Which one of the following is an example ofbh ex(k,k 4td*jryee5b1.yi/x2p i7 k a vector quantity?

  Which of the following operations will not changrja.0c 1h9x9l9s bydce a vector?

  Which of the following is an accurate dg ii 3r wwc*gp)o6.9g1um9ajstatement?

  The resultant of two vectors is titcbvo z;pn5ylry,-wd sv/m0 9 zw -*+he smallest when the angle between them is

  Two displacement vectors have magni8wy5x e (p/slh j-gl0atudes of 5.0 m and 7.0 m, respectively. When these two vectors are l5h w8 /(yg0 lpajse-xadded, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, ar m-m da:no5l+re added. Which one of the following is a possible answer for thed-m5r l: n+aom magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directiocy)2h3 vusv9ws2 o nw1ns that avscsv1w wu922) o nyh3re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknobpmvc 07 loi1-wn vector is

  Ignoring air resistance, the horizontal ce8qkh9vvo p)1lr1c. a3- : 3znvvprtqomponent of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an a/7zl6 9ltsoskngle 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,siz1 :f+/wz0q. mvnr j the horizontal component of a projectile's acceleration f+.r j/mwsqvzz: n0i1

  A soccer ball is kicked with a velocity of 25 m/s at an angle ofrhr 8h4zwqh9k 6ep43nj/jdi3 $45^{\circ}$ 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 ja5/4*wvnin be *(qex +yaq,e: grp9k anti-parallel to the velocity vector,jpn g ea*b:ek54 i/q+wa*(xvn e,9ryq

  If the acceleration of an object is always directed perpendicular to -mfl8yh-b2toits velocith2-bfol m y8-ty,

  At what angle should a water-gun be aimed in order for the water to /2m h6 ; dyd mupr+xser1i.,tfland with the grearm/s,m.ird6eht uf+x2p; d 1y test horizontal range?

  An Olympic athlete throl*tcfw7cxz0ft75ya*h i yy; 8 ws a javelin at four different angles above the horizontal, each with the sameth8 t5l ;wiy70f*y yc7caxfz * 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 seclsvd506ol io- ond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your fir-doo60v l i5slst serve) would be

  A ball is thrown at an original speed k8anaiq8elz k9 / c4b 5xx0c/pof 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 fieldgnf()n7w.5iv * ww s* *zywzhd goal attempt reaches its maximum height, how does its spzn zvi*wg.s(y*5fd w)hw w7 n*eed compare to its initial speed?

  A stone is thrown horizontally from p(/qxx9 j/vdf the top of a tower at the same instant a ball is dropped vertically. Which object is travelinq(9p/vx j/fd xg faster when it hits the level ground below?

  A bullet is fired horizontally, and at the su* .x-g4bm k. a-78lwkvumdjdame instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fawgk bm d7jlxam- .4v u8u.-*kdll of the two bullets.

  A plane flying horizontally at a speed of 110.8 m/s and at an elevatibci5fm:r//vwu2 (1:b b v2h)y yt*ba ejyh8ymon of 123 m drops a packagyc8j y5mwb bbv: 1m yiah* v(bhu/):t2e/y2r fe. 5.6 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 (, m:pzzh, qips ,cpa2second later a second packagzszp :h qpc,a ,2i(,pme 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 spee ym7hys:c v3byx(tft.6r09 zbd. Neglecting air resistance, when the bomb hits the gy zstvm3(0 xrby7h.6y9 t:cfbround the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earl .x1ml9iqyo9th. If you hit a baseball on the Moon with ti y9o. ql1ml9xhe 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 relative to a str udg:t fm401bmaight, level road and pass a car traveling at 45 mi/h. The relative velocity of f4g1dm: 0t bumyour car to the other car is

  You are trying to cross a river that flows due sfg phdib5*,l3outh with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from yourfgdlh ip*b3,5 starting point. You should head your motorboat

  Your motorboat can move at 30;dx7a+ ae 5,hzldxsfa4 z:q u. km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing ah7 ;l5a z :dafdquz,sxx4e+a .t 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 deoe6k+tl u+ bmk3+tgq4grees below the +x axis. The y component of Ag e36mt 4q+klu+ktob+ is

  If a ball is thrown witwbxx ,c yrj ejal(,: lqm-bkub :b)175h a 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 direc+ ,i upms/ch.ggf i3ri)tz 48uo)x4 jdtion north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east hasi3.44 izuug+ /toxc,jfd ))pgi8 mhrve you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of x/ n.je kwlf0ir7o w(1its velocity is 8.00 m/s. The angle betr0 /nfjel x1kw.ow( 7iween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angl wa x2jc49vhvu(f ,wu (7tw3qqm2bpp)e imp2hxc3bj,uwpfq vvwuw4 9)a( (t72 qs the Sun elevated above the horizon?

  Two vectors A and B have components x0/iu7qq xu 1e(0, 1) and (-1, 3), respectively. What are the components of the sum of thesex 17xu/qu0q ei two vectors?

  Two vectors A and B have compox 237dp xzgv1eyj1oqr s;,4up nents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectoro7x21sj 4g,3 rzdvqp 1yp;xues?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . :ugc hlf8fd5,h3 teef7+rxj + What is the magnitude of ge l7:5d+ +rfet38fucf,hj hxC ?

  A car travels 20 km West, then )tv2l o;y 11q/ (xw/2-oyapyszbf:qpt / dlzp20 km South. What is the magnitude of its displacementpa1:p2wq ); (stoy/yx1o b/d-z vq/y2ptl zlf?

  Three vectors, expressed in Cartesiau/3ykdlq ng+ ; pasn2,n 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 co9o gxl3pqif0r3;irl2ordinates, 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 vechz(z(j*e: :drvwkfv5wmk*ala w4 ,4e tor B = (+3.0, -8.0), what is the magnitude of vector C = :e(5 *ajdwv f rez*aw4l(4h, v:kkwzm A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dy1jjw 1n ;dza6isplacemndy1 j 6;aw1zjent of the jogger?

  Two forces are acting on an object as show 7 bw3b9p8s(rcn5m nwhn in Fig. below. What is the magnitude w8w r9nc7p s5(m3 bbnhof the resultant force?

  Two forces are acting on an object as shown in Fig.bukateztx /b;:)1 (jo below. What is the direction of tejb ( baz)/kot;u tx:1he resultant force?

  Vector A is 5.6 cm long and points along the positive x axis. Vector treq.:,fl:rkB is 5.8 cmrq ,::.l rfket long and points at $+54^{\circ}$ 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 53 cm long and point(mp9eec6;lq won/ mc 2s at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 45 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 27 m/s6cjin ju;2ypjbo7 5: l from the edge of a cliff. A stob y 2j ui76lj;o:pnc5jp watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.3 s. What is the height of the cliff?

  A girl throws a rock horizontac22t6- dpua,/ 5zg yse0crjdhlly, with a velocity of 7 m/s, from a bridge. It falls 24 m to the water below. How far does the rock travel horizontally c /h,0d ugate2csy p6-rjdz5 2before striking the water?

  A ball thrown horizontally from a point 19 m above the ground, strikes theu+awz;x + a59dp.n y,.mofsiq ground after traveling horizontally a distance of 16 m. With+quysaa nxfmz+9 iwo; d5.p,. what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an:en ozm;2 gd7l angle o7l2 :;e onmgdzf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump gorj1 (v peej+fqp/3ldt9 ))vv7sseicp +v7 r-jes into the jump with a speed of 12 m/s at an angle of pjp)r9 eetiv( e/ f+vs jj73l+rp1cs7 ) dvvq-$36^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 47.*+l+3uq9lp h.bt bp6*ca zg-e6em cni2 m/s at an angle of $22.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 36.8)rglz pn d:z--t0ulaw1) yp(y k-mt w5 m/s at an angle of $10.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at7- ploaoqy 7+mv; zeu5o ojk)7 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 h(hx)fp7lqy4ejuf+xvq-m41:dy8wi g orizontally at 23.7 $m/s$ from the roof of a building 40.2 $m$ 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 level with an initial speed of 49.3 m/s at a mhjwu;lfp-+de7 r.8on ahu;polm8f+-rj . ew7d ngle of $42.6^{\circ}$ 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 ofw :bvgnp2eqy) /psi./ 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 yo. sg / w)q/pnyie:pb2vu to finish would be

  A plane has an air speed of 200 m/s due North, and is in a y *o5zgq (ugf8:d7tsi ge1s)7ibka t5wind of 50.0 m/s to th(5i) :5yz*ska7t7ugi qb1 fdo g8etgse West. The plane's speed relative to the ground is

  A plane is flying due South ( 9m8unb* albp y/w2;nk$270^{\circ}$) 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 speei m 5u9ht ./++xey(t4 zed)t eakz(qn:tvf3fnd 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 200 m/s horizontally fires a procav.g-4siopx q+acw a ;-zt (:jectile with speed 50.0 m/s in a fo-vo g;:4 i( ctazpwx+a-s ac.qrward 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, gki3ct:k 9esbs1 (l()e-iamw,a : trdis directed across a river with a current of 6.0 m/s. What is the speed of the boat as egm(k,)-: l9sb( teakiwisad1cr : t3it crosses the river?

  The driver of a motorboat th46qh2s0 vycn bat can move at 11 m/s in still water wishes to travel directly across a river 1.3 km wide in which the current flows at 4.4 m/s. Howsbhvqn 6y4 02c long will it take to cross the river?

  The driver of a motorboat that can move at 10 4q ) /bbyb4+t btxih8bm dz0i5m/s in still water wishes to travel directly across a narrow strait in wb b4bh/+4 y bq 0)ztd5ixmb8ithich the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acr.ug 4n 8wbm37dm+jo;y scajj8oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She isn8b jdu;+yma3.8jcwm4gs o7 j swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly aci/-m zc6ah;5q wgra o2ross a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is 2m6a z /craiq;-who5g the speed of the current?

  A boat, whose speed in still water is 0.92 m/s, must aimgow(gxc7j,. tw e)gk- upstream at an angle of ,wx)e7-tojkgc(w .gg $28.6^{\circ}$ (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)  $m/s$