Which one of the following i0c( p*wsfi) xys an example of a vector quantity?

  Which of the following h (nu8)vslm8 ioperations will not change a vector?

  Which of the following is an accurada*,qxa5l fofd( s -:6ibz)bdej,: efte statement?

  The resultant of two vectors is the smallest when the angle betwe8x pt-a9t x(.t ki)ehren them is

  Two displacement vectors have magnitudes of 5.0 m and 72bicy 1 vm9yk).0 m, respectively. When these two vk9 )ibv m2c1yyectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addegb7idg;)t q,k l u1cl--uqdw,d. Which one of the following is a possible answer for g1dcq , ;i-ult-wq )7,kgulbd the magnitude of the resultant?

  Three forces, each having ahv lgx3r1m *za yzd,/rw0 n54c magnitude of 30 N, pull on an object in directions thatarv*0z4 5r 3xgw zhycmdn1/l, are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,sw nyc+x ) 6+wrdd;x;y the unknown vector is

  Ignoring air resistance, the horizontal component of a4apaqwcj00ns 2y+vn c0/(kjx projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angle ./fy .n3speuv:nt p; fof $60^{\circ}$ above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

  Ignoring air resistance, tngf xdg45y:,)cu 1j-gpgpgv ( he horizontal component of a projectile's accelerationp-5gn v j)g(:1 cpxg u,fgd4gy

  A soccer ball is kicked wit+a gu4 fa 8ld;cszdat 5l-,y8r(vrar.6:uz beh 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 object is directed anti-parallel to the velocir1si9//eg(t8y g lj9bp2za t y3r sif+ty vecto /j3 g9(p trseity8lzsay+/9ifb1rg2 r,

  If the acceleration of an object is always directed perpendicular to its veloc;3dpuxsm)4i-sn7ty xk bo4 r4ity 4;mr73tps odi4ysu)xk 4xb-n ,

  At what angle should a water-gun be aimed in order/x5 l9 3a+e1xzs la;jcyhg4al for the water to land with the greatest hori hlg+jy/eaac;lxz 3as91l 5 x4zontal range?

  An Olympic athlete throws a javelin at four different angl68 8tzq)aldis es above the horizontal, each with the sa) q s8il8zt6dame 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 your hand witjpiufee hp5 ,9i: fmku e89b.1h twice the velocity it had on your first throw, its horizontal ra5e9ufp: kfhu jmp1i.e ei89, bnge R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle,i l:4tmvj d8 ;kvk)qj 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 goac .f)i.tbqfg07hu. rkl attempt reaches its maximum height, how does its speed compare to its initial spef.t cfi.q7r h0u)k b.ged?

  A stone is thrown horizontally from the totp d6kr+ i,sou;3 irg2p of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the levelpsort,u+g62 3;kdr ii ground below?

  A bullet is fired horizontally, and 2lwc) g crwr j1b*l7(tat the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the tw) (cb2rwjrl*wclgt7 1 o bullets.

  A plane flying horizontally at a speed of 68.5 m/s alx wx g7jy8-gp5k*q2:z p wxu9nd at an elevation of 284 m drops a p95gp7pl j:*x q2gxz k8uw xw-yackage. 4.9 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 later a second -;d7xx ot .v,llvhs-wpackage is dropp - .vdo7lvth-,lxxws;ed. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizofq* d9hzw:idyw+3x)5ve t ry(ntally at a constant speed. Neglecting air res:* h q)eid9r(vx 53zy+yt wwdfistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Ear ;dm9h rfx 3p 5,lv+;f+o/fdu;kfdjdfth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on E+hdffp;l+x d;dvrom935 kjf; fu ,/dfarth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a strai3ycns fq lf0h rp)*p3g45u:sb: bv2rpght, level road and pass a car travel*3c prlupbns h:3vsg 5) q4frp:f0by2ing at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river thac2(x36i d3dq8 s inbja(zst*l t flows due south with a strong current. You start out in your motorboat on the ei 2cdxt(qs6*8l(3d zsab3ijn ast bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still watx/u pk4a cleod os;-4wmpu6 .6dlod-(er. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/loo6- m4.d4 oad/ewku uxc6s pp-(d;l h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axise vly h4ie-l 0ip qnrt0(/br46. The y compone4b qlvtnpr/ilhey(i604 r -0ent of A is

  If a ball is thrown with a velocity of 25 m/s at an an phq y8mf0ld5ty2l+7 gz /yea-hf+ )lygle 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 directiobg3cx1ms: ): tk0ost xn north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have youmg:obk:x x3c)s s0 t1t walked?

  A butterfly moves with a speed of 12.0 m/s. The x jmh15f(k q: upcomponent of its velocity is 8.00 m/s. The angle between the directi hm:1 upjfq(k5on of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At (+l0n8a j6h*.p uvmu7eheaej what angle is the Sun elevate uaajenuj p hle*7(06v+ .mh8ed above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), resp6:+is mfpte l.ectively. What are the components of the sum of thes 6telim +:f.pse two vectors?

  Two vectors A and B have components (0, 1a uqv9m24:czwqh jdc.o 432 )blel9zk) and (-1, 3), respectively. What is ma3q9jz l ukh 44m v9qb:)el2zda cwo2.cgnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C a2w*5dry le-h= A + B . What is the magnitude o-2hdy 5* lrweaf C ?

  A car travels 20 km (2:z+ evg9urbod4w n2 yi3yg yWest, then 20 km South. What is the magnitude of its displacemey :dv y9g e3ur wo2n(gyzib2+4nt?

  Three vectors, expressed in Cartesian 8:l *zw17 ieasgaxid7 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 Cartesilr8k/ y f;s a)jqhhed8)0hbi4an 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 = (+3.0c0y gd0 f6zs:a, -8.0), what is the magnitude of vector C = A - 0g 6szafd:yc0 B ?

  A runner runs halfway around a) pn+e-,(azz**jtrn d 3 kg91vpfpmjc circular path of radius 10 m. What is the displacement of the jogger?-nd1 m,p)nefkgp+tj9*cz zp vaj (3*r

  Two forces are acting on an object as shown in Fig. below. Wa-)f7 b8nqnsfgmd.9k hat is the magnitude ds7mab9)kg n-f.8qnf of the resultant force?

  Two forces are acting on an object as shown in Fig. below. wh*92airkean7y (1h7rstc4 kWhat is the direction oaktc1ir(7s w k henryah42 97*f the resultant force?

  Vector A is 5.9 cm long and poy wr c7vb.k,z q-3aby+q-p ,hsints along the positive x axis. Vector B is 5.2 cm lon yp+- -c ,z,h7yb.wva rqks3bqg and points at $+42^{\circ}$ 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 80 cm long aptutj4det bsa5-w-4k 74 6qydnd points at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 38 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 24 m/s from the edge ofhj3(s4e3m4pg 1 dl thw a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.7 s. What is mjedtl4 whp431( hg3s the height of the cliff?

  A girl throws a rock horizo/7 +j wa5rvrxh-y5rh0 w(siq. gn,usl ntally, with a velocity of 12 m/s, from a bridge. It falls 23 m to the water below. How far does the rock travel horizontally xn yg-i/+(r.hj5 u 75 awrw0r, lqssvhbefore striking the water?

  A ball thrown horizontally from a point 22 m above the ground, strikes the t53mb 6epmuw j*sei sy.7du64.b,scmground after travelinp um.its65w *c u4yd s.7,msjbb m36eeg horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump withl- -whne e;l0*i/33 epapodkx a speed of 12 m/s at an angle o*ildkp/heewna lp 0e -;-o33x 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 6 jaeau+i1q /n11 m/s at an angle of e6 +j au1inaq/$34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 211d9 :qfs5(eqdicr ajum 9.e(.s.k zir.0 m/s at an angle of $35.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launche) bgjx(+o nc8sucg5 b,d with an initial velocity of 48.3 m/s at an angle of $22.2^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an+u : o1rjloaig t1k 9 )ctc53bg*kv5jqgle 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 16wstm8fc9ozyf5 7x n;9 .4 $m/s$ from the roof of a building 44.7 $m$ 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+v/7chm8b vsz (.wi9 hhwxl3m+ wz;sy an initial speed of 67.2 m/s at an angle of7h lm;w9s+/8b hi m(xhwc+w v3v.zysz $40.4^{\circ}$ 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 race at a velocity of 49i,f3h 3 upacx.0 m/s. If you ran the same race on a day when you had a constant headwind which slows yourip3hx9,ac fu3 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/savck i;dn( ox8s;;2t p due North, and is in a wind of 50.0 m/s to the West. Thxk ;p os;cn2ait;8(dve plane's speed relative to the ground is

  A plane is flying due Souti.3d .t6/h y q7/aqw3 hbdylquh ($270^{\circ}$) 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 isqwi9,/*u8nz1 q m+e; bznptlu 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 horizotvdfm7qt l-txcodj17:d+45o wg.2jc1cv5ulntally fires a projectile with speed 50.0 m/s q to2 l1:tc75v+1wd4-x7l5 cmgduj t.cd ojfvin 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 in still water is 8.0 m/s, is directed across a rivbsgu)8q wvl /s vj2batm803o /er with a current of 6.0 m/s. What is the 8j2 l/uvgt8b3a)om qb/wssv0 speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 16 m/s in still water wishek wf;l*lxo q 3;h0fy3as to travel directly across a river 0.9 km wide in which the current flows at f;y*w0lfq3olk3 ; xah4.2 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 wip qu)/wrmd bslc(a,0,ft)0z 9(b hjj dshes to travel directly across a narrow strait in which the 00jpsdma rb/f)lwzc(d, hqb 9t)u j(,current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acro; 8b qt7xlv-gh) tszs5; sv f3v4m 272eksgzzvss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stillv)qxbthv5sgvl tvzkf3;-z 4es2;s 8s 7 g2z m7 water?

  A swimmer heading directly across a river 200 m wide reaches the oppm.0ms -w9j) x dm1a(z(qolhw posite bank in 6 min 40 s. She is swept downstream 480 m. What is th-)aldo(zs1qw9pm h 0x .(jwmme speed of the current?

  A boat, whose speed in still water is 2.18 m/s, mustd(f993iqmzf v :y 9zys aim upstream at an angle of9:dyffqz v9 m( y3szi9 $13.2^{\circ}$ (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)  $m/s$