Which one of the following is mxe-1sf.j7c 8 9becaw an example of a vector quantity?

  Which of the following operations will not chas kv yp3s6+ 0-hsk5pucnge a vector?

  Which of the following is an accurate statemeik (kzeqn3u 7n)d5vfqc c /l(4nt?

  The resultant of two vectors is the smallest when the angle betwf )icg2.ynsm m50 ujco4 *0suseen them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. Wheny9((tfnip.aglakfr4r:zyq0 p k+8a 2 these two vectorsgpri+aftyk(y 2:8k.z0 npl aa(9 rfq4 are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and4eh2au.uf 2qdvw442qsv vo)s 50, are added. Which one of the following is a possible answeh )u.v 2u q42wsqo4vfv 4sda2er for the magnitude of the resultant?

  Three forces, each having a magnitude ofhc w y(;qgb0d*7b q9n*cotug0w m4eh; 30 N, pull on an object in directions thao w h0;c9gy0cb*q*;tmudhw q74en gb(t are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectordx8n/ y; 1c:3 g bj0/sbo,argdtz1.zd amq v9x is

  Ignoring air resistance, the horizontal8kuflkb g38vj 6-u9fr component of a projectile's velocity

  A ball is thrown with a vwk.i d54ra vb+elocity 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 resista/ s4u8xrrmyz4wpyhs(no2 8rfu w6 8,ence, the horizontal component of a projectile's acceleration e(y2 4m rpf,zo n 8rr6xw/8usshwy4u8

  A soccer ball is kicked with a velocity of 25 m/sikn6:-by g3 erx5ogyw74lh kd)k9 l i.8owu.q 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 dire;t,*rwiarc s 5svc,ss y25.ofcted anti-parallel to the velocity vecyv,fssi5s, ws rocc .2*at;5rtor,

  If the acceleration of an object is always directed perpendicular to itkr,o qixvdt-77+o1bbs velocit7x-b+rob7k,vqdt i1 oy,

  At what angle should a water-gun be aimed it/)+ b daf2mpsghna 82n order for the water to land with the greatest 8tdagm)+2ha fnsb2 p/horizontal range?

  An Olympic athlete throws a javelinb r8zanw:8 l 1i4kxt v15 kdn9un,x)xd at four different angles above the horizontal, eaczxxl5b8nak,nk x:n)tdw41 18vi 9 druh 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 ;g1o njk 17xbwe--dtethe ball leaves your hand with twice the velocity it had o;ew jo-xkd1en-t1b g 7n 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 fq4.e*qrgpuu l,f1 x 8of $35^{\circ}$ 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,ti, ls77zpb(g how does its speed compare to its initial spee77s zigptb,(ld?

  A stone is thrown horizontally from d6gh)q+ .:w zell9r qwthe top of a tower at the same instant a ball is dropped vertically. .edg6w)llw+rqq z:9 hWhich object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bulf4lye r0l7 6jlm,d,ha let is dropped from the same height. Ignore air resistance. Compare the times of l d,r6 h le0afm7ly4j,fall of the two bullets.

  A plane flying horizontally at a speed of 111.5 as 1;h(qk)jk sa*7tsqm/s and at an elevation of 270 m drops a package. 5.6 secondjtss);hq sk7qk(a1* as 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 pla08eow r1ikd v4vp:uhc2l9x s ;+) bnxcne, and one second later a second packa) rx0ck8 : +pwic1xhs;uvd4l9on 2vbe ge is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed.cxb,9yge v+9t Neglecting air resistance, when the bomb hitsbgte9yx+ c9 ,v the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is on*b)jqe7iplx+skkr,lc n20-i ly one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at kl*k,0+ enq) icl x-jrb 7pi2sthe 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 rol)xo*y9 +67c uhqtnqjad and pass a car traveling at 45 mi/h. The relative velocity of your ca * qjuly6otn7hx c+q9)r to the other car is

  You are trying to cross a river that flows due southk js*56f6l aji with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your startinik*jljaf 6s65g point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time ih17walw:j1w yi ;t c70gdzg6will it take you to move 12 km down1;1 ww whtiil6y0dc ajgz7 g7:stream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 40em 1ebad ya.o5(lgipbr- f;degrees below the +x axis. The y component of bpbgyear 0e1lf .5a (;-m o4di A is

  If a ball is thrown with a velocity of 40nvpip)(ywu :vo,az 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 straigh. 5 rgjiaza2kt5;c lqt7f):x;u4p yott 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 you walkex ;z;f).laouy k54caitrj ttq 72 pg5:d?

  A butterfly moves with a speed of 12.0 m/s. The x componenw1hqy/t9 z+ wct of its velocity is 8.00 m/s. The angle /y w1h9ztwc+ qbetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow ov g4nr2ob pgqe 5uy*9v-er a level ground. At what angle is the Sun elevated above the ho9 yqe opg2*n4 urb5gv-rizon?

  Two vectors A and B have components (0, 1) and (-1, 3), res:pf1frdl: i: rpectively. What are the components of ir:d pff1:lr: the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. ns9yrwc6,)zvbu9+fd What is magnitude of the su bs9zw ,vnr69uc+yf )dm of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C =n l;/bbr3mtk wu.v*4q A + B . What is the magnitude ofrmnkul4 t/wb.q; v*b3 C ?

  A car travels 20 km West, then +j7sbk+yc1w 0 bfqw* u6ntsy520 km South. What is the magnitude of its displacfw cub +b*y617j+sy0s5tn qkwement?

  Three vectors, expressed in Carte+.3 w gc -opt;cd;kwsqsian 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 Cartesian coorqk. i8df)q65 v:huuny u56lmk dinates, 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 vg dyi3g0 ,(h j7ijwck:k sjq66*ve.d bector B = (+3.0, -8.0), what is the magnitude of vector C = A 67*vy hd:jg3k 6jgk.cw q0i j(s ,ebdi- B ?

  A runner runs halfway around a circular path of ra) 5txjey,0s8ms hkk7 gdius 10 m. What is the displacement of the jogk, )j 57t0sm 8yegkhxsger?

  Two forces are acting on an object jdam js mko4s(1- bx3mnv9w. (as shown in Fig. below. What is the magnitude of the resultadkj3 v1. s o-s(9m m4wabnx(mjnt force?

  Two forces are acting /-s0 a)hw-- qvu b0wdb9 yfrpwv0v/id on an object as shown in Fig. below. What is the direction of the resultant f 0)vu/f- a-- hwibrb0vv90 dqywpw/dsorce?

  Vector A is 4.0 cm long and points along t832n8:toqi* wj9j :t-sa rwc)q pdrwhhe positive x axis. Vector B is 6.7 cm long ans:n 2)3rqwjhwp* i a8do9 :tjtcqrw-8d points at $+27^{\circ}$ 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 71 cm long and points tyv72v n7 x pqeum: 2n-fny x+4o0ca3xat $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 46 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 init./n3k c,bmsv bial speed of 17 m/s from the edge of a cliff. A sto ,mvkcb/3 bns.p watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.9 s. What is the height of the cliff?

  A girl throws a rock horizontalqn3 m u3:o3hvqly, with a velocity of 7 m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizont3 ouvhq 3m3qn:ally before striking the water?

  A ball thrown horizontally from a point 26 m abov0 c g5sd2txkv5 c q4zxcv5+*h-qj dhr-e the ground, strikes the ground after traveling horizontally a distance of 14 m. With what hqvc 5zr5g t 04hdjk-* q+dccxsv2x 5-speed was it thrown?

  A jumper in the long-jump goes into the1yk1c vo6c ihi :u:dh; jump with a speed of 12 m/s at an angle o1 1hi :vdc6uk: ocy;ihf $20^{\circ}$ 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 jumfb5;(u mge8zi fr0dr(p with a speed of 11 m/s at an angle be uzdgf(r r80i(fm;5 of $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 23z9 -5/fu9a+af) tkags o1ycmc.0 m/s at an angle of $37.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched3/tars km q2;v8 5mekg with an initial velocity of 43.2 m/s at an angle of $18.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firbv 5xx7d7p: zjed 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 horizox jhg27siq+ d1)j6o: )ku7kyvh lub u4ntally at 19.4 $m/s$ from the roof of a building 39.2 $m$ 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 (t0s4+te/foqg;l l )b40x zyc-wu q 90zzujgt level with an initial speed of 50.9 m/s at an ang/t0ut xgwzj(90 z0qly clsbftgu4qz e+4); -ole of $37.4^{\circ}$ 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 vel-ke d;xl /)lobocity of 4.0 m/s. If you ran xo; )/d -lklbethe 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 sp gloti h:+2y-beed of 200 m/s due North, and is in a wind of 50.0 m/s to the :to2ilh +y-gb West. The plane's speed relative to the ground is

  A plane is flying due So 7:18ca ;cnltbr8q app0fnzz:8y bp o4uth ($270^{\circ}$) 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 55 r(n7r(r7nq cll wecis 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 firhf2(kx* fx;cm0a 9t ules a projectile with speed 50.0 m/s in a f(h2f09k lca;x*xf m tuorward 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 direba :v mp()pn8rcted across a river with a current of 6.0 m/s. What is the speed of the boa pba(n:vm)pr 8t as it crosses the river?

  The driver of a motorboat that can move at 12 m/s in s lx0 zns+ fvttuw*27nkk,,u2atill water wishes to travel directly across a river 0.9 km wide in which the current flows at 7.9 m/s. How long will it take to cross the rive 2kv0au*2ltns7,+, wxfz n kutr?

  The driver of a motorboat thabt, wy +q b fg2v-0g9wvhr9z ,ft-e9ckt can move at 10 m/s in still water wishes to travel directly across a narrow strait in which t k0yb-vg fgfwc9q b+,h- w9v2ez9r,tt he current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a riverwhlu0g+t;7z rjq5 : vxvir66r 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. i 7jv5rghlv:; rrt6x0+q6uw z How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opp,7 zb lrnmy+5ji hwcit6 ,d2f2osite bank in 6 min 40 s. She is swept downstream 480 m. What is the speet6f,cyrh,w d7i2m nl 2b+5 izjd of the current?

  A boat, whose speed in stilz3zoqo2o 1m7hn7 ov:hl water is 1.40 m/s, must aim upstream at an angle of onoh2q7 3:z1hvmoz 7o$14.8^{\circ}$ (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)  $m/s$