Which one of the follo g2 b1riw9xajmi; a49gol5yo3 f:s0 mrwing is an example of a vector quantity?

  Which of the following oper5x+gmv(qwto wa/5 3auations will not change a vector?

  Which of the following is an accurate+ic f5 n-hokp1 statement?

  The resultant of two vectors is the smallest when the angle between th drn/o(bt 2lyws12og s6qb,q *em is

  Two displacement vectors have magnitudes orh( ,i. 3zljembj9uh6f 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the si zjjhuh ler(9,3 6.mbum

  Two vectors, of magnitudes 20 and 5sqi f3prg+5+s *rt4mjo2oca zz 7 6le.0, are added. Which one of the following is a possible answer for the magnitude of the resultant.j532*gi f6a soo+ 4rstlc+mrzp 7zqe?

  Three forces, each having a magnitude oa6t9tk r9tqkcex6p /9 f 30 N, pull on an object in directions that arx9a9 k 966rqctp/tte ke $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the un0l qq-jftr*m ; i,fosqjf9; 1oknown vector is

  Ignoring air resistance, the horizontal component of a projec6+d8l ps cmvin9p43watile's velocity

  A ball is thrown with a velocity of 20 m/s a ex3rlg:kqs,cv-5(dab-/ 8u9ur pf a yt 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 projectile's accelerwo1 kj45ic3:o,7 jbubn 3lxuj ation7oujj53c 4i1 uw :,bkx jnbl3o

  A soccer ball is kicked with a velocity of 25 m/s at an anglou(h*e itllc,q* w8+( 1egr fnor*h/ue 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 the*gg*p/;orr p o velocity vectorop*r o*rpg/g ;,

  If the acceleration of an object is always directed perpendiajq5g99 j9aqe/k10bf8kg s c icular to its velocity,19jiga q8cgj efqs 99b5/kka0

  At what angle should a water-gun be aimed in order for the wa ivda*ukpig4hf/art ,b*u60( g3lj w0ter to land with the greateslvg3ai*4 tbjdh gw , 6(/ap f*k0ur0iut horizontal range?

  An Olympic athlete throws a javelin at four different angles aboveziesov7p..t, wf/r,ewlrx /+ the horizonta,pvozwei+ r,.xetf/ 7w. srl/ l, each 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 f cc(kw.j6xsoee:d rp9wb/36 ror the second time. If the ball leaves your hand with twice the9 ecrww3xk6c b. 6de:op (/rsj velocity it had on 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 a wrs0 ne,f 7kttwiulo,8j:1f: ngle 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, how does in0ctp7+ pxzi4(cu+i 3y* qwi; rss- pwts speed compar siuwn+q3y+7rcwc p(;0szitp*i -4 p xe to its initial speed?

  A stone is thrown horizonq0wuzxh3g w9ydp/:,m 0z+r nn9w fvq/tally from the top of a tower at the same instant a ball9hr3mn qz:zw 0qxw,9 ugd/wfn 0 +y/vp is dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a s pg40d-;fdyn (p5 ijrvecond bullet is dropped from the same height. Ignore air resistance. d 5g4ppjrvd y0;nf-i(Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 74.4 m/s and at an elevation ofh,h b /:i:5uxi6 8epwyn2wudb 155 m drops a package. 7.7 seconds later it drops a second package. How far axu2pe:wwhnb yib, 6:5d8h/iupart will the two packages land on the ground?

  A package of supplies is droppeqiou6k rnehol33 (b no*glc-: m2,+rkd from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling pac3+ or(nql, mlk g3k:bo6n2-i c*h uorekages will

  A pilot drops a bomb from a plane flying horizontally at aqh16lt2+ ptqxw8s1fq constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of thqtl +q 16q12sxphft8w e plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. Ifhqb1d3 96ln 6a ub:geg h-ql,l you hit a basebalqqlbhahen 96g:1l gl 3 6b,-dul 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 relative to a straight, level roa2 .e haj5ala:0xgkou.d and pass a car traveling at 45 mi/h. The relative velocity of your car to the other :g o h.jl0 ax.k5eua2acar is

  You are trying to cross a river that flows due soutg5-,wh ,ffz)n u1gbyzh with a strong current. You start out in your motorboat on the east bank desiring to rezuz,n gwbg yf)51,f-hach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in sn ; aeq2fn( hk98hm9cq2g/uxctill water. How much time will it take y;99c8/2g2nq n huhakexfm cq(ou to move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees belfi:0psmna5vz4 p*d2 row the +x axis. The y component ofnp*rf 5idz0samp : 2v4 A is

  If a ball is thrown with a velocity of 25 m/s at an ag+1m /o m(dgrhh8 t7zvngle 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 3m hzy ;co eyi;3je2s2direction north of east and you end up 2.0 km north and sihm ;3 ce3ysjz22yo e;everal kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12s uwdy30uw,0y.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x ax0 wy,0s3 uduwyis must be

  A 400-m tall tower casts a 600-m long shadoddva 1u,)t3x k phebb2p21-how over a level ground. At what angle is the Sun elevathped-d a2 3op vth)1bb,xu 1k2ed above the horizon?

  Two vectors A and B have coky) sz4r6mr/ep s4xgl6b07 rpmponents (0, 1) and (-1, 3), respectively. What are the components oy 6k7gr r40eb/64sppm r)zlxsf the sum of these two vectors?

  Two vectors A and B uiyjfl2 .5 ewb- or3z jh3n;(vhave components (0, 1) and (-1, 3), respectively. What is magnitude of the sum o uyn-vfwjl3zhe 3(o. ;2i5bjrf these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). c.q*l q axr,b:sk, 2e)mao ch*Vector C = A + B . What is the magnitudec 2,m k,sehoxqa* r.baq )l*:c of C ?

  A car travels 20 km West, then 20 km Soud9si8: *0pvj w3xsq8h;renfw th. What is the magnitude of its displacemen9n sxrjef i wp :838vh;*0dswqt?

  Three vectors, expressed in Cartesian n nh--2 alnnegl-di ;1n/jwh8coordinates, 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 corv7d5s 7d7xm fordinates, 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 vectorp opzhp.vmcqkw 7i90 u5(97cg B = (+3.0, -8.0), what is the magnitude of vector C =vcu 7ip pgh 0c79.k5wp9moq z( A - B ?

  A runner runs halfway around a circular path of radius 10 m. What isg kx//o1cbg e- the displacement of th1b /kg-go c/exe jogger?

  Two forces are acting on an object as shown in Fig. below. W z l 2mqwi-hti 36:i .sd0r,w67 tggo.nrzpbd2hat is the magnitude of the resultant force?3tszrd:g7bmq 2i drzg,pt 6l6w n.w- i .ohi02

  Two forces are acting on an object as shown in Fig. below.;vi idampu9zznjk r18 f f)*:7 What is the direction of the zp1)9f u*8r;dz : kajv7fmini resultant force?

  Vector A is 4.9 cm long and points along the pq(qp0vd, )wz) rqxau+ ositive x axis. Vector B is 6.5 cm long and points)pd(a+0)wqr qq v,xzu at $+36^{\circ}$ 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 57 cm long and points j 7e;mkf v/zkxb 97xmjs*.v4d at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 35 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 458g mc7q* dvnz /zdn t8cel4ian initial speed of 20 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 4.5 s. What i edq8*47 zmvl 8izc5dcnngt/4 s the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 8 m/s, from a i8e ej.9 4djpvr /sga*srp4(u bridge. It falls 21 m to the water below. How f49pa /e vsjj*gs dui.84pe (rrar does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the ground, strikes the+21lxrbj .l7yb 73-vp 02n kyz plksqs ground after traveling horizontally a distance of 23 m. With what speed zlq03 1- x7 r7p.lssbnkj l pb2y2v+kywas it thrown?

  A jumper in the long-jump goes into the junfvn.i 62 9qoxjyo:+mmp with a speed of 12 m/s at an angle o6qn. +x : yi2mfvo9ojnf $20^{\circ}$ 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 sn/hpxb 9f )r /28z3yzag pips9kx*x+ypeed of 12 m/s at an angle ofp s9p xz)3*/xyyn2pbfkigx+zh/89ra $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity - rfar05yt3af of 51.8 m/s at an angle of $23.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched tq, io7hkeer ;/l :o t3niw.t0with an initial velocity of 34.2 m/s at an angle of $36.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired q)ms rhx w682x3gqrqw+g wp:6at 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 ebh 60g 7db (m;hgh*m2xohzl6at 20.8 $m/s$ from the roof of a building 50.0 $m$ 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 37.4 m/s at ajx0hq7kh h)yz4g(ru 5 n angle of uxhzg0j 4q)hy7 5h(kr$44.3^{\circ}$ 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 ra qa;powg+9e9u w7-jja odj ) :,*kgqvzvok9m.ce at a velocity of 4.0 m/s. If you ran the same race on augj.zvk 99wo:)-;7apok9 wd+a qj e ,*jqomvg 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,6ehgvj zc7 (po4hwtr*/:4 ith and is in a wind of 50.0 m/s to the West. The plane's spe4zot( 4e :pijtw6/hh7vhr*cged relative to the ground is

  A plane is flying due Soefxc pn;lsgn iw-r0 4h(exw4 11w5oe;uth ($270^{\circ}$) 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 is head 6el5/ 9zf w egefong(xtc1b l,+*v0aked $30.0^{\circ}$ 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 20;m)8vgvcbxu mr9- 2oe0 m/s horizontally fires a projectile with speed 50.0 m/s in a forward directionu-mgbrv92)c v; xe8 mo $30.0^{\circ}$ 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 acrmn**q 2;n*2ydvyj xfn oss a river with a current o*vn d**mqxnf 2y2;nj yf 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat tha.(5adbf;xq ,kby (j zwt can move at 14 m/s in still water wishes to travel directly across a river 1.2 km wide in which the current flows at 4.4 m/s.d5f,aqkbb( .wz ;( yxj 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 4j ex1mqzx;i( travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the drivej ;ex1 qmiz4(xr head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppo8v+4 sq,m ww8qltd: a,oh 2uyrsite bank in 6 min 40 s. She is swept downstream 480 m. Hol :,uh4rdw yotv, sam8q+2wq 8w fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank mi 7/z05- ji34 aoi;chhju nsisf p)o0in 6 min 40 s. She is swept dowjh-fiaz0ojs /sipi7 i mu0c;4h3o5n) nstream 480 m. What is the speed of the current?

  A boat, whose speed in still6 *pb-sqqbxlby( 1cmk65 *rkox/2d sn water is 1.87 m/s, must aim upstream at an angle of- sdmk*lo2 q*(xx 5bb6rnkpcs/by16q $30.2^{\circ}$ (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)  $m/s$