Which one of the following is an example of a vect4vlayv9sa8ta ,3 z 1bfor quantity?

  Which of the following operations wilckoofn7s9kzv jo;7, 4fmj 6w(l not change a vector?

  Which of the following is an accurate statem geo:vpmmmn ;fp.x61qb+m(; b ent?

  The resultant of two vectors is the smallest when the anglxf* mp m/e.lr.e between them is

  Two displacement vectors have magnitudes of 5.0fya(cn 1mzqe4vl2/ j,l-eu d- m and 7.0 m, respectively. When these two yz fu,1en4cv dme2(/l-q j-alvectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, ard9(+q(pqti0c j l /rb*mpls7df. s(cue added. Which one of the following is a possible answer for the ma 7bld dc*rf(qts(+pu9 i(.lq0p/m c jsgnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directionajw)rx y attqw h6v)z).lpxp;da 162 *s thatxv* t)j.a6)y 2w)htl x pra;wd1apz6q are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the q mj,lar3ppjqctg 47b e q*.(6jna+f 5unknown vector is

  Ignoring air resistance, the horizontal 4s .ec:e(sbr9m e vo h9pybn69component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/sc6 hll 4fi6l.u4a j9g8sb. )wc+udvby 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 projecrbur.kd4jbc 19a t1) 5 qu ;k7dx5amobtile's accelerationj4k1bba 7rx5b19.c; q5at udoukd)mr

  A soccer ball is kicked wik(bkx5 2pvu8u4 1pne bth 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 directed anti-parallel to t,r;l oc*qo v8ri jsc91he velocity vectovcr81ij o;s,orc9 *ql r,

  If the acceleration of an ggb6;0jw sn a7vs5ci/6 mim8dobject is always directed perpendicular to its velocitygds0 j6nsvaiwb ;g mm6i5 c/78,

  At what angle should a water-gun be aimed ine dh 33nfm8vo,vbc 8n4z( *xmn order for the water to land with the greatesh3 4 ndb8n(evfov*mmx,8z 3nct horizontal range?

  An Olympic athlete throws a jav:c7 l-;ie2 n+ro rkqss zne:l8elin at four different angles above the horizontal, each wosn nq +:e2scr i ;z8k7l-:erlith 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 m*5u/uiq bns /i27bl htime. If the ball leaves your hand with twice the veloci nhm7lbub52i u/i/q s*ty 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/s at an angle ofoi p-x z/dkm xv2z(rdz,q/7gl jh11jah :84qo $35^{\circ}$ 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, ah +ll kn8hvfmz0q3+ mm6.i/whow does its speed comfn03m wlvhl8mh im+/z+.qk6 apare to its initial speed?

  A stone is thrown horizonta1c*vuxf:t w a-lly from the top of a tower at the same instant a ball is dropped vertically. Which object ix*a ufc1 tw-v:s traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet 0 cysp v -9kerxl73kanr4yh/8 is dropped from the same height. Ignore air resistance. Compare the times of fall of the two buy8 p7 kan csk3l4rv9-xh/re y0llets.

  A plane flying horizontally at a spef.+xa7 *pfbteg ;kno3ed of 47.2 m/s and at an elevation of 262 m drops a package. 2.9 seconds later it drops a second package. How far apart will the two packages land on th;tg.xa3e* fobpf + 7kne ground?

  A package of supplies is dropped from a plane, and one second latxng3 m/f0kwx q 29rf2kiglm e3z 6+m4zer a second package is dropped. Neglecting air resistance, the distanx fk 3zgxzi2l3m r9w 6qm0men/4g f2k+ce between the falling packages will

  A pilot drops a bomb ,5nnxm 7ll 2p7hm asq-from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizh nm s-n,7lq7ml2x5paontal location of the plane will

  The acceleration of g0 xh(0i3r gh*h,1lcaiik75pwjbf r y0ravity on the Moon 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 i hw ab01rhgl(7 rjxpi i3f5y ,ck0h0*on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a f 3pc fbu4;5p u*sh:zwstraight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the cbfzsw:pu ;3f u45*hpother car is

  You are trying to cross a mdlar7 :qf:a u)h+r4j river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly westf)dl+arh 4:m:ra7uq j from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in s i*/pc :t20)ic gdilbftill water. How much time will it take you to move 12 km downstream, in a rbi2tcc)gl0 f ip *d:i/iver flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at a*zx2;,1wbdhi h i3j u(vn; ekbs/um4 bn angle of 30 degrees below the +x axis. The y component of A3d,b;uik wx2j /bh1;vb 4*snz i(meuh is

  If a ball is thrown with a8 2oinch4b5wi velocity 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 direction north of eae*dh)+gmcf;nx v.o n 6st and you end up 2.0 kmn ec;)x*m+n ohgd 6.vf north and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s *.9/ fauqhn;wn5c7o ,tjkv mk. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis mus7qwt/k f.vm5;ka*9 uhjc non, t be

  A 400-m tall tower casts a 600-m)zj0-)jke 2w4t 0bh oek.soy r long shadow over a level ground. At what angle is the Sun elevated above the 2sywk4hbe0kto zj0- )jo .r)ehorizon?

  Two vectors A and B have com qsi8)ru)w9v wvd -sy9ponents (0, 1) and (-1, 3), respectively. What are the comwuq)dsi) y- w9sv 8vr9ponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. xb: nu :rl8k 7gkhbft)*nuj5 zpb/(;m What is magnitude of the sum of these two 8 puku;n rtlkmx7fb:bz()/nhj*5: bg vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What 4mne, focf.uu8l +r2kis the magnitude of m.+28c efrokuul ,fn4C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disp)fm/ ibj80 rsm.aejweac1 e(4lacemen.1mce je /m4 0ajb8fwa(se)rit?

  Three vectors, expressed in Cartesia+kx bi+-o4q4xbs4(q3 : oxntrua 9 jhan 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 i-i 9be6bqvolq,bjlk(55 he. in 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, -wow+ n1 gxm46o8.0), what is the magnitude of vector C = mw ong ow4+6x1A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the displcm id/gq3 +rvyl. v rgdj/0a3d c,vw()acement of the0i/3 gdlv.,r(v w cm yvg/d)qjdcra3 + jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnitul mqd:3. yhk,-js 2e zxh;+zwfde of the resultant fory zh x; sze:-q fh32.mldw+jk,ce?

  Two forces are acting on an objecjh-voqz ;ib lr6y593 st as shown in Fig. below. What is the direction of ;sjy - 59irb qz36lvohthe resultant force?

  Vector A is 4.4 cm long and points along the positive x axis. Vector B is 6.6 x/-aau:zt8 rmcm long and points at a: zrm-/u8atx $+33^{\circ}$ 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 69 cm lon35gevzi-z (w x6pd7xp+m - qphg and points at $30^{\circ}$ above the positive x axis. Vector B is 21 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 horizontally wita ko,+(kyyf5ld ip99 kh an initial speed of 23 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time f9ya5ik9d,yof +(kp k lrom the top of the cliff to the bottom to be 5.0 s. What is the height of the cliff?

  A girl throws a rock aq v lzfl ev8c-0z)k:o4q.-iyhorizontally, with a velocity of 6 m/s, from a bridge. It falls 11 m to )k4- leqzvq. yc8v0 a:liof z-the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above the ground, stri fc88s8vyc :q9olx 7slb chm)k.,r(fb kes the ground after traveling horizontally a distab8lh.lvk o):8(cfc7br98q y fc ssx,m nce of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes z/0dm*z2rsiqhs3x j 9into the jump with a speed of 12 m/s at an angle ofzjq x i*93rmh0sd2zs / $20^{\circ}$ 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 1 zonu **b6i4a5eozyuo l 6uqq/6 c8ci30 m/s at an angle oioy ec 8o*5q3 ia4ouulb6q*z z6uc6/n f $16^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 56.7 m/s at l f:p:vs +8no.z4htwcan angle of $49.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of;fwz:o7tv(9; ii yjn o 54.0 m/s at an angle of $24.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anny:v9f. g318 f kaagyp4m 5lj2dl fgq(gle 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*st22w1/ n f j5simptf at 25.5 $m/s$ from the roof of a building 51.1 $m$ 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 with an initi0w;ogv kz+mfrk48 75cl. wecq(+ mtw.g8ok kcal speed of 45.5 m/s at an angle omclktz ;o.rmk( gkqw+ c7e0 kfwv45o88c+.gwf $42.1^{\circ}$ 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 1l )b(h/pgot/nkk -ytao,+ ; bkwk6j+q 500-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 you to finish would bk/kyotbkj g6 t,/-k )ao;wnq+hplb+(e

  A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s ogu/w)y33.vq zk o,j o6bhbo q 34s4fwto the West. The plane's speed relative to the ground fbqu g3,36o/ w3yko qwohovbs4j4.)zis

  A plane is flying due Souta )2t mkkofr1awal41(h ($270^{\circ}$) 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 i0;ri fa .2ul0gzbu nyz5ww4 -hs 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/3bye;v9o 1vx:3yhq dks horizontally fires a projectile with speed 50.0 m/s in a forward dqxvykyo; 3vd1b e :93hirection $30.0^{\circ}$ 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 8.0qsesk.u3i 0(e wks4 y6 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as 0. kqss uyk3wi4s6 ee(it crosses the river?

  The driver of a motorboat that can move at 12 m/s in still watvftt(8sp kdc+8e,z93tmt 3i ver wishes to travel directly across a river 1.8 km wide in which the current flows at 5.0 m/s. Ho+vmv 9kt s83tztd ,pfc(38iet w long will it take to cross the river?

  The driver of a motorboat that cadkw4yw.0uy( x d(ilwe- l7/tfn move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?wi4wl x.7 -0yt(defu(wkd/ yl

  A swimmer heading directly across a river 200 m wide reaches the op-ojs( .ton5ygeix2r :posite bank in 6 min 40 s. She is swept downstream 480 m. How fast jgey2.srx-(i5:oo n tcan she swim in still water?

  A swimmer heading directl eir/e p.web r15;ecf(y across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is th; 1 (ibpwe erce.5f/ere speed of the current?

  A boat, whose speed in still water is 1.99 m/s, must aim upstream at an angle ofq3y.3gfdokr);l 3tv d lvrqt3d;f .)g3y3kod $16.1^{\circ}$ (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)  $m/s$