Which one of the following is an example of a vector qugn*qss9wz2; s0m ..cux u4qogantity?

  Which of the following operations will not cha8t3fl0 hr(6hn vb8n* s t8bkzhnge a vector?

  Which of the following is an a4pok6ydg( j p07nket (ccurate statement?

  The resultant of two vectors is the smallest when the angle betwee(eu ,1o ftvq761mlbryn them is

  Two displacement vectors have magnitudes of 5.0 m c +f-l / 6:.nv wzsbu/a8snszland 7.0 m, respectively. When v/w6:s lnanlfcsu /8 +bs-zz.these two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, a91ode65nkhz 1:aml hu re added. Which one of the following is a possible answer for the magnitu 6:zk mael1h9n1uh5odde of the resultant?

  Three forces, each havin 2b;er6we 1bky*vp1bhg a magnitude of 30 N, pull on an object in directions that a *e11bhrwey pk6vb;b 2re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector is*r0q h,hgzw4l

  Ignoring air resistance, the o: ydk godxi4* +h)(b6wtl j-ehorizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an anglexf,6s e 9 y:x2s. 0nyjfsvir*y 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 coz 9 r4oam9rghpm tg8,g)i31xrmponent of a projectile's accelerationg3rg r rox94h it9m8mza)p, 1g

  A soccer ball is kicked with a velocity of yq 6zc7vd m*jt124 yyfuv(z 8z25 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 ofzsq u binxdbzn/;,3: v emrji3an7 (4) an object is directed anti-parallel to the velocity vector,dze 43, avz; b i(7sx/nr3:)qnjnbmiu

  If the acceleration of an object is always directed perpendicujrwyq5 5 y)ri.ni .a0j0qau akr,a3ti mlb3.(lar to its velocitya q ri3mbltw 5y ..qr, 5.ayuai)0(jnkr j0i3a,

  At what angle should a water-gun berpzzws 50 oq/+ aimed in order for the water to land with the greatest horizontal range q5s/zwrop+ 0z?

  An Olympic athlete throws a javelin at four different angles above the horizacml40 ydc3b6 9sc sz8ontal, each with the sa mccc89034dsz6sl aybme 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 hanxgg amb k w*b;f5l(4mj ixp;*,d with twice the velocity it had on your first throw, its horizontal range R (comparedm*jka b; w(b*,lgf4xgp; mi5 x to your first serve) would be

  A ball is thrown at zudei9fig/o +/w+arr-j 9t*fan 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 attefl 7wdu(5/* dpfy.ss hmpt reaches its maximum height, how does its speed compars5d/yp(ud*h sf. wfl7 e to its initial speed?

  A stone is thrown horizontally from the tml o6o,z1,spllrpm9 + op of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits t po ,,ps69oz llm1mr+lhe level ground below?

  A bullet is fired horizontally, and at the same instant a second h5r/+*0ifsw9cecxal bullet is dropped from the same heigwe+f9*clix /c0 5srahht. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 11rj/+h28czcfzl)a unm 735 ejr 8.0 m/s and at an elevation of 222 m drops a package. 5.8 seconds later it drops a second package. How far apart will the two zz8/5lh7 r)r+ j ajfce23uncmpackages land on the ground?

  A package of supplies is dropped from a plane, and one second laterm)o n:aiil 9g9 uh3-we a second package is dropped. Neglecting air resistance, the distance between the falling packages wil 9l hieuwnimg9: 3)ao-l

  A pilot drops a bomb;dmq+s sth/d ynr0*kn 0j fm08 from a plane flying horizontally at a constant speed. Neglecting air resist0dnyq ;k hm0/0fjms 8+ s*ntrdance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moo8uu0pny0)evb.a .k: cze a7ih5geal9n is only one-sixth of that on Earth. If you hit a baseball on the Moon with the sa ce0zuh:0 g7ue5 lp.aane8)b kayv.9ime 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 road3x t i29j,4 sfyys/kig and pass a car traveling /iyij3yt 94,xsg f s2kat 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows ds bx:rp z83h-hue 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. You should headpbrs hz 3:8x-h your motorboat

  Your motorboat can move at 30 km/h in still watie ywkz: n0bc3e1z4i1er. How much time will it take you to move 12 1bnkc0e:y 3wz e1iiz4km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 mg wpqx0i2ix:hpd6 2u 0 at an angle of 30 degrees below the +x axis. The y component of Ap62 px0hi 2 uqwgix0d: is

  If a ball is thrown with a velocitqddrqz) ,cwr 8ie t a99t5j:;fy 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 +gjuyica:+hq/tg qq3a;h 9 o/ direction north of east and you end up 2.0 km north and several kilometers east. How many degrees nor j/qag:qy3c+9/;ut +haoqhi gth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. Tynhpe:0 3yx )ohe x component of its velocity is 8.00 m/s. The angle between the direction of its pe 3 y:ony0h)xmotion and the x axis must be

  A 400-m tall tower casts a 600-m lg:dy 1. sq np.e8mfle-kvpzv g.*f(sh(5s(vmong shadow over a level ground. At what angle is the Sun elevated abopvgv.(qmlm p. v1z: n5d(kf.s8f e (*sey-gh sve the horizon?

  Two vectors A and B have components (0, 1) and (974l tus cjlq)-1, 3), respectively. What are the components of the s9l u ljc4s7qt)um of these two vectors?

  Two vectors A and B have components (0bmav1 . g e,s i4io)9oj9)mnhj, 1) and (-1, 3), respectively. What is magnitude of the sjn) m4gjih oai 9.v9)oesb1m, um of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . 2tqy wgx04 dn/s of0e4hkn2 .fWhat is the magnitude of .wko0/2s0 eynft4h2nqd4 xf gC ?

  A car travels 20 km West, then 20 km South. What isu8 lry ve,0 19swti e)aalhlujp.h0q1 4u8t.h the magnitude of its displaqh0v8j9upasle h u81wth u .l.01ra) ,i ye4tlcement?

  Three vectors, expressed in Cartesian coo9-2tt98ocret jojq 6bdol:n;yh,+s prdinates, 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 coordiv8lakhax n87lw6(s - b+:ayz hnates, 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 = (+-e4s0pp,6ob61xc a vp9qhqxw 3.0, -8.0), what is the magnitude of vector C = A - B ?6vxeo p9wpp61 a4x,q0b hs q-c

  A runner runs halfway around a circular path of radius 10 m. What is the -aqe1 ao v44yxahxl r)c;p (/wdisplacement of the jogger?;x4q)w/p(1rva ao a -x4hecyl

  Two forces are acting on an obx4i 8z(ov; gvdg8f05vevy fvz 6wg .1pject as shown in Fig. below. What is the magnitude of the resugxyv8 (o4z v.1fpv gwi0defg 6v8 vz5;ltant force?

  Two forces are acting on an object as shown in Fig. below3hawya/ e7x9kvm*0 :/imxwdr. What is the direction of the resultant forkhmm/3x/di0xe7v9yaaww *:rce?

  Vector A is 5.9 cm long and pou ;b;70vy 6ixondgtv3ints along the positive x axis. Vector B is 7.1 c;7d;b nvgo0tyxu36v im long and points at $+29^{\circ}$ 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 89 cm long andx/u nzxow80h,xf wspn s5 1 xyr2:m6(a points at $30^{\circ}$ above the positive x axis. Vector B is 27 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 6 n8ppnww); ro9 jrzkz;7not4w cr y9,an initial speed of 25 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the two;w9 ,nzprjyp9r c7 ) kz;n4w8nor6bottom to be 3.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 10 m/s, fro h knu(r0*xszj; le::gm a bridge. It falls 22 m to the water below. How far does the e:r skj;(gu xhn 0*z:lrock travel horizontally before striking the water?

  A ball thrown horizontally 1n49hnylw b 3ofrom a point 18 m above the ground, strikes the ground after traveling horizontally a distance of 19h1o w4nlbyn3 9 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spe do1h ugfms/:9/;mqymed of 12 m/s at an angle om9m/:umd ofy g;/1qh sf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes intovov9k;z f1rp +ypg*b6 the jump with a speed of 10 m/s at an angle 16ob*v9v y+p kzr; fpgof $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 44.2 m/s at wigd)u pu,5 t+an angle of $36.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial,t txyoqvmu1)l* (b8q velocity of 48.6 m/s at an angle of $36.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired atp*k/gn8tw*rec6x ed- 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 horizontally at wvm2xa j 91n(7xns nz- c ta)qo0(y7aw 24.2 $m/s$ from the roof of a building 63.3 $m$ 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 lerh t, oivc or4f29l)h0o t9g,cvel with an initial speed of 47.2 m/s at an angleo2c09,ior tvh9 lo 4,g)rf tch of $39.0^{\circ}$ 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 can run a 1500-m race at a velocity 5 hvs/fcto* / qv5mh4c bm7 n9s,/ubymof 4.0 m/s. If you ran the same race on a day when you had a constant headwind which /5,vm9hq /b/u7smn mcf* o4v s cy5htbslows 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 du b.mrl6zx2 z*he North, and is in a wind of 50.0 m/s to the West. Thhxb 2. 6lrz*mze plane's speed relative to the ground is

  A plane is flying due Sou,6an es9vhqu6k66dr eth ($270^{\circ}$) 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 spee;psaxovd:18wji;y 4b zrd ,42 g.untvd of 120 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 200 m/s horizontally fires a projc6*lijgq9ks26 jajwy s53k+u sp 0dn8 ectile with speed 50.0 m/s in a forward usn20ia ykjdcq5j3* 6 6+gpl sj w8k9sdirection $30.0^{\circ}$ 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 dire1stiyv1cr 2u5 cted across a river with a current of 6.0 m/s. What is the speed of the boatsy uvc5 r121it as it crosses the river?

  The driver of a motorboat that can move at 18 m/s in still wandhqjq1h , 1:)ubxze*ter wishes to travel directly across a river 1.7 km wide in )zqnj1 u:x1dhh, ebq*which the current flows at 3.4 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 wishenen 41u8p ,,: fljunqxs to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstref 8,qu1,j nle:nun4p xam should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reache ciwiglos9 5n3nhx,90s the opposite bank in 6 min 4 5 o9,h0swlg3ic9xinn 0 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across al.:) zinaf 7or river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreamfoia .lr)n 7:z 480 m. What is the speed of the current?

  A boat, whose speed in still water i6a:f 1njh* 75qay ulfuj)j y;bs 1.85 m/s, must aim upstream at an angle of:j ujya) yq 1ahl6buff5j7;n* $22.0^{\circ}$ (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)  $m/s$