/s. If you ran the same 0a9 :uvxi(pv xrace on a day when you had a constant 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 t:g48vln vjs. due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground ivn.slgj 48vt: s

  A plane is flying due South (r8yqis:s b/d qad/93f $270^{\circ}$) 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 headed:x ; /;xg:px,ybegm)rna uz4j $30.0^{\circ}$ 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 hvyd(rmr *:uh8orizontally fires a projectile with speed 50.0 mmyh* 8rr :udv(/s in a 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 i8bwr 5(6-q ymjxj,z*p6 ax fgkn still 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 t xf jrjzybpq,8 a656wg *x(-mkhe river?

  The driver of a motorboat that can move at 8 m/s in stillx0 n84lbwmlfw5 01u ri water wishes to travel directly across a river 1.6 km wide in which the current flows brlwx00 5 fn1uli4w8mat 7.2 m/s. How long will it take to cross the river?

  The driver of a motorboat that can moveai*tshs-9k i 13 rfp;)tc cxf3 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 angle upstream should the driver ifcxc1*ps9-)tai3sf kt hr;3head the boat?

  A swimmer heading directly across ;(n;2.ahp5krjkj ybslnn /jw+.k f ,z a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can shey;wn/.bh,jjfnkzn ( 2la ;5sk j.rk +p swim in still water?

  A swimmer heading directl /-/qzb7 hotih3 mzx4ay across a river 200 m wide reaches the opposite bank in 6 min 403 4/mqohb -hxi/7az tz s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.52 m/s, mushmjzsm5r(/1*wf0z,x ,uch v t ekn84et aim upstream at an angle ofzths84e*c1h nmex k ,vw( frm5j/u, z0 $19.7^{\circ}$ (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)  $m/s$