Which one of the following is an ex0ve5o //-vv 3iz q uuqnm7uvo-ample of a vector quantity?

  Which of the following operations will notv7;) *d wxmhsf change a vector?

  Which of the following is an accurate statemen*rt dnw(d0 gv3t?

  The resultant of two vectors is the smallest when the angle betwbglm8v72pcvky (bd ;n;jy8hl ,bf8b6een them is

  Two displacement vectorst2if fu-em8l * have magnitudes of 5.0 m and 7.0 m, respectively. When these two vecttue8* lf -fmi2ors are added, the magnitude of the sum

  Two vectors, of magnitudesq: q40x +xhym2osy,m+(-c 3x cpxtny)1d cguz 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resxt-c0x2x3cozs c4,d)y +px u:n1 gyhmqy qm+(ultant?

  Three forces, each having a magnitude of 30 N,y ;x wh;9cu)xd pull on an object in directions that auhy c9x;w); xdre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thsyrqb453fr8 ke unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's veloci.t2sr7hsf eqyw bwh;i:m43q / ty

  A ball is thrown with a velocity of 20 m q om/ib0e+r)ljytf;axnym,c6n8h fc))nt * )/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 horizontaln ebtcvo5wkf/c e9e89 . f;g;t component of a projectile's acceleration8 otwc5gb;;t9eveff ce k/n9.

  A soccer ball is kicked with a velocity of 25 t *67)upimz61lk9o 9u5fynw0 m ec*o. kgwjcmm/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 vectr7nx3ke;ukj 1 or of an object is directed anti-parallel to the velocitr3 u jxn7k1e;ky vector,

  If the acceleration of an object is4s lzp ba mv5(*,qck4e always directed perpendicular to its velocit,b*e c( pak44mzsqlv5 y,

  At what angle should a water-gun be aimed in ordwnrhu4 b8zec,u,( v2zer for the water to land with the greatest horizontal4c2zuwnb u8v,,e(hz r range?

  An Olympic athlete throws a javelin at four different angles 9 lu47rwz n,zeabove the horizontan,7zwz rl4 eu9l, 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 for the second time. If the ball leaves y-liy*:+ pqo 6jdcigavi5 9o5wour hand with twice the velocitygqo w95-y i5iva j:lc* odpi+6 it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original jom xke a+g95 0e ee6f8bhi27*eok6cm 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 goaltf-t4mxjy.+qxp8 6opiye7 j 2 attempt reaches its maximum height, how does its speex7tyx fmeo2 .jj y6 qp-+tp84id compare to its initial speed?

  A stone is thrown horizontally from the top of a t5z;2zyaaf( 0m-o5 j7 gagagwiower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the levea oa-f5yz(7 2i5ga; 0ggw azjml ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is dropqzp +jpm 5l,h2ped from the s,mq2+ph5 zjpl ame height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 96.8 m/s and ah3o3vz g-t,w77uj qrdt an elevation of 266 m drops a package. 5.2 seconds later it drops a second package. How far apart will the two packages land on the gro qu 7twrzo-j d33gvh7,und?

  A package of supplies is dropp- :9mtspiml,fzv i;( ked from a plane, and one second later a second package is dropped. Negleip 9m;fiv z-m:st(lk,cting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a cb)rxa+ jlulf3)j; y4 * g4fxqgonstant speed. Neglecting air res)*4jrgulxfx)g4a3+ ;qf b lyjistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth ofel u08ifxc*ma- c;(v p that on Earth. If you hit a baseball on the Moon with the same effort (and at the s;iu0a xecp8l-( mfc* vpeed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the n1d9z (it f2sts6(iuh+x axis relative to a straight, level road and pasn9uif 6itd(z(h1 s2tss a car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river fo5hml4am3q)w2mb+ ev0w4 iti8hmc 6that flows due south with a strong current. You start out in your motorboat on the qwa2 v 4i )wl45htbi6mmc8e +fmoh03m east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at5jrh0k), mdi26egu on 30 km/h in still water. How much time will it take you to move 12 km downdi)k 56 ,0jur2hngmeo stream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m bjcv5-k9+1w1 :w -fp mi vasjlat an angle of 30 degrees below the +x axis. The y component of A ip51wlwmvvk1+j-ca :9fj- bi ss

  If a ball is thrown with a velocity of 25 m/s al6 pq33cr pdg har)+(:yts:r lt an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straigh3.m ss-jngy.ft line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east nsmjyf3 -.g.s have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compon tmd:2 4m0j*3(rsv 7e hus/-c djrhgbhent of its velocity is 8.00 m/s.dj7g: (* smv/c4b jmrh-h u t2d0hser3 The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m)rglx.ybkq,/ b7 dz :g long shadow over a level ground. At what angle is the Sun elevated abov g)l,z.gbk/ xd7rq:ybe the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respec 4ng(ogkq3f3 + twe5b9tg+i futively. What are the components of the sum of these two vecto9(ki3fgqn 3fbg t 4oetu5g+ w+rs?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiwp uz ,,tb b7isc+o)g3 qe8uv93/j qsfvely. What is ma9bb3 ij7)g,vq+ u,wz /q esstc 8upo3fgnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vekaug jp/mr .g8t x2k-*ctor C = A + B . What is the magnitude og p krt-xg*/juk2.a m8f C ?

  A car travels 20 km West, then 20 km South. What is the magnitude ofj7 jovzl- z:sm70(k,war mcy1 its displaceme mla7,w r:k(j cz0zjos7vm1- ynt?

  Three vectors, expressed in Cartesi7ca s0u1xif 9riq f/v)an 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 coordinates,cejadjd,-5w 5 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 vec.qsg9h+0ilsly+yzi:- ;t re ttor B = (+3.0, -8.0), what is the magnitude of vector C = A - B t+gi s se9l;trly0z+y:h- q.i?

  A runner runs halfway around a circular path of radius 10 m. What iswgap r02,y q ycj91dr9(pa q0u the displacement ajg qwrpr a9p2y yc,0u9qd10( of the jogger?

  Two forces are acting on an objemt03yeu. f rkh*.yp4c /gk .ijct as shown in Fig. below. What is the magnitude oj ru fp3y/hy. ti4*0ekc.g.kmf the resultant force?

  Two forces are acting on an object as shown in Fig. below. W lx i2xcir9r45hat is the direction of thirilx5 42cr 9xe resultant force?

  Vector A is 5.0 cm long and poi62tqr mhv(2 vs81f /d kae.,wk cewnp;nn8b8ants along the positive x axis. Vector B is 9.1 cmhb(p1nwqk8 c/ ;nf28d2nvek s,8amt 6v.ar ew long and points at $+22^{\circ}$ 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 66 cm lonn -:zutsee5 hi 2 8+*xc/npoa2wfa 3ijg and points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 40 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 horizontalnas+ eycb 6r8cytyai*0d-( 9qly with an initial speed of 19 m/s from the edge of a cliff. A stop watch measures the stone's trajectory tiyaqc (8n*b 6sy t-c0r ya9id+eme from the top of the cliff to the bottom to be 2.0 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 19 m/s, from a;qhmmyt.n3mrmj)ov(p gl1/(c +i5w a bridge. It falls 22 m y) .pi (t3/mmawn(mjmohrv1cqg;+ 5 lto the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally fro 9(t3kv . annyyjw14;eqkuhd5m a point 25 m above the ground, strikes the ground after traveling horizontal k1e3dkuna9jyh 5nt 4 .q;yv(wly a distance of 16 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed ce/pnb9v(a7kql2 5 ncof 12 m/s at an angle o5k cnbl2npaqc(v7/ e9 f $20^{\circ}$ 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 10 m/s at ankzsxjn 2+ k/b1 ut,-bn angle of+kkn zxbtuj,n / 1b2-s $30^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloc ss s)psnz tj9.o+g*e.ity of 57.3 m/s at an angle of $46.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an 8yfa7 6klisnlz ;+cs,03hqqu 7j ftm-initial velocity of 32.5 m/s at an angle of $16.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at ,.oxltg/w wp1kj7ruomd*5a cvh (c1 ( 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 at 24. o1;e9wrjs+a:waxmq 3 6 $m/s$ from the roof of a building 59.8 $m$ 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 1 d ltj1065cnlwqr cgh*z7tj/h8h1bk level with an initial speed of 39.3 m/s at an angle k11jl8bcl7hjc*/g 015qzhdt 6nhtwr of $43.6^{\circ}$ 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 windq 1eim38a ;zuhu8ksq,), you can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you hadehmzq88 3a; ku qu,is1 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 osujdtlx7/. -m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the gr dxtjo.7- l/suound is

  A plane is flying due South (e ; e8jbd+ 2u1occfglzfx*-y3$270^{\circ}$) 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 nd +jjsk)a 4 u;iw5 iq9(vfg4vheaded $30.0^{\circ}$ 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 speed 5bjnn;2 5pn j8w0.0 m/s in a forward dir nj5w2 p;jnn8bection $30.0^{\circ}$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

  A boat, whose speed in snr1p++ qn01j jnatn )mtill water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What p1j n 1q)+jmrnn0tn+ais the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 16 m)sg uz/ j;ybi+/s in still water wishes to travel directly )z/juigb+;y s across a river 1.7 km wide in which the current flows at 6.7 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wggk,8 rmbw9 iobauh/ / w,j0;aishes to travel directly across a narrow strait in whi,//;uaimg jbwgka9o0 8w br,hch 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 200 m widevu2n- cjrao px+vj2/, reaches the opposite bank in 6 min 40 s. She isu j2vrcn2 -j/ ,vpox+a swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reacheq ngn84;hpfd f*9yobv.y-y+j4qx 1 hts the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the ct nn4ghjq4p qy-yvfb9*y+o 1;h. 8xdfurrent?

  A boat, whose speed in still water is 2.12 m/0c,e:0 bvlu7 e(jlyzps, must aim upstream at an angle oflzy ,(bj lc e00:puev7 $27.9^{\circ}$ (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)  $m/s$