Which one of the followin5jy:p p s)9pagg is an example of a vector quantity?

  Which of the following opera;+lw3*dgp f5bik mu+mtions will not change a vector?

  Which of the following is an accu tyi tls/up4x (cbdc+7t-4 gd,rate statement?

  The resultant of two vectors is theyk,7 / sabzr9s smallest when the angle between them is

  Two displacement vectors have magnitudes )0152c(t msw( diqu. 6gno9vnjvfies of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the su9ot eifvwj( 51(gicqu6ssdvm .02 n)nm

  Two vectors, of magnitudes 20 and 50, are added. Which one of the following is 17 4ire ,8 :rekx.dltqyedwfbi;f c(3a possible answer for the magnitude of the resultant?w q3kif.:deixe(r,;l8t rdc ef4yb1 7

  Three forces, each having a magnitudw ;-r9ux 0rmvue of 30 N, pull on an object in directions th0r; 9-umxrwvuat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thgyz,6ry 51dg gi-z*t ne unknown vector is

  Ignoring air resistance, the ht.ut im((k rxf6-h ob/orizontal component of a projectile's velocity

  A ball is thrown with a velc: q8 msr3n9mgil0t(ftw:w-xocity 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 horizontal componobc6, 4:avuko ent of a projectile's accelerationak:, c6u4 oobv

  A soccer ball is kicked with a velocity of 25 m/s a 1hc jdxxw*mdf 4trz1uwp, ;yu*wh+q):(f1h gt 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 obj u/vc0ydhhoey3) a6b*0cxlg/ect is directed anti-parallel to the velocity vector,a3 )0bvgdc yxch/ 0*oy6uehl/

  If the acceleration of an object is always directed perpendicular to ry t833salb jgtb.fg(n o*( p1vibor0+v6d 0u its velocitypry dn6votsjb+83i. g 0(3av lf1 gbo(t*0ur b,

  At what angle should a water-gun be aimed in order f xl *xb1q76yf j,pmh8bor the water to land with thj6ym7xqpx8*l b1 ,fbhe greatest horizontal range?

  An Olympic athlete throws a javelin at four different angltesl u/0f a4y/,spq 2fes above the horizontal, each with the same /a/0 fsy4 sp2qf,eltuspeed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 hand witht o4;bif 4lcun o8)9ikg 3*sma twice the velocity it had on your first throw, its horizontal range R (compared to your first smi;4is gt ufabl3o4 k8nc o9*)erve) would be

  A ball is thrown at an origiyx tn27c9l)taju(xi6/ o1r qwnal 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 its maximum height, how oo*ehw / (fx pse6kvk)uce+ uo6,q63 xdoes its speed co+pwkk 6qcu*/)xxov oeuof e36 s(,6 ehmpare to its initial speed?

  A stone is thrown horizopv 9 w8a,ctk:xntally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster whe 8xw:, c9apvtkn it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is d*6dx2s0j7 caa4ttx cx24 xkvdropped from the same height. Ignore air resistance. Compare the times t46dxx4sx0ccak*2jvt d2a x7 of fall of the two bullets.

  A plane flying horizontally at a speed of 105.6 m/s and at an elevatf4 hnf rpoi+,2ion of 170 m drops a package. 5.0 seconds later it drops a second package. How far apart will the two packages land o, n fhio24frp+n the ground?

  A package of supplies iqh:uir34a3q2jd ilk su j3 g;5bz-u 0ks dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the fallin-sjlrhz:2ga3j5kq0k3bqi 4; d3 uuui g packages will

  A pilot drops a bomb from a plane i : kq 9wqtqcc nrs)xav+,.)l*flying horizontally at a constant speed. Neglecting air resistance, when tc:w*)ks+qti qa9).nrv, q x clhe bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-s5eknao zhj18hz3z ;e 0ixth of that on Earth. If you hit a baseball on the Moon;h jza3 5 0e1zzkoe8hn with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 myryva r b1d 9-bb7h3:ic)np xiapv(+2i/h in the +x axis relative to a straight, level road and pass a car trx rirb yhd7 )1(vbvipyc 92n3:ap+ab-aveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a 5guf2)sr ee1 wriver 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 startin)g5eeu fwr12s g point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much timz dao kb8*w,.be will it take you to move 12 km downaw 8bdbo z.k*,stream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at( cimbmj0r )l)rj /pz) an angle of 30 degrees below the +x axis. The y component of mjl)rr))zcij (0 mb/p A is

  If a ball is thrown with avx 08b5 ,po osdow(i1o 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 direction north of east and youa;u x(/cdz3)8ig8q v iqg )vld end up 2.0 km north and several kilometers east. How many degrees north of east )g8gqxqz dia8()v v3 udlci/; have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x;dl3ub-oix4wq-(kfzr5 ;)b jho*tdv component of its velocity is 8.00 m/s. The anglex-3 h(oqi dtbr*-);ku zl4v o5dfbj;w between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over wbcpdz t,onk zjc 0i92b27m*l;-- bwf a level ground. At what angle is the Sun elevated above the hori- 29n;twlikbb o zz2m*bj,d 07p-wcfczon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiv8z skr5c:wb,y/xd7i0 +fierxely. What are the components of the sum of0:x /s8 eri 7rcxdyi5+,bkw fz these two vectors?

  Two vectors A and B have componen x4:o3qd yb v 7.h-z/1ndr7q .hszlffots (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these .o d/o 7yrx-7l f:qshv4h3q.zndf1zb two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitukcz )/pnhc5( dde ofc cn )d5zk(ph/ C ?

  A car travels 20 km West, then 20 km Souee:hl0h7 mgz-th. What is the magnitude of its displacemenzm7g hehe-: 0lt?

  Three vectors, expressed in Cartesian coordiod74 5hkx-kgd nates, 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 Cxbety zlwrb9u9tq uo/( v* )-)artesian 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, -4.0- w7ngulpew byw)5 +y.) and vector B = (+3.0, -8.0), what is the magnitude of vector ulg.be +7 5-wwynp)wy C = A - B ?

  A runner runs halfway around a circular path of radius 10 8gohwfth;w-qdm:c uo * d,4)fm. What is the displace-fhthfudm w c ,g*q:w8d 4)o;oment of the jogger?

  Two forces are acting on an objuz:f6b2udb0jcv3uj, bhj m7 gw )l 9c/ect as shown in Fig. below. What is the magnitude of the resultantbvf ju96/ )j2d,gwlu c umjbz:c073hb force?

  Two forces are acting on an objecytu/)byg,y2hrkb8(fl *z x0n8c (y g ct as shown in Fig. below. What is the direction of the resultant uf(h*g8y2y )gy (l,zcbcx/ y8 nrkt0 bforce?

  Vector A is 3.5 cm long and points along the positive x axis. Vector B isn3b9k l;w ma (nmw*hq+ 5.9 cm long anwn n9m(bk* w3m+qahl ;d 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 79 cm long and points a in/y1 g9j7ek lk1jq+gt $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 50 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 horiz otx1t0v.z gh-cj9epr a a**,,a;miulontally with an initial speed of 18 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 4.2 s. What is ;0cal**-xjma tot pe ir1vuha,.9, zgthe height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, from a brieh4ppy s7o(r3v l5 p4edge. It falls 21 m to the water below. How far does the rock travel horizontally before strslrophee y534(4 7vp piking the water?

  A ball thrown horizontal7db, dli7wq5dz -vgvzj:tl1f : s4 r*lly from a point 25 m above the ground, strikes the ground after traveling hosv1ifddg5-:dq l 7rt4:zz bj*wvl ,l7rizontally a distance of 18 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an cmy*pc+-4e(x; :x 5zxornlcx angle ofo-:cc4mxnx x+x y *5le rcz;p( $20^{\circ}$ 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 12 m/ssd2gon4 x)f3u at an angle of gosu2dfn43 x) $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 31.8 m/s at an aed 2j+iy8f0p syp7 jia 0f;k*bngle of $41.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched 2cb4y .dor 2 gek,*- t,-yp;viac hjxcwith an initial velocity of 50.8 m/s at an angle of $38.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an a z49k.enp 61 rrb)jr,j vi16oeig-i exngle 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 horizon;2d1-sc+2 sqrtazagp tally at 16.6 $m/s$ from the roof of a building 57.2 $m$ 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 lev0r9dyf pkbr7f3 t:kb:el with an initial speed of 67.2 m/s at an angle orb0 fy7rf:k3p:9dbkt f $45.6^{\circ}$ 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 of 4.0 m/s6ncpq2j9lp 4m. If you ran the same race on a day when you had a constant headwind which slows your speedqpncp9 l42mj 6 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 duezk+h,p(6c +cjs qe2bu North, and is in a wind of 50.0 m/s to the West. The plane's speed rel hqc p(ubsj+62zc+ e,kative to the ground is

  A plane is flying due Southkwfy4j+nc8 0a0icaxgt rgrp)11 t8)d ($270^{\circ}$) 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 hel6j:w e/.(v yfwiphu f93:d9cnr8vaqaded $30.0^{\circ}$ 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 horizon 5 hb(jd8q6f7e0bm ;a0f9k gp6hfuzfotally fires a projectile with speed 50.0 m/sbf(d06 9 5zojguhmfb0fpfe7 68qahk; in a forward 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 i gv -k 6 .3knp qhiu;t0vxv5njbtv77u4n still water is 8.0 m/s, is directed across a river with a currenk j4iv7 n-.ukb73ht px5g6vut nqv0v;t of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 13 m/s in still water wisf f48 e-kqssd4hes to travel directly across a river 1.0 km wide in which the current flows at 7.3 m/s. Hq k8fs4s-f e4dow long will it take to cross the river?

  The driver of a motocjjbzo3 /2tka- lue wr9(*( qzrboat that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the dr rkjlz/o qc*e(wj3at 9b-uz(2iver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite c::*anahp,bw mqw2p, bank in 6 min 40 s. She is swept downstream 4n,p *hcb a:pw:,mwa2q80 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide ke7/j3o hzzut qx7+i,reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the currzu/ zjk7x ,et+ih7 3qoent?

  A boat, whose speed in still water is 2.11 m/s, must aim upstream at an neq2e2w8*us i angle ofequ ew*i2 8n2s $25.2^{\circ}$ (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)  $m/s$