Which one of the following is an example of a vector qe5z7fggh n,u k;u)zn:( ibnt, uantity?

  Which of the following operations wi k,m,//ozqyczfw+o;ill not change a vector?

  Which of the following is an accurate st275nxvcht vuz9y0 mr7 dg5 2rvatement?

  The resultant of two vectq.q-b8o57 q,k 9vhta ,cnyblwors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively.am75k5m sn xm6b gar193u/kez When these two vectors are added, the magkue 5g xzm bn7k163sma5m r/a9nitude of the sum

  Two vectors, of magnitudes 20 a dr0v:(nsi nds ) 90nlb*wag8gnd 50, are added. Which one of the following is a possible answer for the magniturwnddgi) 0v0sn( a bns* :gl98de of the resultant?

  Three forces, each having a magnitude of 30 N, pull (- *7 /hys,:dtp zjhez(gvkmkon an object in directions that are 7:js/k(zzm ghkd,h( p t-v e*y$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown wm7 5 /mp/zdt7jla mof.s(k)evector is

  Ignoring air resistance, the horizontal component of a projectile's velocity(x: sqm/tofs4

  A ball is thrown with a velocity of 2:/wqaw, dqm4e0 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 props;e-b ,yys ;w./e,ed s9rrwajectile's acceleratione9,a-sysb.; r ,depsy /w;ewr

  A soccer ball is kicked with a ven /x+adaj(1ok locity 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 lt9nxzj nh 8tt(v+9mwxt (;/q the velocity vectwmnljt((9 ;nxh9x8tzv+ /tq tor,

  If the acceleration of an object is always directed perpendicular je5eg ohu37d8to its velocity 3h7j8udeg5 eo,

  At what angle should a water-gun be aimed in order yk;oge )4ywfyhg: )(f for the water to land with the greatest hgw :gkyy) ofhe(y;4)forizontal range?

  An Olympic athlete throws a javelin at four different angles above 5xcwp lo1idz0jzeqk ro7f 7 ,r;6e4r .the horizontal, each with thc,ofjzl1 0i;de.rpez 7k6o 7r5 wq4 rxe 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 m/5jlk2fnxf1qwgeb57 d* tff0p6t7b hand with twice the velocity it had on your first throw, its horizontal range R (comp2n d7bjbmgxf50q6 kef 75t1pt*flf/wared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle ofd3wbkko *5 x )zbiy-,w $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a fielo 6koszzb- 4*g:o8umud goal attempt reaches its maximum height, how does its speed compare to its initialoz o-:mu64ukb8s *ogz speed?

  A stone is thrown horiz1ddz7duhn 11kqsh22wt3 j8 xv,b8jmcontally from the top of a tower at the same instant a ball is dropped vertically. Which object is,hns hv 288jd7q2bj3 k1 xudzcm1wt1 d traveling faster when it hits the level ground below?

  A bullet is fired horizontao0j0w2 ewu/l qlly, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the timeej0 w0uw/o2lqs of fall of the two bullets.

  A plane flying horizontally at a speed of 65.4 m/s and f (yeij (bhdo:s - bb44form-(.h:uzoat an elevation of 298 m drops a p zm.h o-:oo(4:sf ujb- br4f(dy(h beiackage. 7.8 seconds 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 one second later a selkog*7xq8g, nyt . g;bcond package is dropped. Negl o8g.gx;tybqk ln,g7*ecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a 9xnpiwp)e; ,kconstant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wilw;pn)xik,e 9p l

  The acceleration of gravity on the Moon is only one-sixth ofxz1,q(xixt ua gg:8mw12t:4mzdqy 3 h that on Earth. If x4 :ghq8mwzyx aud31qz :2gmtx1it(,you hit a baseball on the Moon 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 relati*: :guelu5q spve to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other cagpque5:u :* slr is

  You are trying to cross p2 wpa/x/tiix8d ;xy+a 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 west from your starting point. You should head;8wipt x+ ax/iyd2x/p your motorboat

  Your motorboat can movef 4 izi- + od5-r,bzq3*5 np/d o)5yuqtzsfhvx at 30 km/h in still water. How much time will it take you to move 12 km downstream, in *)p5/5q- dq5zt yif+rzvzsdf xoi3 o- u bh4n,a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +l fny+pxh((6e x axis. The y component oef(ph yx+6ln( f A is

  If a ball is thrown with a velocity of 25 m/s at an am-0hax 6tlwjx 9,r31m-ij bplngle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a str l(e+tslfogmz 1b 9i phwpe9;s*l601c aight 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 have yp ;sw9 l6e1(hcl*ipzogf01+blst em 9ou walked?

  A butterfly moves with a speed of 12.0 m/s. The x component :o58wv+: ws rvr dcmcal5e4,y of its velocity is 8.00 rlra e:s5+mv cwc4voyw 8: ,5dm/s. The angle 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 leve nmxa .,ao0wus, xq)s+l ground. At what angle is the um0 xnox awss,+q) a,.Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What/xyoo3u9km i 3 are the com3m/x3 uokiy9 oponents of the sum of these two vectors?

  Two vectors A and B have cs-,tejx 8ot y0omponents (0, 1) and (-1, 3), respectively. What is sy0x8ot,je -tmagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = 9einxilw-cj2qm8f:4p/y/ .2wck5 o r k .xgkq(3, 0). Vector C = A + B . What is the magnitude of C ? kemix8yko qi:c /5kxj rgqw-2wl.c 9.2p/4fn

  A car travels 20 km West, then 20 km South. :y, oxz+ iorq-fe 4vi0 What is the magnitude of its displacemeni+,4ie-0 zfoyx:ov qr t?

  Three vectors, expressed in Cartesi*9 wena2i)nb mtd(di;an 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 Carpy c hs/fg,d6qas,79ftesian 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, -4l5t m,u;b8vp xgs* ky).0) and vector B = (+3.0, -8.0), what is the magnitude of vect5 lg*k )yb8; xsv,mputor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What0n18 1hdm/5,jw c p kw/cko 5z(bsatxc is the displacement of the jz c15 / ck5 dm0nsjw,/8 (hbxpoa1cwktogger?

  Two forces are acting on an obje/o sdwtx97mdx(+*i6o.k xh fvct as shown in Fig. below. What is the magnitude of the resultant /+*k6dt ( . hix97mvswfodox xforce?

  Two forces are acting on an obje av( olxu4hte ;-4 te9hu)9wsyct as shown in Fig. below. What is the direction of the resultant fo x ho9v(9ea;4eutl4uyh ) -twsrce?

  Vector A is 5.0 cm losdga-541cfzd9 y8l p mng and points along the positive x axis. Vector B is 8.9 cm long andc415d mpzld sg- 9afy8 points at $+40^{\circ}$ 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 54 cm long 8 ;4aaae a(h.bpy gp-qand points at $30^{\circ}$ above the positive x axis. Vector B is 23 cm long
and points along the negative x axis. Vector C is 44 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 a vl j;;snw:gdu; ;jko n hv/tsdc5;*:fn initial speed of 23 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 3.4 s. What is the k5;fvhw*d l; j ;gnvon :s:tu/jc ;s;dheight of the cliff?

  A girl throws a rock horizontally, with zo3h(9k fksp h95 ivky xf(j:/a velocity of 6 m/s, from a bridge. It falls 20 m to the woxhsi9kfz59/hkp:(yk v3 j(fater below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a pointy1cn*a2,3jl tgv4 /cgn0je ag 29 m above the ground, strikes the ground after traveling h13yec0n2 n,agg/jv4 gl *tjcaorizontally a distance of 17 m. With what speed was it thrown?

  A jumper in the long-jump goes into4fjk/jd;5 q5n ru-28 nsn ldiu the jump with a speed of 12 m/s at an angle 4k5jul n2 ;i8s5q /jfrnnudd-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 the jump with a speed of 9 m;zlo)dlq2: xwb p; 0zy/s at an angle ofxlzd o:zq2 p;;b)yw0l $35^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 28.1 m/s at qmw5rb7 js y .noguegy7/ 0a;/an angle of $23.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veloci/(/bub10 atb ui0qm asty of 25.9 m/s at an angle of $30.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at - )lta8g,uinlan 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 horizoock)ney i jdh;tmx);b, r5e76ntally at 19.4 $m/s$ from the roof of a building 30.1 $m$ 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+fm h 2g*v r6:7gl9o djvppg)a from ground level with an initial speed of 62.6 m/s at an anglegl9j*f 6r+ ph:7 a) dovgp2gvm of $42.2^{\circ}$ 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), y06bb*+t3vkcsvb hjs *ou can run a 1500-m race at a velocity of 4.0 m/s. If you rakb+* bjv3s0 vbc*h6s tn 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 be

  A plane has an air speed of 200 m/s due North, and is inq(mk6;pa4eh;xxfq48lhn i:se 5i r l1 a wind of 50.0 m/s to taxq k ;eh4: ll4;e1fx85m inqh(ps6rihe West. The plane's speed relative to the ground is

  A plane is flying due Sou(b gp fm:ycz36th ($270^{\circ}$) 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 c:u ibp;.o;;o4ysxu f 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 fires a projectile with speed 5q88) gh *dpa:x bxyhtpqp8 ,j)0.0 m/s in a forward di88htjqq )x *p8pd:x ,ayb )hpgrection $30.0^{\circ}$ 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-5is 6nx :5fnlma.t gp river with a current of 6.0 m/s. What is the speed of theni xtf.sl6g:5pmna - 5 boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still water wishes to travco64pch1mq13 3yfql m el directly across a river 1.5 km wide in which the c 34m1lpoc qc1fmqyh36urrent flows at 4.0 m/s. How long will it take to cross the river?

  The driver of a motorboat t .; mnp4o.uja-lsy a e 3hu7r*sh-xsm+hat can move at 10 m/s in still water wishes to trave-sop3m ln.he+xsm.7-;u aajs rhu*4yl 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?

  A swimmer heading directeupjecvg*. .y4u u59yly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swimvuy4* egu.j9. uyep5c in still water?

  A swimmer heading dirb6 4d1w*ph9sqd,l3t jkva 5am)fnn,dectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept dodf )9*4a63a5wlpdnb knj,1dh,s qvt m wnstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.74 m/s, mqxbj7 h fd;i1aga/)v8 ust aim upstream at an angle of ;av xhjbfqd7/ga 8)1i $21.9^{\circ}$ (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)  $m/s$