Which one of the following is an exakav(s cv7xc )s.gf 2- 5odona1mple of a vector quantity?

  Which of the following operations will not change *9 wwwe4x,2gpc 00q32nlkysy/q;) cwrtive r a vector?

  Which of the following is an accurate statemenri gri :kcfd,;4;p/tp cx:0xat?

  The resultant of two vectors is the smallestc2rf )hb1k8i 6h1cgjv+e 9 z2pb+r zibpf-v) c when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, re er6gm ef+fx+ 7 xyv1ee2(usd6spectively. When these two vectors are added, the magnitude 6sxf uy m++de(x efv6e 17eg2rof the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one o2;b:tnqg 5*wbz 5go gof the following is a possible answer for the magnitude of the ;w :5zg otb5gqg*onb2resultant?

  Three forces, each having ui (e p u 4: qhqstlm3786o-eh4byq/saa magnitude of 30 N, pull on an object in directions t syuuse/q :4t3m8 7haoi 4(6hqe-plbqhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the 8q6qb8t ikxe2unknown vector is

  Ignoring air resistance, the horizonqu9abzy1dlfp q/f5u lr0h+.o o37kg6 tal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an anm hndf*;ss5 n0gle 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 component of a p /)c ta,ogyko2 s2t.)g qcx0rrrojectile's accelerationo 0ora/g . rcyk)) cqtx2tg2s,

  A soccer ball is kicked with a velocit0,u *vdna7tcqx5m)i ou(l4 rfy 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-parale1 ck 3jyx,(fm+(d swmlel to the velocity vector,mjy,sx3 fdm ((k w1+ec

  If the acceleration of an object ixuln+/4eq a3b s always directed perpendicular to its velocity,bnx a+ 4/q3leu

  At what angle should a water-gun o)rml18c5u.rm c 1bpput4 e d+be aimed in order for the water to land with the g pld8mrtc uub+c)e r1pm.4 o15reatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the* e-cq/gt n2e+,c tjrg horizontal, each with the setjn+c rct2-,gq/ ge*ame 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 han kt51l;ow (eep .ofw,x z/3x j-ar-lwtd with twice the velocity it had on your first throw, its horizontal range R (cz ef3 ,e-5kx-xtjllo.a ;pr1 ot w(ww/ompared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle of x*m*h9iwtv,b$35^{\circ}$ above the horizontal. What is the speed of the ball when it returns to the same horizontal level?

  When a football in a f0gws )y5 yugow2/k ll6ield goal attempt reaches its maximum height, how does its speed compare toy2 0w)w sk6/ ggylul5o its initial speed?

  A stone is thrown horizontally from the top of a tower at the saj nzk 2)a gx2/qo(w/, -m8hujinznry 8me instant a ball is dropped vertically. Which object is traveling faster when it hits tnj8 j /r2u,ax2ngz-ymzhq8k(o/w) inhe level ground below?

  A bullet is fired horizontally, and at tf )5ft 2bi0iifhe same instant a second bullet is dropped from the same height. Ignor i5b)i0fif2t fe air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a spee5iesvfnic7 fo7 y*suc3k0 l48d of 98.3 m/s and at an elevation of 241 m dropfk7e l 3c7cy540* 8onivssiufs a package. 5.6 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dlmi3 3ucrq) sqori 5 .6ov7kd2ropped from a plane, and one second later a second package is dropped. Neglecting air resi)l6o5qvqrk c or.i7i2us 3md3stance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizoca .kj/qn+5h i+krcu g7 xv+94yo 9pblntally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane wnl i+ q4p7j.bokyh9+au 5v+c9k r/c gxill

  The acceleration of gravo:dc bc8w:w :*w)cbeg ity on the 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 and angle) that you would on Earcwb:e wdw*c:gb:co)8th, the ball would land

  You are traveling at 55 mi/h in the +x axord +jrhk2/0/ xcy*/n 3smwtlis relative to a straight, level road and pass a car trsytkrjnr mx/2 3 o/*+c w0lhd/aveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross +rv liroq -p, x+gt)u0sz ah(/a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to /q uat( gl+)0z xr+vo -hrsip,reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in sti:*jwv (r(vyhf7c 0;z koe2ydmll water. How much time will it take you to move 12 km rw0v*dyc vh(2o(;:y7mfkejz downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an d md6 oz5./vz m8hdnz7angle of 30 degrees below the +x axis. The y component d.dd8o56n zvhm7zz/ mof A is

  If a ball is thrown with a velocity of 25hk8 at9xw5l*7gk1 beol3x l0 x 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 inq.8;/yqa/qfsk 1aw ee a straight line in a direction north of east and you end up 2.0 km north and several kilomet y qae8s.e;1f qa/qk/wers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. q*d)vx6/y9 z.)tujb9bpb uxlsub 2u1 y2gu w,The x component of its velocity is 8.00 m)uzg16,q )y2bbd*u9.xl9w2tuy/su u pvjbx b/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower ckh .s yw7h2dasoh 7;cv*ne ,t0asts a 600-m long shadow over a level ground. At what angle is the Sun elevated above the hvhd 70;*a .w2s yck sehh7nto,orizon?

  Two vectors A and B3 6 zhkmfn l9hhg,u/n+ have components (0, 1) and (-1, 3), respectively. What are the components of the sum of these two vectnhh+mg/ h 3zul fn96,kors?

  Two vectors A and B have compon) - -voiexp7seents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these t--)s 7pxeio evwo vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . p n/og0bar7b75s/v skgi0; d qWhat is the magnitude ofbv/b 7q 50krd;go/a n si7gp0s C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of i, puc,ojvty )z66 *gns:bvpq)d)wad2ts displa,d6 :jpp6n*db)oc ) vvzty,as u2)qgwcement?

  Three vectors, expressed in Cartesian coordinates,c32/+quqy mjx 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 i :tebymt97r6si,n( v )cbr8ttn 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 f m f5g6s9+(qonnxl i(vector B = (+3.0, -8.0), what is the magnitude of ix sq 96fg(mnln( +fo5vector C = A - B ?

  A runner runs halfway around a circular path of pficq0mpp79:,l/ha-hv:m pkradius 10 m. What is the displacement of them7 h: ip /fvkp9 qh-cmlp,ap:0 jogger?

  Two forces are acting on an object as show9;cuv4 cja-x8ico,uk / 8 xzszn in Fig. below. What is the magnitude of the resultant fciak c 4o;uc9z 88zs x,-ju/xvorce?

  Two forces are acting on an object as shown in Fig. below.wz 11 j+p 5ijmvl.w-,b:g6sgx,upt nq What is the direction of the -jp+xi1z,gvjp qsw n5: .6mbg1,w lutresultant force?

  Vector A is 5.4 cm long and points apu,azr*ex5 gh) viwo203uy *t long the positive x axis. Vector B is 9.8 cm long anugpaw)5ut z0o,v *e3r x2h*yi d points at $+40^{\circ}$ 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 85 cm long and points le9qj2msdu3t 9b9v :xat $30^{\circ}$ above the positive x axis. Vector B is 30 cm long
and points along the negative x axis. Vector C is 35 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 1 mk3 :c*r if- :xnd1bnl,hfjn14 m/s from the edge of a cliff. A stop watch measures the stone's trajectoryx3 1-h,mnbrfndkc :f: 1*l jni time from the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 6 m/s, from a bridge. y 6metuc2 :0zo It falls 24 m to the water below. How far does the rock travel horizontally before striktz:m6 yo0e2 cuing the water?

  A ball thrown horizontally from a poi0th1x r,n,.f g.r tkwcnt 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. Wit ,r.0tc1f,xw nh.ktrgh what speed was it thrown?

  A jumper in the long-jump goes into the jump wd tv/yl( 7dsdtj9 n()zith a speed of 12 m/s at an angle ofjd(d)(td 9yt7vsl /zn $20^{\circ}$ 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 1y2m4bm qe0 hq9rzjx/33 m/s at an angle of0ry/x mje q293bmhqz4 $17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 39.2 m/s at am+bbk;/fs3:lc m k- xin angle of $14.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velof(3yew(v, e y uw3ap 0x-jeil:city of 20.1 m/s at an angle of $34.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle of wj.xtieqn;0sw )p1x* $30^{\circ}$ 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 2h.qgao kao,j:(xc7 f 21.9 $m/s$ from the roof of a building 56.3 $m$ 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 initial speeyxws+ /x6qez dp:v 14zd of 52.2 m/s at an angy/6+ewxvqz4 : sdpz1x le of $43.5^{\circ}$ 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 velocw(;dwl 7xd3mx tfhg0+x59m*g6h i b h;n)vcag ity of 4.0 m/s. If you ran the same race on a day when you hafnvxgwxi5ax;03hdw d;b m9gh(c7 6hm t) *gl+d 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 o zn.u bispgun f,+3cd5h) +ch1f 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's spesc u1 hcfn)n u+3,b+hg.dzip5 ed relative to the ground is

  A plane is flying duejv:zbt0 ,m0ax (y mf3wuffw09 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 spe)he, o +zjmww2ed of 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 mb0uvu0f 0 e)ro/s horizontally fires a projectile with speed 50.0 m/s in a forward diu ur00e)0v bofrection $30.0^{\circ}$ 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 directytlg n8cc97cgu1 d-- led across a river with a 1 culg nydgtl7cc 98--current 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 18 m2 fna:mnqk*: k/s in still water wishes to travel direqnmk *:afn2 :kctly across a river 1.2 km wide in which the current flows at 7.9 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s i pdw.vkcbojy09 j.qd z48/zk-n 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 dc -k0vzoypj d. b.w 84/jdq9kzriver head the boat?

  A swimmer heading directly across a river 200 m wide reachen /tax( dawq7ii57tnh1mg7h6 s the opposite bank in 6 min 40 s. She is swept g6nxi7at75nh(i/ hw a1dt qm7 downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opl(.ga2or(:os cxfi2o/*tzmb posite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of thm2os/ cofo lxt(ba g:( z*r2.ie current?

  A boat, whose speed in still water is 0.84 m/s, -rsd,8wj7n dna vahm9d 8op)w*a i.1wmust aim upstream at an angle of n 1* woaw dnr,)9jad shwma878- i.pvd$17.0^{\circ}$ (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)  $m/s$