Which one of the following is an exfv yi ld-h/ x/;f/hzy1ample of a vector quantity?

  Which of the following operations will no/ 5kdi n7 +).pc ym:h.tuzaqdvt change a vector?

  Which of the following is an accurate statms(03bsyghwzkh-- 8k 4z ivby, *j+h pement?

  The resultant of two vectors is the smallest when thtuupkrb +:5g21gk;espi: s+z e angle between them is

  Two displacement vectors havez6k v:4:qywqi magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the maiqy6w: qz: 4kvgnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which oned+ upy(sz/r( r of the following is a possible answer for the magnitude of theudy/+r(spz ( r resultant?

  Three forces, each havip ljal:/ u3jsej0j*:f ng a magnitude of 30 N, pull on an object in directions tu*p/fejjllaj3:s :0 j hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,elb)yqg :h; 8z the unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's ve)br u h2,uimj *o94ymglocity

  A ball is thrown with a velocity of 20 m/s at an angle q-mtca:+ 9)c 2mxfsv iof $60^{\circ}$ 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 1+4m cjho :andwgj+q1 a projectile's accelerationmjo1+j 1cq: 4+d hnagw

  A soccer ball is kicked with a velocity of 25 m/s atet xt2)+85pj (ap5ov mecfwz2 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 d 8qhqkbm;g4n*) aw0wu irected anti-parallel to the velocitya4;qw h8*g)qmb w u0kn vector,

  If the acceleration of an object is always directed perpendw oj)4uu.uh: jicular to its velocity,jo:u4wuh)ju .

  At what angle should a wate l5,cd7k eqb)xr-gun be aimed in order for the water to land with the gdq,) l ekxc7b5reatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizy+w5i+y,q:9vpjwnu w) :v fl -rnjpd,onta p+,nw) plr-+uyw :ny5i:9v fj,q vjdwl, 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 the ball leaves your hand with6hk kw ;9a(7+j -,ew* p,f,fryzxyd7slw xd ui twice the velocity it had on your first throw, its horizontal range R (compared to ze9*wj7lp h 6, xdk,r f+7-,ukiww(x;ysafydyour first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an k(/jltcz/8 56nucfu5 ru0tu cangle 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, 1oel fs cb od1(.48pzuhow does its speed compare to its initial speeb(d1f 14es . zucp8lood?

  A stone is thrown horizontat4)awbcfyd,4x 67k2 sh/r ezally from the top of a tower at the same instant a ball is dropped vertically. Which object is t,tk) 46y7e sf2/wcax ab h4drzraveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet j* shcn6d -lpq ( ca-2jrpl3w6is dropped from the same height. Ignore air resistance. Compare the times -pl nsj2 l-q*(6w3p6jcrad chof fall of the two bullets.

  A plane flying horizontally at a speed of 55.1 m/s andp8 fbi ,/jdbl,rju2 xjh .33ph at an elevation of 122 m drops a package. 6.0 seconds later it drops a second package. How far apart will the two 2hpbl3 /,j3 uhird,j. xb fp8jpackages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second pj53a q:h gos9emm;m.qackage is dropped. Neglec3e;moaqjs mh: q.m5g 9ting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a cons1bcaiyp.yd 7qu-u. 5p-n t5zktant speed. Neglecting air resistance, when the bombb cy q5 uy.7k.z-dtpa5pi 1u-n hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Eatt :fo*uu;z+ vv2tmb) r)2wkarth. If you hit a baseball on the Moon with theft mo)au t +;zbrkvuw*t2 v)2: same 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 + lmcdfvx: p4uddv. ;4road and pass a car tv:dx;.4+ dcmvlu 4dpf raveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river thl6q.*agy8sr;w qky r i:f:b j*at flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the w*b.q:qfjw 6i8 g; ryaksr :l*yest bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 qrncu(/ .wm7v km/h in still water. How much time will it take you to move 12 km downstream, in a river florw cu7.(m q/vnwing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axik18db c+8q fjns. The y component8d1 8 jb+qfnkc of A is

  If a ball is thrown with a velocity of 25 m/s at an anw2envm.sd5c 1k2 :cax gle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a strap+rj.dr vvsdht*1*+r ight 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 havesp*t*+hd+jr. dv vrr1 you walked?

  A butterfly moves with a speed of 12.0 :a 8+0i)myuf ivslko7 xrgvbe72.u k4m/s. The x component of its velocity is 8.00 m/s. The uf 2 iisr:gkv)ym4 ko78v +l x.ua0eb7angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level g ipwz;u+ai 1+tround. At what angle is the Sun elevated abov+i u zwt1+pia;e the horizon?

  Two vectors A and B have component7y5q4(mvqmpc g7,t ihs (0, 1) and (-1, 3), respectively. What are the components of the sum of75 p,qvyc4h im( tq7gm these two vectors?

  Two vectors A and B have components (0, 1) and (-1, jcq0) qm/j 6r 7ei6hh4n2n sur3), respectively. What is magnitude of the sum of these two hq h7r6en)c/junrq i4 20jms6vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . l;focjq k *d44 What is the magnitude ofjcd4fk;l 4q o* C ?

  A car travels 20 km West,+m(fx-,h q bcd then 20 km South. What is the magnitude of its displacemen-b ,(mdc+hxf qt?

  Three vectors, expressed in Cartesian coordinates, arw3vi pagewtbp)o kt6 q . 1c)2jx87;bpe
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 ih/-m8 3e1y (( dm9nfof:ec8zjd jgtkvn Cartesian 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) and vector B = (+3.0, -8.0), what is the magnitude *lh/ wwut,r 4a zd3.tdof vector C 4 h,wd*wtda./ul3zrt = A - B ?

  A runner runs halfway around az48( dtvpeyz ; circular path of radius 10 m. What is the displacement o4z(dpv8;ze y tf the jogger?

  Two forces are acting on an object as shown in Fig. below. What is theml 4hhvf 3,a7i2,xah hhka:f ) magnitude of the resuxav )7mihhfk :l4fhah3,h a2, ltant force?

  Two forces are acting on an objecw y 0s g)buno6e15fg4bt as shown in Fig. below. What is the direction owsg1ngu045e)6 b ybo ff the resultant force?

  Vector A is 3.5 cm long and points a6a3 3 prxz7ztelong the positive x axis. Vector B is 5.2 cm long and poinpz6 zr 3aex37tts at $+51^{\circ}$ 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 77 cm long and points ;mmux6 e sm ehc .i5(-)lsvrjf.e/q r.at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 27 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 horizontal-rpy c.2g6gf2 :l oypwly with an initial speed of 26 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 3.9 s. What is tho yg6 fwcgpr :y2lp.2-e height of the cliff?

  A girl throws a rock horizontally, / ;xi9z1kdvli-u 0yx jwith a velocity of 7 m/s, from a bridge. It falls 25 m to the water b z lvx/9-0iyu;djikx1elow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above sh; q0n+3daw.bkn 5jed)2iue p-5 yohthe ground, strikes the ground after traveling horizontally asehe +ka d-ndby3w5jh5).i0;on2 uq p distance of 14 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a f jy/bxl43.8 ehwh- xtspeed of 12 m/s at an angle 38b/the- hjyf.x4wxl of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes into(8(equj8 o-fbql6 jml the jump with a speed of 15 m/s at an angle ofbf8 8m -lj jl6(qeuoq( $31^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocirr(f* +pihc3 fty of 46.5 m/s at an angle of $49.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 59.0 m/s at an angv( fmyf d,zj/:t ee4 ;3hrred(wwr,yd/4d6nule of $46.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firee: ,k-nn:ly3qzutk 7 cd 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 holie lxpx, )g(*3dj 8gprizontally at 27.3 $m/s$ from the roof of a building 65.6 $m$ 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 spbq8b3raa/g :g3ub1 iqeed of 55.8 m/s at an anglerb 1b8a:ai/qgqb33g u of $39.8^{\circ}$ 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 of 4.0 m/s. If d+vwamhl* ldd5 r ./6cpg*b0 gyou 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 woul *hm /5wrdpg*dg0vl+6a d.lc bd take you to finish would be

  A plane has an air speed of 200vdl4 zjm8 *+yv7mv (xn 9,wvcj m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to thcvm7 89 +(xywdm*vn,vvl zj4j e ground is

  A plane is flying due Sg5lm0pu /lyd4outh ($270^{\circ}$) 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 h* x3u ;(.zzkfuoflb 7u m3kw+beaded $30.0^{\circ}$ 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 speedoj3 zgp vpvd9al*q4/ 5 50.0 m/s in a fpj a3zgo/dql*v549 vp orward 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 acrvz2 dil4q+ (kx2r0igxoss a river with a current of 6.0 m/s. What is2z2 v xdil(0 rk+xg4iq the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 1w2- .tfwlbknq al xm/6i5g3 0l6 m/s in still water wishes to travel directly acr2 i65xnak/-gw lm0w3b qf.ll toss a river 1.5 km wide in which the current flows at 6.1 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 wishes to tra) nc,z+g x: -;zxcix4aw.0 edvtrq9ye vel directly across a narrow strait in which the current flows at 5.0 m) zyew:-ccxr xaqv9,;g 4.+dz0 ti nxe/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposiv:vsi n su(85ete bank in 6 min 40 s. Shv5s:i 8unesv (e is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide remuts-+ v(: cluh:do q 3hzj x1e4306 )jpkjnauaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the currenm1s+ uel4atjuc- 6qp dx : u)(j:zo0 n3j3khvht?

  A boat, whose speed in still water is 1.25 m/s, must aim upstream at ag, c 1s ph5 2+,t2bmvkh*ls* zyl(uvnin angle of ,s5h2n bksl pcg,u vi*m(h*yz2lv +1t$23.3^{\circ}$ (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)  $m/s$