Which one of the fol4y r65c-f fyvp+l7.e hbuw ho;lowing is an example of a vector quantity?

  Which of the following ovipv(dv7dc1 b.2w /fhperations will not change a vector?

  Which of the followihwuvl oug 8:7umo1.7xng is an accurate statement?

  The resultant of two vectors is the smallest when the angle between them imuzr. 37uy 0:uk+rj,fwk vvqa+1y p/ns

  Two displacement vectorsmd(e*g(vly 0( bibb .r have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, trmvb*yebl(g(.( d 0ibhe magnitude of the sum

  Two vectors, of magnit.b j ttnx; rmlt7(59dgudes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultng9;m l.( tjdt 7rtb5xant?

  Three forces, each hak q2dr90 -xi gqxi, pre5.:tirfxs3+rving a magnitude of 30 N, pull on an object in directions that arrqs2 0ip9x fx.xit5 -:q+i rgrrd, 3kee $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unk (t:*hgi;dk8v 8o bl /tqiuhj++jahf 1nown vector is

  Ignoring air resistance, the hom/p+ 3e. sv 0e kznwzoy3.ajn3rizontal component of a projectile's velocity

  A ball is thrown with a 1 b).fa4gm8rmlgx ;sk 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 horizontal compone9v) xpm0a,zpint of a projectile's accelerationp i,m0xp9)a vz

  A soccer ball is kicked with a velocity of 25 m/ssba-4om78x*ssks g1 sp.(tx w 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 directed anti-paralln q3z12m2p-fblp4r wlf ;7h loel to the velocity v7o fmp4wp2qn2 bll31f-;zh l rector,

  If the acceleration of an object is always directed pertu 3faiyem(n03lpj z5 -7zj3wyzn.; tpendicular to its velocitypzjl(5njzf0a3ywi- yne; 3ut 7 zmt3.,

  At what angle should a water-gun be aimed in order for the water to land withs t/6evchwrlo; - 29uf the greatest horizfe6ow 2-c l ;tuvhrs9/ontal range?

  An Olympic athlete throws a javelin at four different angles above the horizonta;i4qtu *2. m:injshkd u6 j1rwl, each with the s2wr:nkt 6 mjsuqi.j1;u4 *dhiame 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 ef pi9rd q5n66ql (bw6the second time. If the ball leaves your hand with twice the velocity it had on your firsteif6n5dq6bqw( 6prl 9 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 o dibtv8l+dr bj)q ++6lf $35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a fie4s/ v/yvm-a oald goal attempt reaches its maximum height, how does itso/yav-4 ams /v speed compare to its initial speed?

  A stone is thrown hors-g a; ,;uhftydx;tp xk(z,v( ncf30p izontally from the top of a tower at the same instant a ball is dropped vertically. Which object is travkht,vz (n3 ,xd0f p; g;xcp(yu-s t;faeling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dropq( btla(i:lmp8lf9 2c ped from the same height. Ignore air resistance. Compare the times of fall of th blit2 8l:m9(lqp(a fce two bullets.

  A plane flying horizontally at a speed of 84.3 m/s and a9x7 gqg;gnu rjwx7-xqlx*q -u+ oec4: t an elevation of 142 m dro*7e-; grwxxulg-:j xn +7qgx9ou q4qcps a package. 3.7 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 second g:n. sr8 k)wcalater a second package is dropped. Neglecting air resistance, the distance bet k:naws.c )gr8ween the falling packages will

  A pilot drops a bomb from a plane flying horizontally arapivcn,rl25vp2gzbjb 7m e 6 i03)g3 t a constant speed. Neglecting br3i3z2 6ev,2 pl 0gm)rbngai7jpc v5 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-sixhf 4h/;z/lwkl 3ia6ioth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you woulkhiwa /l; 4z hf/6li3od on Earth, the ball would land

  You are traveling ata ky0f. ;wr(ems5p mq9 55 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 4r;qkwe sm9y( f0.am5p5 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that fdk z 63nt g* kp3mt(pdp3;ho4llows 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 starting point. You should he(3tmnp43p6kdpo* z3tgld; hk ad your motorboat

  Your motorboat can move at 30 km/h in still waterlid)fs4jng o jw,gcp- m9;:3c4fxwb8. How much time will it take you to move 12 km dog:c94o pmn8jbc3x- 4d)lw wgi;jf f,swnstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8. v+1d+.umoojig6s,o+nmxrt / 0 m at an angle of 30 degrees below the +x axis. The y compon txo o,go 6vu/ ir+s+m1jmd.n+ent of A is

  If a ball is thrown with a velocity of 25 m/s iyc.v ;si,d1g,- svg aat 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).s f m156t9nb gjm2l+ybprge a direction north of east and you end up 2.0 km north and several 6tfs nej1 mb9p.2+)5 rgglbmykilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x z; ;fx.ejjxt vp4ku;2sd 0yf +component of its velocity is 8.00 m/s. The angle between the direction of its motion and the0jd4; xps;.fyjkev u 2f;xz+t x axis must be

  A 400-m tall tower cgz ;nnd : f8pih;14vzkasts a 600-m long shadow over a level ground. At what angle is the Sun elevated aip4zd8k;h 1;nngvfz: bove the horizon?

  Two vectors A and B have components (0, 1) and a5j -xfgk 3lc.(-1, 3), respectively. What are the components fxcjk5l3 . g-aof the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), res2:lj-1g c wevqpectively. What is magni1wljg qv2-c: etude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is1 1nx1/ ij9o4,qyyx.jra f w c)-dyaue the magnituda1 fq1u/.o 1dcjiy )rxj4enaxy ,y-w9e of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude 1dpw lu7la1v+ of its displace 1pwd7+ullv1 ament?

  Three vectors, expres 8h 6gmxk)srp2y h2m5dp3pp.ised 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 cxa* 2:d6t 9.dcakveycoordinates, 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) a-e8y 8yql-jb vnd vector B = (+3.0, -8.0), what is the magnitude of vector 8eq-lby8yv -j C = A - B ?

  A runner runs halfway around a circular path of radius v :0up) joieeq outns2w +8-e810 m. What is the displaceeq i2 u+v-)08etjne: o uwps8oment of the jogger?

  Two forces are acting on an object as shown in Fig. belok wa xnl6*7+huw. What is the magnitude of the rehx7 6u+n *kalwsultant force?

  Two forces are acting on an object as shown in Fig. below. What is the dtaf l0 xdhb*twu) 7pr* b,))frirection of the resultant forc )blart0 )f )*f7dhtw*u, rpbxe?

  Vector A is 5.9 cm long and points along the positaav jlonh1b;m a/l3: 8ive x axis. Vector B is 6.2 cm long janh l a8:a1v3;/oblmand points at $+47^{\circ}$ 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 75 cm long and poi)p piw-nkl5(u nts at $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 22 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 14vlofs se3syj;:;ai *jz.mp4 7 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of theal3eyp;*j 4zfs:7 soj s.imv ; cliff to the bottom to be 2.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 18 m/s, from a bridgd9m yx6 (jmg+z ajc;l2e. It falls 26 mjg6mxy+ c j2zdl9a;(m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, stq 9tg fkkwk-9eo3 k.;nrikes the ground after tg toqken;9f3kw9 k.k- raveling horizontally a distance of 13 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 anspvr x9g6k291omr2 z8 i*facb angle o9kp iaf2*6mvbx g9ros81zc 2rf $20^{\circ}$ 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 spdpkc +ur3.;/uw j ov*heed of 13 m/s at an angle vj;du.3p r k*+w/ chuoof $33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an inne xzoe; 88b konb5-8k:grc*i +e,ur titial velocity of 22.0 m/s at an angle of $28.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocium;lv q39k1/ a +wa koccsde9;ty of 46.2 m/s at an angle of $45.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of 6g 4m:wn*r iqb$30^{\circ}$ 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 3n) *r*sv+v pm2dtmlj 22.1 $m/s$ from the roof of a building 49.1 $m$ 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 from ground level with an init a uhoiow7h o/.e7t.)tial speed of 51.2 m/s at an ao /)hha .e7it wou.7otngle of $39.5^{\circ}$ 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 gy9:qsyf02pu6 4wxg:bs3z cr /s. If you rgs3:qs y46z yxwp 9fc2 u:b0gran 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 finish would be

  A plane has an air speed of 200 m/s due Nog e43 (hbv5cl mmbzo77rth, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grou4zm5heogbm7(l c3 7vbnd is

  A plane is flying due 3 uxkip xrl147k+wwleuzs4xy46(c h-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 is heo)zc)oab; z;8bv d1.vfg im7aaded $30.0^{\circ}$ 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 firesf9 yf9knuwvxn 8 x64*kqg;7t y a projectile with speed 50.0 m/s in a forward direct x476 uy9wn;n 8gyfxv*9tkkqfion $30.0^{\circ}$ 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 ui0vd( *lb jh/zj7.wbv i/o65xe ;ggh8.0 m/s, is directed across a river with a current o6h*/o eu;/5(ib jj i.wlvb7zhggxd0vf 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 11 mt o8d ;7nkx6jx/s in still water wishes to travel directly across a river 0.7 km wide in which the current flows at 6.6 m/s. How long will it take to cross the 8tx7j6no;x dk river?

  The driver of a motorboat that can mo8mle v65 v so/zg53rtsve 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 thems/ ot6rsv35lz gv58e driver head the boat?

  A swimmer heading directly across a river 200 m wide vnh( r3 1et xv*,ma 31iea7gyjreaches the opposite bank in 6 min 40 s. S3xay7tgj aei v11,h3m (*vnerhe is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the op8 ww jo6x(pkvv6tbs),posite bank in 6 min 40 s. She is swept downstream 480 kb6w,xs)w8v(v6 j t opm. What is the speed of the current?

  A boat, whose speed in hjh98(s s kmoemn m +;f9rh,u5still water is 1.73 m/s, must aim upstream at an angle of h9,sou+e(nfm; km 89rjshh5m $15.8^{\circ}$ (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)  $m/s$