Which one of the folhz4):nr 2zjzs wewt80 lowing is an example of a vector quantity?

  Which of the following huromlu -)1 -re5yu(i mu /qn1 x:9dnhoperations will not change a vector?

  Which of the following is(/w godt (4)wb kf8q*w9 kdtur an accurate statement?

  The resultant of two vectors is the smallest when the angle between them 9er vxz2x l7exva40 /sis

  Two displacement vector )3,gr*4xfe ed9mii4, a;qb ijs)tnlts have magnitudes of 5.0 m and 7.0 m, respectively. When thesrtnted*bx;e 34mi9) isfga), jl4iq, e two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and h.5f2 lozun;olct 9,r 50, are added. Which one of the following is a,crfon;ol h 9t5ulz2. possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude ono*npu3v o1 ;ff 30 N, pull on an object in directions that arp 13nnfvo *u;oe $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown)4 fcf e-yyj1 z - d,gpah57j;vo8tuww, the unknown vector is

  Ignoring air resistance, thelh)wsx3 5 yjasss0b 3-g8sfi( v8 ibf7 horizontal component of a projectile's velocity

  A ball is thrown with a velocim. w-28dqefie u )ccpn4uqa8 4ty 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 proje,bp ve: mi0 +1up7ltbpctile's accelerationvuepl7bm0 b,i1:t+p p

  A soccer ball is kicked with a velocity of 25 m/s at aj ji8zfnqffsk4z1) e-bi5*h 9n 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 directed anti-z9 d/su,st)tj parallel to the velocity v s9us/t jtd),zector,

  If the acceleration of an object is always directed per4settvq r( l2/pendicular to its velocity,/lrs(24t tvq e

  At what angle should a water-gu3vpukg;k5d.c n1z 8 bqlmj-*un be aimed in order for the water to land with the greak5l.18 u3pj* ;gqndv zbk-mcutest horizontal range?

  An Olympic athlete throws a javelin at four diffe ti/lo 8nv, a.ui42fd*k dsf:crent angles above the horizontal, eachd *,fiovaui/ 4n .sk2ftcld8: 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 leav 27drzmu kgzel *5p;c+es your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve)glc 72r ;+e 5pzzkmu*d would be

  A ball is thrown at an original spe-eobcj ysl 4-:ed 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 r56z:c )vwdf.o df4u wbeaches its maximum height, how does its speed compare to :o dzf.4 cufdv)w6w5bits initial speed?

  A stone is thrown horizontally from the toz5(pp g/+jt-uxhx 8p+uxpz:/ b7nbrop of a tower at the same instant a ball is droppeu/p: xx hb8 r-p/+tpbxnzoj7p+(5zg ud vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, apk:jrc v)- l4 lqvdb:;nd at the same instant a second bullet is dropped from thpcvl;bv4:ql: rjd)- k e same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speedalsd:z(.hwm:pk, bc76yg +ap of 46.8 m/s and at an elevation of 210 m drops a package. 3.2 seconds later it drops a second package. How far apart will the two packages land on the grounp l(6 agb7mdc,.ks+ wzya::hpd?

  A package of supplies is dropped from a plane, and one second l 6;0wlkwxtv ;xater a second package is dropped. Neglecting air resistance, the distance between the tx;k;0xv6 lwwfalling packages will

  A pilot drops a bomb from a plane h n4mkf+s,o7vfhq,5h flying horizontally at a constant speed. Neglecnhqh57 , ffvhksm o4+,ting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gtc8z xs9z* 2xyravity on the Moon is only one-sixth of that on Earth. If you hit a baseball on the Mooc28xsyx*z9 t zn with the 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 relatnzyy y))6d py7ive to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car isny) p)yyy 67dz

  You are trying to cross a river that flows due south with a stro26 )ynf af1xcg3ou9ryng current. You start out in your motorboat on the east banxo uyf2a )6c1gyf 93rnk desiring 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 much timdimnqp): bh6) e will it take you to movqbn6d ):)pih me 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle kui*glih3(+lw4ldy 5of 30 degrees below the +x axis. The y 3i5+l(d kih 4yl*gwlucomponent of A is

  If a ball is thrown with a velocity of 25 m/s a; pn6zkfk3/m jbkg n cl(()lq3t 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 dirpu7r*kauu6 v5n gz aven 9e56+ection north of east and you end up 2.0 km north and 7vevn pu nz95*eg kauua65 r+6several 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 velocity is 8*s2 ;hc fr1bnp.00 m/s. Tsb*n2 p;hc1f rhe angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts ajf- :kghyu5b2 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizon?bujf:5-g kh 2y

  Two vectors A and B have comp+f2ctdeoz,r) onents (0, 1) and (-1, 3), respectively. What are the ofd,tr2) zce+components of the sum of these two vectors?

  Two vectors A and B have componenoj,+uuvu :-1 lgno:zkg+ qs(vhx e2 *fts (0, 1) and (-1, 3), respectively. What is magnitude of the sum of uf:e 2lugx1gzv+-u+:k ohn* voq,( jsthese two vectors?

  Vector A = (1, 3). Vmfcmjc:a /lhh2k:( wi8d z- m i n7fc83:b1kkaector B = (3, 0). Vector C = A + B . What is the magnitude of C :-nlack a z:f3c(ic2 i8m 1jkfb: m/m8d khwh7?

  A car travels 20 km West, then 20 km South. What is the ma7+bu.pjyn/ ylgnitude of its displa y+u7njy. pbl/cement?

  Three vectors, expressed in Cartesian coordi/rpi otz 8l (a6)hczs)nates, 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 Car1u(z-1nuo 9oi9tvm qe tesian 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 isxaf.yzq7.h k) the magnitude of vector C = A - B ?khq .f.7y )xza

  A runner runs halfway around a circular path of ra po5n* 0 taos.j1:yycuw:zt/p;2gjptdius 10 m. What is the displacement of theo2zp:;/t1yo g*y sjw utap0:.n 5jctp jogger?

  Two forces are acting on an object as shown in Flbo:xfw58.e2qur h.big. below. What is the magnitude of the res.2bof quxl5h:. rb8weultant force?

  Two forces are acting on gh( gs:: imw6wv8w f.kan object as shown in Fig. below. What is the direction of the m(: g w:iskwh8g.fwv6resultant force?

  Vector A is 4.8 cm long and points along th)l v9hfp.z-due positive x axis. Vector B is 9.9 cm long.l z)u-vpfh9 d and points at $+55^{\circ}$ 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 80 cm long and oay)lywu5a3;+ xzg;z 4;rt)k y6zyhjpoints at $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 39 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 of4zbxwuu7g33 x 23 m/s from the edge of a cliff. A stop watch measures the stone's trajectoryxb33gwzuu4x 7 time from the top of the cliff to the bottom to be 2.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, from lmuwew3 -dptaur), h g+6 aj13a bridge. It falls 24 m to the water below. How far does the rock travel horizontatl) g1jprh6a wum3u3w+-e, adlly before striking the water?

  A ball thrown horizontally from a point 27 m above t,-w4 eui9d /7f bmj5iqws+bjuy4/p othe ground, strikes the ground after traveling horizontally a dist+ /45mw u9, /dwi e4uj7ibbfqty-j sopance of 18 m. With what speed was it thrown?

  A jumper in the longb7 6ta g-vzy)y-jump goes into the jump with a speed of 12 m/s at an angle of y7zy ab6vg -t)$20^{\circ}$ 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 v.o/c9lje2 h ,vc.xygn/ st4uwith a speed of 13 m/s at an angle o.h/uxevc 4gv.c/s tnylo29,j f $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 20.1 m/s at an angl5f gjo 5q,tmc 91k6pohe of $27.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initialo n3/ hub8rbco s/(jj, velocity of 21.3 m/s at an angle of $33.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an ang1 j1vy*hb9 ,p5 iebsey)gjz)mle 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 horizontallyuq,8mz,of1c8 pfzq d)*lv 5 eq at 23.5 $m/s$ from the roof of a building 54.3 $m$ 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 gr: is upsg y/me4p/6u)qound level with an initial speed of 60.0 m/s at an angle sys/pg4 mu /p6eq)u:i of $45.3^{\circ}$ 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), ycrm (ai hvs5f+3m3hkci5.pv ar);+y rou can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when +3 cr;mr3av(k .m5ciaih +y5vfp rsh)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 spdg7ji;.e0* rt1cot g jeed of 200 m/s due North, and is in a wind of 50.0 m/s to the Westr g ed7*gtjt;.i01o jc. The plane's speed relative to the ground is

  A plane is flying due Sgf t, 0k+rg(fcouth ($270^{\circ}$) 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 n qo zbwrl9+q( (cx(zj0u2f*l$30.0^{\circ}$ 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/(nrbbx0ngu v e*i,fs xt /3v5:s horizontally fires a projectile with speed 50.0 m/s in a forward directi *ufr(/:5e gnib3s,xvnv0x tbon $30.0^{\circ}$ 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 acrjdnxe.x zg :2u03 wsp: j *k6rng2)gwkoss a river with a current of 6.0 m/s. What is the speed of the bu 0j*2gng2:jrdxwz. k6sn3: epk) gwxoat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trki5)tnq8edhd2)4s eu avel directly across a river 1.9 km wid uih et))8q2d5sn ed4ke in which the current flows at 4.4 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 x)r3,vb dat;nm/s in still water wishes to travel directly across a narrow stx)b ; vrdan,3trait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppositez j3rb (mgmp b412kre7 bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wag1 bjz 4p(2rmbmke73rter?

  A swimmer heading directly across a river 200 m wide ;zl3.k p4uj( oh4 uzzvreaches the opposite bank in 6 u.koh zu(; p344z vljzmin 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.06 m/ q(s f-dyii,(rs, must aim upstream at an angle ofq( ,sdir( -fiy $12.8^{\circ}$ (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)  $m/s$