Which one of the following is an example of a vectvvm)c *h u8k6nor quantity?

  Which of the following oi(wt ys0 4ghc3perations will not change a vector?

  Which of the following is an accurate staht 5zazqf);i2;yj icoq75k7xtement?

  The resultant of two vectors is the smallest when the angle between t2q/*w 1htrqqqlo+:vd5y5 e cz hem is

  Two displacement vectors have magnitudes of 5.0 m and 7.vza ft9,zw ni8:0 pjbwuf. 2.w0 m, respectively. When these two i a vwu f,:w0z2f8jwbz.npt .9vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are add3nex vy/ o6gr;ed. Which one of the following is a possible answer for the magnitude of then3y;6 rxgoe/v resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in direcubiyfv9gq* :a39j +eznu i )y:tions thay3ev:j9+zuq9biyfg :iu *) nat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown z:p :r*/m:ma 1ka6 u1thrjc.k1hr tdfvector is

  Ignoring air resistance, the horizontal component of a projectilly8zh yg 9zu -4+gzml/o(o 7qglw4-d we's velocity

  A ball is thrown with a velocity o23ok(t tu uhgzizh7tr** r7o1 f 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 componib(si7 im :e 4b;qd4bment of a projectile's acceleration7;bq:e (ibdm 4ibm4is

  A soccer ball is kicked with osjipsa;m5 lo2t3*j: 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 dire d(2;x bwzgkcvpt1 )v(cted anti-parallel to the velocity vect z2vb d(v)k;1xc(pwtgor,

  If the acceleration of an object is always directed perpendicular to itkoqb;;hmhx;k+mw4 ,ez9b f*ts velocityko kh,+bfbqh ;* 9e;tx m4mzw;,

  At what angle should a water-gun be aimed in order for the water to land wilpgb +nooah. z0x; 3.x;a- yl-/rl jskth the greatest horizontakxb-/ . gnso03l;jl-zolx; .ya raph +l range?

  An Olympic athlete throws a javelin at four different angles above the horss- c.irmd(zy:os c+.izontal, each with thm . (.rci+c-szsoy: dse 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 bw a:k(k.*l x-;shd; i:b hnttsall for the second time. If the ball leaves your hand with twice the vstwb:k(*;kisa dh. n h;:x-t lelocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/l *j+(8 ohfu wto*9mvxs 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 atb8n cl9 n0su qk5/dy9otempt reaches its maximum height, how does its speed compare ty09qon8nc uldskb9/5o its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instant m 2g)fz6uj9pl(7+cebc +/knaia x+mma ball is dropped vertically. Which object mlm+ uk+ b (cj2apfi7 g9x/ ecz)+6amnis traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second b yzspt 522h,bk77lav 15rrtgf *w0fc jullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the twk57yv r22 tstrf g5 a0hf,1z7pwbc*jlo bullets.

  A plane flying horizontally at a speed of 50.8 m/s and at an elevation of 135 0k-q 4/xo rwrx/h, bmqm drops a package. 5.2 seconds later it drops a second package. How far apart will the tw4rmx kqx wbh /oq/r,-0o packages land on the ground?

  A package of supplies is dropped from a plane, and one second later a secondqy;pbp0hr4w27eh xiy1z (t (r package is dropped. Neglecting air resistance, the d7 pp(zw0y iy4e hrht2b(r1; xqistance between the falling packages will

  A pilot drops a bomb from a plane flying horm wp.s;t:ei ,gw;u*ruizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the he pw;. mu,;ti* ugrw:sorizontal location of the plane will

  The acceleration of gravity on the ) ytt d o92,+hgp4bbnjMoon 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, the bagp 4 n9y+tbbdojh,t2 )ll would land

  You are traveling at 55 mi/h in the +x axis relative to a straigh/qi d8uaub8u/jv- iahf)(;d st, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the oth;jai s/d(8u q/)v8dubufah -i er car is

  You are trying to cross a river that flows due south wiubb) jd n2.88-oz 8)nkhkezwith a strong current. You start out in your motorboat on the east bank desiring)ik8z2neh.8b-jzk on wu8d b) 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 m :+ xoi, sl462 z*ovzizgbhfz0uch time will it take youb fo+h* xzg ,zozz24:60liv is to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m a7pi3rn0 0fcrs5mtt y 3t an angle of 30 degrees below the +x axis. The y componentt0 ti0fm5y73crr p n3s of A is

  If a ball is thrown with a velocity of 25 m/s at an an 2 migtu/vl,(zgle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a strqj (y1ni y51ilqsk,;uaight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you 1(jqniuik l1qs,yy ;5walked?

  A butterfly moves with a speed of 12.0 m/s.a,zji//oyv 7u The x component of its velocity is 8.00 m/s. The angle between the direction of its motion a uvoj7,zi ay//nd the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At z2: a4 ,y2yczlm2 johgwhat angle is the Sun elevated a ,ayc4ozgl m2z :2yh2jbove the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What s; x+mf9kfm i-are the componen+ xm;ks-9mfif ts of the sum of these two vectors?

  Two vectors A and B have comc8n:za wct0/4ie f 1biponents (0, 1) and (-1, 3), respectively. What is a0ift1c8:bz weci4/ n magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mm3fpn hm:e m,2z0qq(hagnitude of C 0eqnmmh,2:3q (f zph m?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disjzb9tn2/g 6np place6b pz2t 9gn/njment?

  Three vectors, expressed in Cartesian coo eb9:xdhuadu8 25uu (yrdinates, 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 Car2 pqr3p o:-uchtesian 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) anduk sn*gr1;ga5 j2eg,d vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?djag ugkr;5nges ,2 *1

  A runner runs halfway around a circular path of radius 10 m. What is igx e2 miarn1,w 0k +6nw)5klbthe displacee6w1bwna2,ik)ikn 0 g+ mxlr5ment of the jogger?

  Two forces are acting on an object -za vyfxo )m16ktt43mas shown in Fig. below. What is the magnitude of the rem3xvt1fzy) 6 ao-m 4ktsultant force?

  Two forces are acting on an object f;c/r la-e3iq as shown in Fig. below. What is the direction of the r3q-/f ;i elcraesultant force?

  Vector A is 3.4 cm long and points along the positive x axis. Vector B is 99 utmkc u7t/-zq5iq(b.8 cm long and poinb/tq 5 u (t9u7c-qizkmts at $+46^{\circ}$ 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 87 cm long and poinebo.t 5*+/5tto j;eecl4myhq ts at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 46 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 icpzo1v )uic+bw ,*jytxt6/:initial speed of 14 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to thei:zti v+x,cu/wt y p )*61bcoj bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocp ygw*pk,0-gkg xoby h;j +*-bity of 18 m/s, from a bridge. It falls 30 m to the water byh*kb -g kp, g+wxb-* py0gjo;elow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the grgc3k.qyc6 yf8 ound, strikes the ground after traveling horizontaqkyc 6c gf8y3.lly a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into thoszh(eq+z. qt7dc) d ,e jump with a speed of 12 m/s at an angle z(+coqq )e7d zsd, t.hof $20^{\circ}$ 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 11 1bfe1 (ehggt avd05 .tm/s at an angle d5(t ggvh0tea. fb1 e1of $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched withecs3t w s1ij )fr42ru8 an initial velocity of 53.1 m/s at an angle of $28.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launc; ) m 0hztb,jsw bk(/olh- 6vac9z/bguhed with an initial velocity of 21.1 m/s at an angle of $49.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at q c8ol 5e7p+0 gg6s6dfuikb6a 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 horizontaxr w0t6da0o 6zfto5(mj)w kc6lly at 27.0 $m/s$ from the roof of a building 54.5 $m$ 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 initif 6zy24 pkdkq((3bqln al speed of 47.3 m/s at an a(b2yn6qpkq(zf l k4d 3ngle of $40.6^{\circ}$ 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 150fdcuorz+,h) ,gr5 ;o erxi5m4 0-m race at a velocity of 4.0 m/s. If you ran the same ra ;f)4g+x,,oocmd5uzre h 5r rice 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 due North, and is in a wind of 50.0 m/s r+ (9*fqinqwvt kzr240 cbv1uto the West. The plane's speed relative to the grouvu fq92r kqnr z01vc(*i+w4tbnd is

  A plane is flying due South p;u )mb2-visp ($270^{\circ}$) 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 i2jq ja 4-ewz0mdi e jyoj360d .sjh(o9s 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 fires a projectile with sp 0:n/+q dk s-hdx0kmtdeed 50.0 m/s id /0sx+kk qndht0:m- dn 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 in still water is 8.0 m/s, is directed across ay+ r))xakufj5tog1,by66 r jvdkoad x9 zd14* river with a current of 6.0 m/s. What is the speed of the boj6yo9ab+5k1 v kxty x d,)4uzforg6d*r1 d)ja at as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to tr4u duzlj 284etavel direcej2u84 4zld tutly across a river 1.7 km wide in which the current flows at 4.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that canuk0 )9 8x7 gdyv1pdzygijx9r- move at 10 m/s in still water wishes to travel directly across a narrow strait in which the cuxy9g -x r vdu ypd1g9z80ik7)jrrent flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading direct b2nq .iqty e124wqlj7+dw be.ly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How wq qei12 wje2 b+q4tblyd.n.7fast can she swim in still water?

  A swimmer heading directly across a river 200 .ny,s k1 +:f,iio 84pdbsujhl m wide reaches the opposite bank in 6 mi1+4ksfb,l uo n ij.dsyhp:8 i,n 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.4x cy;g. -py4 u1hpan4j6 m/s, must aim upstream at an angle of.g x;4 cpj 1anupyy-h4 $25.4^{\circ}$ (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)  $m/s$