Which one of the following is an exampl20rziov4 eh,m e of a vector quantity?

  Which of the following opera8rdlx/f opv9/ tions will not change a vector?

  Which of the following is anu)od;p 3m,ptzg*/ sb6 l ldum+ accurate statement?

  The resultant of two vectors is the smallest r6 f2xag2 exx) lt*lg0when the angle between them is

  Two displacement vec9mvr 2t)*fpw;qxjt 2xtors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magni v)pf2;q2 jtxwmt *rx9tude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the folt*qsr;,js qk0nn j 8(glowing is a possible answej,j* sns t0kr(g;q8qnr for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, -mzcl 6g r v-ho5*o. zbo4(i-z ,mkixopull on an object in directions that iz,m- -oozc hg*b4z5 ro(.-i 6xlovm kare $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectorz sa+ztx5z5+qn*7 tn k is

  Ignoring air resistance, the horizontal component of a proje) ihm8k.: 2vl bszzo9gctile's velocity

  A ball is thrown with a velrj 68 kc4ptg40 8;hqs abs2ceyocity 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 compone:r 0 6125fzgeu y xhnycnlj8y0nt of a projectile's accelerationye1y:gjx5fl z n8h00nry2c6u

  A soccer ball is kicked with7 xc-u(f k*3qu0yw erl a velocity 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 o/dr 3b(h)fedtuh5 )zcw3 u4xx6ncc. ibject is directed anti-parallel to the velocity vecto3c cdwhizt(n56brx)).4f3xe /c duh ur,

  If the acceleration of an object is alwaysm1* 0apthhkhos i1.p5 directed perpendicular to its velocity,h 15kopp it1*a.shm0h

  At what angle should a waterihmu* w.:.z js2o ) ulk*awl4q-gun be aimed in order for the water to land with thjhwu k*l2 4o q..mwuis):*alze greatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horiz;bygg 7m 2h*hy nry-.pl a1;ruontal, each with the samey a-.b hg m2h;yp ul1n7rgry;* 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 second time. If the);wo jma gf-t. ball leaves your hand with twice the velocity it had on your first throw, its horizontal rang fwt- .m)ojga;e R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 ms4wt41h3 s/rhmt(c o u/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 zbd;qchi618u y1cku(ysc.v0goal attempt reaches its maximum height, how does its speed vkc1cq id10u;zusc.8h6b y(y compare to its initial speed?

  A stone is thrown horizontazai3u: 2: qd2kw od1mtlly from the top of a tower at the same instant a ball is dropped vertically. Which obj:otad w1dmi 2:u32kzq ect is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is drovcd;x 2-mxl 50tr rq1fpped from the same height. Ignore 2mqc5r x1 d- ;xtlv0frair resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 67.lp 39oq(f8pm e )bo3-oy zo9i )luu.he8 m/s and at an elevation of 230 m drobplfo -u eyi9(uo )3)pq8mol9h.zeo3ps a package. 7.1 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped0 3 iat5-+jxs+xek o+w i8ha:9axjaau from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packa38auasx:5 tx+ao0k-eiw+jx jihaa 9+ ges will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Ne0to:1sxmk(ldp/ow a-,u s 4a xglectina0 d/(o1:wa ,smlux xos4kpt-g air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the dn/*teki*r-c Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed anc -/*ditrn k*ed angle) that you would on Earth, the ball would land

  You are traveling at5qsh x:m)/txxzll wtgi l;; .. 55 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the othe:;wlx g./ms)i z .lxqhl ;t5txr car is

  You are trying to cross a river that flows due south withprq)fn6( iv0 rl7p(w cb:b1 gv 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 r p6qv(frwic v1bbg70p)n:(lshould head your motorboat

  Your motorboat can move at 30 te(g9iwl9 -fysd6;zkg 3 wnj0km/h in still water. How much time will it take you to move 12 km downstream, in a rivtgzd6we f09 s;yw j3-9glikn( er flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle o xh3b1l,j; g:hxycdn 7f 30 degrees below the +x axis. The y compone:cjxbg,;x h3h ny1 7dlnt of A is

  If a ball is thrown with a velocity of 25 xxokw i uf+q.f b-)-jky*i9st*7yn /gm/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 strai7r9wszob5 hg9 mcrvh:).1 wh lght line in a direction north of east and you end up 2.0 km north and several kilometers east7vwg59h9 wmsz1 .):hlcoh rb r. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x coz zyl kq)ljx+z+63 e*zmponent of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axiq*z ezljk6z+) x ly3+zs must be

  A 400-m tall tower casts a 600 n,3s (z:tbmfz-m long shadow over a level ground. At what angle ibmf3(z n :z,tss the Sun elevated above the horizon?

  Two vectors A and B have ovk r v0x9r791hg p,0fd2ejqo components (0, 1) and (-1, 3), respectively. What are the components of the sogrfd 07j2,r hkq1vv 9 p0xeo9um of these two vectors?

  Two vectors A and B have components (0, 1) and (-1jo)aj3g vuqgok0w(4) , 3), respectively. What is magnitud )( au0ojgogvqj3)4wk e of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Whats y8i1ri4gq w4 is the magnitude 4 y14iiswrqg8 of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disp- +n6 vxmjx : n2y3s)gcjkjv.olacemex v ykxmg2cn+6 )n:-josjj3.vnt?

  Three vectors, expressed in yu se)e jdtlu t)3 v h;6i77d4wqt;.kjCartesian 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, expre9ttp2ub xvy 6c6seg,vy );ve709yc cassed in Cartesian 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) and vector B = (+3.0, -8.0), what is the t 7dnv;+oe 4komagnitude of vec odet 4vn7+;oktor C = A - B ?

  A runner runs halfway around a circular path op y6l)x :2g2klonsk4of radius 10 m. What is the displacementy)2g42x6p:kl k nosol of the jogger?

  Two forces are acting on an object as shown in Fig.s:24 bi s-6frueq qph: below. What is the magnitude of theqe fhqp 2-s:6s :r4uib resultant force?

  Two forces are acting on an object as shownhg)9 rzj2j1 1+(7,pobanm* jcesp fcw in Fig. below. What is the direction of the resultant forcen,)o j9bpar2z*s7m+1(wpchgf jj ec 1?

  Vector A is 3.9 cm long and points along the positive x axis. Vector B is 9.2 u6m am;pnx.6;rl .lxj cm lon. ;;raxxj.pu ln l66mmg and points at $+53^{\circ}$ 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 63 cm long rb0 0nvj x+h.land points at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 31 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 spy-r9c ;k g+h*yz3jm/ ,offxgsf-: kyjeed of 16 m/s from the edge of a cliff. A stop watch measures the stone h;y,ffgy*3j+/kykzcf g oj:s-9-x mr's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, fromvvo +,t0 lted4gd n3x; a bridge. It falls 15 m to the water below. How far does t4l ;ntdv3,gt ed v+o0xhe rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, strikes thejr-heax 4au*: ground after traveling horizontally a distance of 15 m. With what speed- xe*hu:aj4r a was it thrown?

  A jumper in the long-jump g r5na2e j.atat; :sgf3oes into the jump with a speed of 12 m/s at an angle a.:s3tg aa2r5jntef;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 with a speed of 13 m/s at ia txel m906*j.u4bf i*:non can angle : a m46bnexjniilo f*cu. t9*0of $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 34.1 m/s at an angle og8-2 d1e3azqo tmaw6nr8t v2j f $44.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity ofg mixs.+mmc6cco09:3 fmx u;m 30.9 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 atoy 92wpnug5) k8ur-uqt-(ed o 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 horizon; c kwxt0poiz9 89xju)tally at 27.1 $m/s$ from the roof of a building 31.4 $m$ 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 bdz2fyz6-e+0z7 t l+ a nk/fxnan initial speed of 55.2 m/s at an angle oyxk zz62d blz fan++0e7nf t/-f $37.4^{\circ}$ 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 racegj+gwm 6 liu3 xuhdqhm:+al859omc .0 at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speedc9gighu m830 qm 5mh+dj au: ow.6l+xl 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, and is 8yyt6:uwf o*b*., g8 eqshprkin a wind of 50.0 m/s to the West. The plane's speed * :y8eg s6.r*uk,t wohpyb8qf relative to the ground is

  A plane is flying due South ( bf8afp olg.6c nf19d;$270^{\circ}$) 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 ofg9xc cq9 4s+usj7bu, / urke2)qwfgl 1 120 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 projectile with sl *2ge: bcgnpvgm)(py ,aba-cylx+) 0peed 50.0 m/s in a forward dip c* 2g-a+,0ynl:y)gblbc mag )(vepxrection $30.0^{\circ}$ 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- i1-6patuh6y0l y coxg ,jrq, river with a current of hy y6g uo1-r-ict06,q,xpa l j6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that c cy4q qm;;xjn+icps6+4d,.zddb rr -pan move at 9 m/s in still water wishes to travel directly across a river 0.6 km .qn+b iq4j + 4mpscx dr-r6 ;y,zd;cdpwide in which the current flows at 4.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s ta 8 mhfv8ii63:a9mtczvm0 n+in still water wishes to travel directly across a narrow 8mt9vhi 0 va8fmn3 ct6i+z m:astrait 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 236e+ aza y/urr00 m wide reaches the opposite bank in 6 min 40 s+z6rea r3 /yau. She 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 opposite baddbdl.0o ,/zznk in 6 min 40 s. She is swept downstream 480 m. What is the speed of/d,.ol z 0dbzd the current?

  A boat, whose speed in still water is 1.22 m/s, must aim upstream at an angle wbwm.1 .u//r bs jc-zn9uict0of/cm1ur j 0c nwz/t-.9bb.su wi $23.3^{\circ}$ (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)  $m/s$