Which one of the following is an example of a v; yc,o+ienm25f c ge*jector quantity?

  Which of the following operations will not chang/ sq9ga*ef qq8 3p. dsmkhq3de 0r)+ode a vector?

  Which of the following is an3cgdd7 bn3jy8 accurate statement?

  The resultant of two vectorji:va4+ 2: v lhcms6xps is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m anm )u0a wx*n8byd 7.0 m, respectively. When these two vectors are added, the magnitude of the s n a*umby)80xwum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follou3y/hz+r(as tfi0 ui*wing is a ih(a y0/us+fu3zt *ir possible answer for the magnitude of the resultant?

  Three forces, each having a mag*q, zp/+ mrpdvnitude of 30 N, pull on an object in directions tha,*/+rdpvzq p mt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the -swpv:tq8qyk51sf0 rag* v+ runknown vector is

  Ignoring air resistance, the horizontal4; x (zdvqtij1ts,0ws component of a projectile's velocity

  A ball is thrown with a velocity of 20 )ejc (et2vj)a 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 comvs mqyav66buh1lr4(*ponent of a projectile's accelerationr6q6 (uvl 4v*ys am1bh

  A soccer ball is kicked with f.0kcwl b wyl2wd/8/3bbqi n 7a 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 ofck8tno4n;wd zvbg 4ou8 a) 3n4 an object is directed anti-parallel to the velocity vectornwknd 4)tz4aconb83u 84 og;v,

  If the acceleration of an object is always directed perp.pc.ynmupyff*jw5np)s 1- l( endicular to its velocity*sfwlcjy )m.-np fu.p np5y 1(,

  At what angle should a water-gun be aimed in order for the water to land with tp,co h ysx .aw qpzc3.g(i32-vhe greatest horipcx2oi h g3ys c3( -w.,avzqp.zontal range?

  An Olympic athlete throws a javelin at four different angl z;j4.xse fa.4g44o- s) aa xhqdqtqb88*eboses above the horizontal, each with the same sbs)sb zhafegqq;- qeo4 xo 4d.jata 84* x48s.peed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 kf0xmd 7;s ;jo*c(ttaj* m x3fhand with twice the velocity it had on your first throw, its horizontal range *oftx7; tx c0ak*s j 3j(mmd;fR (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 /)s e m5rd o2ncj,mrpco c3ov-2 )9nrwm/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 he*tjkhf 9hc i(ex7;x d5ight, how does its speed compare to its initial cd jfhti; *(x59ex k7hspeed?

  A stone is thrown horizontally f3i+ oopk,c4094l4sloh t sv ykrom the top of a tower at the same instant a ball is dropped vertically. Which object is traveling 9i h4oklp4l+ 3sotkscy40 ,vofaster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second b k587ikziprfyt ;eq- 4ullet is dropped from the same height. Ignore air resistance. Co4r t7yzqep8kf ;-5iik mpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of v i+aj 93g.erf109.4 m/s and at an elevation of 192 m drops a package. 3.2 sraveij 9f+ 3.geconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and onsne45k3 ro/a)p kol(y:zx4 hoe second later a second package is dropped. Neglecting air resistance, the distance between the falling p:5zxonl4 o(/)heykar4kop 3 sackages will

  A pilot drops a bomb from a plane fwdcytn;48kt2-;oen yx x2r 0mlying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane28dy0 mn xt4tknx;y o-wc;er2 will

  The acceleration of gravity on the Moon is only one-sixth ovy)g9 b 5gs4 tm,.obs(8j*eocr f9uoef that on Earth. If you hit a baseball on the Moon with the same effort (and at ther.9b 5e9g84oet gcmojfbs oyvu(*,s) speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative toy6-aipv+;dbl7 w qkb / a straight, level road and -vpkbbiy /a ;d+6w7qlpass a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a r0w/wx xmb6 ;ux o f1a4rllg u.m7zca;2iver that flows due south with a strong current. You start out in your motorboat on the eau21cmag xu6 ;7xw40 bf.mz lx;o/lwrast bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at bq4 )+5yhqs ko-yd8jt30 km/h in still water. How much time will it take you to8+j5k h)q-4yobdq y ts move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude n*w0ixcl13 ta/ 2xtgk 8.0 m at an angle of 30 degrees below the +x axis. The y component of A i lwg1t/kc*xxa0n2t3 i s

  If a ball is thrown with a velocity of 25 m/s at k,u x+kr; dw8df m zi4r5cl..can angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a tlm+h qmbp:6ld * /trv5*-rys straight line in a direction north of east and you end up 2.0 km nor 5r l/dq*pvb:m ystlt6m*rh +-th and 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 componentjn.qil32x3e+v5pup68t /ea,ir n 4 mizjel7x of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axexetjje6zax7p5pi4 limlu + qn3,r2i/v8n.3 is must be

  A 400-m tall tower casts a 600-m long shru26szu0z 3ae:mw87 np1q+t c 7fdb)ptlnhf ) adow over a level ground. At what angle is the Sun elevated above the hori:87)bunte+1nf capz dq6zwsrt2)p37 l muh0f zon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What azb lv e-x1j9yah691h).u:vyv ol ,3 hb1bvbhure the componen hv.b1vyva:,bbe uyz19l1 h )vhb-h9l3ju6 oxts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Wh- t,ua8e5bjz 2ye bxx:at is magnitude of the suaeb2y:t,x8 jz5 ebx-um of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What itab yz0 ) hx)9yrmnufsveg )i-w+(;;r s the magnitude un-yvirx;es+ wr9fa)t) )0mzg b;( hyof C ?

  A car travels 20 km West, then 20 km South. What n-xb3li4xu7yv+u3c tis the magnitude of its displacementuxt73xu ci -3+ bn4lyv?

  Three vectors, expressed qx0jh2cm3fg sbr.o ;2in 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 coordinate+bli h5i ni/)as, 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 thpy 4ba1 fsw8x6e magnitude of vector C = A - B s6 b48fayxw 1p?

  A runner runs halfway around a ciw zbi,nk5r90h wk:u b8rcular path of radius 10 m. What is the displacement of thbk089r,u bwzh kniw 5:e jogger?

  Two forces are acting on an object as shown in Fig. below. Wha65njek/n yuz6t is the magnitude of the re 6ejn6 zu/nyk5sultant force?

  Two forces are acting on an object as shown in Fig. below. Wha )hxu1qy x,jyd42onz,n )pki 6t is the direction of the resultunq4,o zj )ni 6kd21,y)hxxpy ant force?

  Vector A is 4.2 cm long and points along th7r1 ota1c2smm, b x9wie positive x axis. Vector B is 6.0 cm lonti1 21a,mm b7xcso w9rg and points at $+45^{\circ}$ 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 74 cm lonkg2: ;3kc lcmpg and points at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 32 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 2t5e 6ff6ymn5n0 eau2gosgx -,3 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 bottom to be 4.8 s. What is the height o6 ff52 gau-oxme5,6s0g yntne f the cliff?

  A girl throws a rock horizontally, with a velocity of 15 m/s, from a bridge. Itr /r-med+ n ugbv2g+m,6zb2qb falls 28 m to the water below. How far does tq+u -zb/+rgmb b2mgv2ne6dr,he rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 18 m aboex/f;pla* i,.l9r vri ve the ground, strikes the ground after traveling horizontally*l aifir;ev/ xlp9,.r a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goesl2t 7ibi8s) i6cx(vrczx/tp 8s/g6 ro into the jump with a speed of 12 m/s at an angle cxg8i76 s pcr )2x/zl /8tvt6i(isrboof $20^{\circ}$ 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 ahi7/ e gy4(5h1h c3sunlknk+y speed of 12 m/s at an angle 13 h ghh4yki+c/ y sl7e(5uknnof $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an (jzr8; x:04g i sdi(qc:,mlm2zjyd w od0o;ffinitial velocity of 33.2 m/s at an angle of $18.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity i q-(eag *vfl6of 53.7 m/s at an angle of $25.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firemr58hwy96hvj*i 0gzd i,6 gee d at 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 horizonz8 efg 6ta29:qydh.tttally at 16.7 $m/s$ from the roof of a building 37.1 $m$ 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 w;8jss( x .hlnij9 iu;bith an initial speed of 39.7 m/s at an a8.bl9; jii x;nssjhu(ngle of $37.9^{\circ}$ 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 37 f jei2a1 x/o87vahg ezu*daa 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 which slows your speed by 2.0 m/s, the time it would take xujh/va2 af 1de7*e g3 zi78aoyou to finish would be

  A plane has an air speed of 200 rjbh k qf;/ojf:qis w 3a6v(*7m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the g/k fwi;* b3v7j( qho j:6frsqaround is

  A plane is flying due South fa2b* ,o)zzue($270^{\circ}$) 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 k;zga w;5hm9p 716 y hx:zhhi3hd, ap2kht;comm/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 fir3rq fyyav2;0h+q ef.aes a projectile with speed 50.0 m/s in a forwardeaq h3y yfq;0.+vfr a2 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 s5k raq5wa wne5u5x x.5wkk 598.0 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 river?wre59u ws k 5.5q55kn xa5axwk

  The driver of a motorboat that can move at 11 m/s in /n,cflnl+ sh4still water wishes to travel directly across a river 1.6 km wide in which the current flows lfncl +/h,4 snat 5.4 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at6buch:4ituv89 d9c bo 10 m/s in still water wishes to travel directly across a narrow strait in which thu48ico b vbdtu9 c6h:9e current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acror6vr a3y ,/hndss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstr,rdy/rh36 avn eam 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide,i2o6r s s +)4l f6bj7frqsf)fc rzr(u reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m(uzfbr27 r is)or f6,64f f)sqcjsl +r. What is the speed of the current?

  A boat, whose speed in still water is 1 8dt-ki;d hmjzhv, ;atzu4o91.85 m/s, must aim upstream at an angle of k jt;h8zdihdvm4, ot -9zau1; $32.0^{\circ}$ (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)  $m/s$