Which one of the following is an examd ewlc;(u u+i,bi,4u a34mi olple of a vector quantity?

  Which of the following operations will not change a vectoo h9b7: jrkph,r?

  Which of the following is an accurate syx, /sf:ysa;9 ilgvl -tatement?

  The resultant of two vectordut9w/eu b,i ;s is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m andiy- q; 8c7/pzr yezaljr(0vg0 7.0 m, respectively. When these two vectors are added, the magnjz0yi-7gyq( 80rrca ez v; l/pitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following is efq:x2 l 0 4mfto p7ac91:seb-2 bnvdca possible answer for the magnitu:-dc tef 2:0n b7mb2 sq v4ocxafp9l1ede of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object r 1j5+pgl*npqin directions tha1 npjr*+ p5qglt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector euk/6/0pk h7 trtw,flvqm+ 1nis

  Ignoring air resistance, the horizontal c6hftsu dj k 0ks1a-(s+omponent of a projectile's velocity

  A ball is thrown with /wn-cgb*8: b9vl1b fesy/ mak a velocity 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 horizontauw+fn /l7xzq qv1(kt,l component of a projectile's acceleration/7v+(uqz,nfl 1wxt qk

  A soccer ball is kicked with a v0)1p q riopc/ e2a.nuso+le(( fc-a rqelocity 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 dir lpdlm2)*zjnr53g,ar ected anti-parallel to the velocit )dj5ml pgzr,lr*32na y vector,

  If the acceleration of an object is always directed perpendicular to its 02p *g,zi devs 7 gxgu948qhykvelocityxgi u2907kvqep hy ,8gsd* 4gz,

  At what angle should a water-gun be aimed in order for the wa6 7wi8xrdh7,a m+hu hj1u,h*dqa(;b7mrjqtx ter to land with the greates xr(t,;hd uwa qd+,7q*78ihh6ma mb ujj7x r1ht horizontal range?

  An Olympic athlete throws a javelin at four different anglesticq-qj. s 7,z above the horizontal, each with tiqj c7.qz-,t she 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 th h2gc9j+0w0jfii g1ig e second time. If the ball leaves your hand with twice the velocity it had on youic0 h1 i29jgw 0+gfjigr first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an orig38 sv3tmzojx s; 94 4c7qpqivwinal speed 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 reaches itst.t2p)-z11z/qs:vdfiiy; x xr6f lu j maximum height, how does its speed p1ilx6 ts x.fdz)2/ qviztu :j1-f ry;compare to its initial speed?

  A stone is thrown horizontally from the top of a t37j e :yitmmm/ower at the same instant a ball is dropped vertically. Which object is traveling faj: i3y/7etm mmster when it hits the level ground below?

  A bullet is fired horizontally, and at the sam-ijzix8a1vhd , 4*6g7jfnd uqe instant a second bullet is dropped from the sameiz-qvjdi1 *d 8,f4xauh 7n6 jg height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 87.0 m/s and at an elevation of 1btxp rfezm0y pw:1 4pk,5y14o49 m drops a package. 4.4 seconds later it drops a second package. How r44 p ,we:kppt1 o zyby0fmx15far apart will the two packages land on the ground?

  A package of supplies is dropped from a plac) rah,9qeb.2o i k-dhne, and one second later a second package is dropped. Neglecting air resista.2 kob,aeh9cqhd- i) rnce, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizonta njv+:m:rdo/d lly at a constant speed. Neglectin/ j+mrv odn::dg air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that o 2ra2z i;nxts1) 3xgjhn Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on 2gji ;1)r xts3x2zhnaEarth, the ball would land

  You are traveling at 55 mi/h in the +x axis relhi qbq/0 2x(ggative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other gigq2b/h (x0q car is

  You are trying to cross a river that flows due south with:/:v0 ml;t gvw 5j/dpyvov d6k a strong current. You start out in your motorboat on the east bank desiring to0/djot/v l:d;v mw 6p:yv g5kv reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h i(gxilk9- 2zgj* (woc pn still water. How much time will it take you to move 12 km downstream, in a rgx (i( 2gl*z-kjpwc9 oiver flowing at 6.0 km/h?

  Vector A has magnitude 8.0*lg fnp)6wdx4wq(m nvec/2 d; m at an angle of 30 degrees below the +x axis. The y componen wv/*g)f l(xpce 4d6; wmd2nnqt of A is

  If a ball is thrown with a velocity of 25 m/s at an a9btyjt l--(bs ngle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a str6* 38a-si z5qs 7nt xvxyl+otraight 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 tvita*xoqxs37 5yl s-6 r +8znhave you walked?

  A butterfly moves with a speed of 12.0 m/s. Thhzwj g- aulsu2gcu8207 n.e*de x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x a l.g8znj-uuuae70w*2 cd2 hgsxis must be

  A 400-m tall tower casts af)6j0 /wvnsgp)8 k crmjf;f*z:rmx 3y 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizon?80v cfkx m *3:jjwfrm)) 6y/;fzpnrsg

  Two vectors A and B have components (0, 1) anurbo(9t0- uvj d (-1, 3), respectively. What are the components of the sum 9-(urjtvu bo0 of these two vectors?

  Two vectors A and B have components (0, h ay7yy6sa e9(zv p.u()bc xk4wg4h3l1) and (-1, 3), respectively. What is magnitude of the sum py4yx3b h)(w9uklae.4hca sz 6v( 7y gof these two vectors?

  Vector A = (1, 3). Vector B = (3 r d+wgc i5xh-s/h6t7o /y)ifp, 0). Vector C = A + B . What is the magnitude of C ?-hoy5pg+ 6dcix/)tr7siwh f/

  A car travels 20 km West, then 2 ow47.iwgw 7ztn2 2b ass.qebb wy*ew)qm.6h60 km South. What is the magnitude of its displacemeew6i4.zq g ) b*nyo.2 2swhbt 7wambwqew67.snt?

  Three vectors, expresseo6w hh)i*ur5wd in Cartesian 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 coordinates,qt3qb ty71l 55u+c lkj 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),w0vc91k( 8a/pi rkezs xqlj// what is the magnitude of vector kzr 09(k/ 8vxw/clij1sq ap/ eC = A - B ?

  A runner runs halfway around a circular path of radius 1ciq dze4/z zk )9.ow.se i*0un0 m. What is the displacement of the k/edzs z04. newcio)9u . zq*ijogger?

  Two forces are acting on an object as shown in Fig. below. What is the m.lc)9jn n3xhjq8uwy+ agnitude of the resultant forcnjq j+)l9xw .cnh u3y8e?

  Two forces are acting on hyfum1:(ecja+q dxp rd6 +( 4xan object as shown in Fig. below. What is the direction of the resultanmcjphxf+dxu6d ry+e: qa4(1 (t force?

  Vector A is 4.5 cm long /9qb t2 bdz)3r5fwjum3 ef0/ xd7uxleand points along the positive x axis. Vector B is 9.0 cm long and poirudxjf0l32udtf ee q)/w /zxmb5 793 bnts at $+41^{\circ}$ 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 60 cm long and points a; v(sm-lf,rs9kp2 59lo;obgqg6a u(ok sc8bzt $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 26 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 of 11 mqo )7kx.cg5w (movbksp z0) :j/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 2.6 s. What is the height of the cliff?.:)k 7vsxbc op5( okgj0zqmw)

  A girl throws a rock horizontally, with a velocity of 9 m/s, from a bridge. by * mr7e a3,xd/no4 mqaz9u2rIt falls 22 m to the water below. How far does the rock travel horizoz/ mq 2ume43n ard,yxbar o*97ntally before striking the water?

  A ball thrown horizontally from a point 30 m abot j;+r2f z ntk13ltd*nve the ground, strikes the ground after traveling horizont3+* lft2 n1nrdtjk;ztally a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed f7cy7f jg,95shjb sb:of 12 m/s at an angle 9jfb:7,gfsc 57sj ybh 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 witbse-e/ rj.4iko +jtq)hmf/ c 3h a speed of 12 m/s at an angle offhjorqm). kt /-4jb /3s+ceie $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 45.1 m/s at an gqwyh51v ;zqf ml;.;i angle of $10.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched drnrcge+,3: gcg9jp5 s/.o n lwith an initial velocity of 38.1 m/s at an angle of $26.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fi-ok6zpqo vm5 )red 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 horizontally at 16. j ju2s6jv ytx/0n-gg5x 6rk,o5 $m/s$ 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 frb65 + 8z(voul;zqzcftom ground level with an initial speed of 63.2 m/s at an 8(;tzlfz5uqc o zb6 v+angle of $39.9^{\circ}$ 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 v/x,:b j r4wa f; 1mhqglvwm v64cxc6.zelocity 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 fwv ,gamcmv4 qbjx: frw6h/zc.1;64xl inish would be

  A plane has an air speed oyj8uum;z6a5 p f 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ga5 puy z;muj86round is

  A plane is flying dueyc*f 5il,yohr v,3ce, 5 iao1m South ($270^{\circ}$) 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 k+0i ma7j pk8zis 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 s) v.pmcn4ja6j1.4u4z zq owzepeed 50.0 m/s in a forward directionzq wuzvc ap 416n.eom.4 jjz4) $30.0^{\circ}$ 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 riv2w zuf0tm7t+ per with a current of 6.0 m/s. What is the speed of the boat as it0 p+2ft uz7wmt crosses the river?

  The driver of a motorboat that can move at 9xokln:e6i3)w :xec mok(c7p3 m/s in still water wishes to travel directly across a river 1.7 k6 l: n7om3xo3xc:) eipkwcke (m wide in which the current flows at 7.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to travn3pa ;z;dc: myel directly across a narroamn;3cz :p ;ydw strait 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 th,tlov awex 90- 4p4t7jzan/v 7bbae,b e opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wate7a e-bwb t p jv,nebo ax97v/04za,tl4r?

  A swimmer heading directly across a river 200 m wide reaches the h5b (.wl*magg05sb-eyuaf 7 b opposite bank in 6 min 40 s. She is swept downstream 480 m. What55mubyfa0 7 .egwh lba(g*-sb is the speed of the current?

  A boat, whose speed in still water is 0.99 m/s, (ggsdu e.81bb must aim upstream at an angle of b1g (8.ebgdsu$25.4^{\circ}$ (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)  $m/s$