Which one of the following is an example of a vec qg- du:3kz.vuhrz*)btor quantity?

  Which of the following operations 54mh6 kjqls((qj0j4s izn5-yu ym*u awill not change a vector?

  Which of the following is an accurate stateme a(- utt ::;pzr a;+c-njenu)vc qi2:tz9byzint?

  The resultant of two vectorx8ft5fifw(j3s- sa c:s is the smallest when the angle between them is

  Two displacement vecto d3tt-r,n l2virs have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the s3d2vn ti,tr-lum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followingapzvtxw: 5aidcz :::r e:b (x9 is i bdxzza: c:a9t: rwx:(v:5pea possible answer for the magnitude of the resultant?

  Three forces, each having 7kiiw8 hq,k lri 5)v*ipz+xy8a magnitude of 30 N, pull on an object in directions t7i 8rx,kiypvlk+i)q iw 5hz8*hat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknowbh itb0jx,e18 n vector is

  Ignoring air resistance, the horizontal component of a projectile's v xemy,g4c;*e helocity

  A ball is thrown with a velocite0bv1i/g i9 fmy 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 projectpx.h1nz kl1 oer4m6-aile's acceleration1z1- xo. nhmp4el a6rk

  A soccer ball is kicked with a velocity dnat.x1 qdgh (e2q7c 7q*k*x)oq9cfo 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 direcq+3gyku:s.td +t g4v wr+t;4-bb vqf njs2)rbted anti-parallel to the velocity vectogqv+v tsb g+q3n)44b2r f;ybt+: tu.jsw dr- kr,

  If the acceleration of an object isxx1t0yi6n/ or always directed perpendicular to its velocitri0onty 6/x1 xy,

  At what angle should a water-gun be aimed in 0hqf+)dfb yx :xjj8 (border for the water to land with the greatest horizontal0:fdx (xfqy j)jb hb8+ range?

  An Olympic athlete th9sw ginq705fy rows a javelin at four different angles above the horizontal, each with yf 09sigq75wnthe 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 se8rn 0qzoqntu;7+c vo98kqah7cond time. If the ball leaves your hand with twice the velocity it had on your first throw, its zt 9n oaqokq +q8un7c807;vrhhorizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s+55):.l p my :ag fhm-nqzwnxr 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 height, hor v( ovyo -+sfjc(ww71yd*8riw does its speed compare to-f*w8 oyio(d cjy 1w +7v(srvr its initial speed?

  A stone is thrown horizontally from d*i*:asj1oy38kj.w 5dqto w; ; orifnthe top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level grou*ia3owdrkd.wto; ; n1:*oy q5 si 8jfjnd below?

  A bullet is fired horizontally, and at the same instant any*z dao j5z/; second bullet is dropped frno*z zy; 5/adjom the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 119.9 m/s and at an elevation b/steh(v1hrd9mw4x,qdgc7s bv jy ),f d-64p of 199 m drops a package. 5.8 seconds later it drops a second package. How far apart will emt-1,yxgrbshfsvw(v4q d 76cdj9 bh ,d/ p4)the two packages land on the ground?

  A package of supplies is dropped from a plane, and one olf/gj12o oo*8a)t z mlr:*sj second later a second package is dropped. Neglecting air resistance, th*toom1 lo8 zjr2lago*/:) sj fe distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally atg8;;j fle b:pznj3 e7r a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wilreb;8 jg7e3lj z;: fpnl

  The acceleration of gravity on the Moon is only one-sixth of ashi(vfo,*+yv2t dsz a:n 3 .ythat on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you wouvhis3a*:voy+ f z.(sd,ty an2ld on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a stjr 8 (cu-b 8vjr/4,ms zp6riruraight, level road and pass a car traveling at 45 mi/h. The rej,rjzr-6v84ur/ icurs pb m(8lative velocity of your car to the other car is

  You are trying to cross a river thf- p0,ckof z1 wa+,dahat flows due south with a strong current. You start out in your motorboat on + dfoh1,0,f-w aazckpthe east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 4x80p;e 3ngpya qzb4f km/h in still water. How much time will it take you to move 12 kmna04byfeqgx4; p 83z p downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degre yak(br 0*ee(wes below the +x axis. The y component owab 0*ykre(e(f A is

  If a ball is thrown with a velocity of 25 m/s at-(sj:rc :nivr 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 eas8r c .lz,:ec5e2obvy ct and you end up 2.0 km north and several kilometers east. Hc l5c2r zyco,v8:.eeb ow 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 icu3kjsftq g r ; (a:*rj(sx58o/xe1zas 8.00 m/s. The angle between the direction of its motion and the x axis ;q3:ausxk tfce (rs/( 1j*oj 5gar8xzmust be

  A 400-m tall tower casts a 6glr3.4ab;j f+ 7bs1qfbda y.m00-m long shadow over a level ground. At what angle is the Sun elevated abob7 l1y+aj q.;bbrgdms.43fafve the horizon?

  Two vectors A and B have components (0, 1)r+t5+t n4pt df and (-1, 3), respectively. What are t r5t4fdp+t+tn he components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3i0 ybphk i1w: k63ki/io9q uostz2 sml/6b02v), respectively. What is magnitude of the io9si2 zkvmiw tokupy2/6:0b6k1 3b0l iqh s/sum of these two vectors?

  Vector A = (1, 3). Vedgwg 2je. .0tc0,qm , fd2 gxdw;xdq8hctor B = (3, 0). Vector C = A + B . What is the magnitude ogtwdq,w8 f g2jx;de.0cx.dhq2 ,d 0mgf C ?

  A car travels 20 km West, thennkfa2:m9abe + n:g*3 j(qm leb76ykaz 20 km South. What is the magnitude of its displacement9:jyan7b3ae lk2nq gba*+:(f m zekm6?

  Three vectors, expressed in Cartesian coorrgqc w7l 3*,agdinates, 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 Carte +d *pxkh:)olssian 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), b8 au;v3 w zhkcv mih8qb;:)3qwhat is the magnitude of v:c8u q8 b3)3 kvhqba;mvi;whzector C = A - B ?

  A runner runs halfway aro 4ld8kz+o(s gvfno44oh/ is i.und a circular path of radius 10 m. What is the displacement of8ls /ohi +o(fzdnvoig s44.4k the jogger?

  Two forces are acting on an object as shown in Fi x ldgb2-yc.6o7s ad cn6,y4nv;uan o.g. below. What is the magnitude of the resultantxg7csnolu .ov acn 6; y.6dnd4-,aby2 force?

  Two forces are acting on/,gxgzw )c)/vhgla x tv2/ynai:8k 1y4yf yp9 an object as shown in Fig. below. What is the direction of the resultant fo,y f:i nva)9gv2y8clw hg4/pxxg kz/ /y ay)t1rce?

  Vector A is 5.8 cm long and points along the positive x ax h9wqkgwqx(2wys *w/s1 gq,(ggl.zg 0is. Vector B is 6.0 cm long and0qz(w 9gyhw*1lg2gq wgq/.s(sx, wkg points at $+30^{\circ}$ 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 58 cm long and points at /b(0*gqt f;jgb,.bsuwyo6ft$30^{\circ}$ above the positive x axis. Vector B is 17 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 62grd txfmd7 ;with an initial speed of 27 m/s from the edge of a cliff. A stop watch fxrm ;t2gd6 d7measures the stone's trajectory time from the top of the cliff to the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velociyna5tmq6x;8j. ymk; * gn6s waty of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock trjsa;; k6 nnt.y*w6xa 58mgqym avel horizontally before striking the water?

  A ball thrown horizontally from a poin iv7y +kn pjq1j)r. w-.5taxkpt 19 m above the ground, strikes the ground after traveling horizontally a distance of 20 m. With what sp7v1-pty.p+5k)krjxi a .q wn jeed was it thrown?

  A jumper in the long-dmzja-ptjt, u6(.suz h 0w 4ab)ro;14xkvwu )jump goes into the jump with a speed of 12 m/s at an angle of) pbwjdhz0mu.,6vz; j4x at urw kt (-o1)4usa $20^{\circ}$ 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 9kyz8pymr *l;+xnd m +gao8r4speed of 10 m/s at an angle of m l88p+ r+;9 oz*mny gkyrxa4d$26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 33.6 m/s5y)s/ fmjf(,nh ixf0q at an angle of $31.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched w(k r+q)4wfp lbith an initial velocity of 45.5 m/s at an angle of $37.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of m8zt2k.7 oluyioam 1vs 6r,y 8$30^{\circ}$ 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 fw fb7 qra3),yat 21.7 $m/s$ from the roof of a building 56.8 $m$ 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 fromkeclat.(m6( k k v/w/:fwekz ( ground level with an initial speed of 53.7 m/s at an an/e.(ef lkk v(k6 ckw(at/zw :mgle of $47.2^{\circ}$ 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 of2/xbl864pl .3ut rgvmf f crr. 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 mgx tl4. ru6bmp3/ ffr.c2 8rvl/s, the time it would take you to finish would be

  A plane has an air sv00e;vbwtg 20mqs8,/ abhtvupeed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's spees gt,tb ;aqv8h0evvw 0m/ub2 0d relative to the ground is

  A plane is flying due Southvq vyrhg5, rt5p1 t2;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 spexki eggd.0p3* ed 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 2 7efdf1c7oi) 2z4i1gceqcjg 800 m/s horizontally fires a projectile with speed 50.0 m/s in a forw 7jegd i7)f18cigcf2z14 qe coard 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 across a river; hx2hi7p7tc x 47apgo with a current of 6.0 m/s. What is t;i77a7x 2hp4 thgcpxohe speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 12 m/s in still water wis7eq3/,b, t kpnu uy 26c)xgjwuhes to travel directly across a river 1.9 km wide in which the curwx uyu/2 3p6eq7g bjnu,ck), trent flows at 7.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can nvg;x8 dnvkt* w6fv -6xt4/jwmove at 10 m/s in still water wishes to travel directly across a narrow str t ftkv-wx 6n8;*/xvw4g6jdvn ait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly ff 3eaklca3i1w4d:: 7y(ucuu across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is s a c lucwu:a33:kyf(f1udie47wept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reauv,j- u2uqyd xkannf+ +s6m /)ches the opposite bank in 6 min 40 s. She is swept downstream 480 m. Whafx-nk 6uj/ ym2 vuun+q+ds,) at is the speed of the current?

  A boat, whose speed in still water is 1.62 m/s, must aim upstreaw k(nl o ukxoac/45wz*y8:c d7m at an angle ofuco al4: k 8/(5ny*ckwx7zdwo $27.9^{\circ}$ (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)  $m/s$