Which one of the following is an example of a vecsur4 (sziuhx 9lf 4)x/tor quantity?

  Which of the following operations will notxhrf qy*g7 5c,nfmh7h554r ky change a vector?

  Which of the following is an accurate ; 1ykrm-xct8hstatement?

  The resultant of two vectors is the smallest when the angle between thely8zw fd3*w8 unh kpx(,b7hv 4m is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectie5db ; y9d,/o-ixvqp dvely. When these two vectors are added, the magni-, 5d/e xb9 voq;ydidptude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Wh o6 w84ngwze)sz/; jcnich one of the following is a possible ano cszz84e ;)g6n/jwwnswer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull 7rz:*lc hsl,kgvs z kvu ea)+;x27e wgxq:i*-on an object in directions tha ek*7)wkvizarx+2cqvs: zl 7gh,el-;ugx :*st are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector iscv8cq 4kufr.:, y0;kj x+oy pz

  Ignoring air resistance, the horizontal component hr2k:jufsw v *7/,82ivdgyrx7-gyr xof a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an angm*-9pw iyjqf9 *rx7thixe: s. le 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, thedoye31 gr1.7fhh w-kz horizontal component of a projectile's acceleration-rhfy.3k117egdhw oz

  A soccer ball is kicked with a velocity of 25 m/s at an angle ofl -e /d*n zwwfphks8/9 $45^{\circ}$ 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 directi ,+ njckhd54ged anti-parallel to the velocit+j4c,kdig5n h y vector,

  If the acceleration of an object is always directed 2*g uk;sv0bt vh j-k/jperpendicular to its velocityj0 g vkb /2-;ktjv*suh,

  At what angle should a water-gun be aimed in order for thehk0.o.rd82vkd 29o.mt pfnj odkz69o water to land with the greate62tkdnvd02ko .8k p oz.h ojm. r9df9ost horizontal range?

  An Olympic athlete throws a jav)sbxqs6 bdr rb/ f5*/kelin at four different angles above the horizontal, each wi)6s5k bb//rbqd sxr f*th 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 ball8q7 lhh5:sm*a,ow,ag o+zj 9g4uv 5k7uj d pzp leaves your hand with twice the vemks,4dw5voa77h+z,aqu9o5 j *gh8 :pj zpgl ulocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original sxw12hh;n,fwnk t xv:9 peed 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 fiellw+ 5cm:*)+e jgyys etx, ege-d goal attempt reaches its maximum height, how does its sy-gsee:+emlt+,) c5ygxwe *j peed compare to its initial speed?

  A stone is thrown horizontally frolzbc)1y: .4y7w)dj3kdtpv eu k h)u :dm the top of a tower at the same instant a ball is dropped vertically. Which o4b 3h ylve :ypu)71:wk.dzud dcj))tkbject is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is droppxbh,c nys89:i z-t4khed from the samsn-4k ,89c:hibxt h zye height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 11akr 9 2*qp( lzc6d/uwtp9ip :p9.8 m/s and at an elevation of 235 m drops a package. 5.1 seconds later it drwpciu*62d papp9qz rt(9l/ :kops 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 sec2;x7 gi bcktwu,4f-ojond package is dropped. Neglecting air resistance, the dibgkf7uwo t;xc2,4j-istance between the falling packages will

  A pilot drops a bomb from az3 6xby,)/nx rpa*mxk plane flying horizontally at a constant speed. Negle*, 6am/xz nrky3bp)xx cting air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only oneuolyyd6-th :drs/ij6 -1iw)v -sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and wr6) /dovy :i s u6y-t1l-hdijat the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level road atjv8x7,kuf*o 8i qli 4nd pass a car traveling at 45 mi/h. The relative velocity of your car to th xt*i8 8iuljo7q ,k4fve other car is

  You are trying to cross a river that flows due south with a strongek lzis4s ,4t/ aj6)bx current. You start out in your motorboat on the east bank desiring to reach the west bank directly west frok , xtal/464ie)zssjb m your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Howo6p*suku4nt 74f2wf-2jzlw k much time will it take you to move 12 km downstream, in a river flot46 lzf2-sk j24uw* kw7fnop uwing at 6.0 km/h?

  Vector A has magnitude 8.0 m vo nv g:r*irj3r0z7 t3at an angle of 30 degrees below the +x axis. The y component zg 3*n r3r7to i:v0vjrof A is

  If a ball is thrown with a velocity of 25 m/s7h0b c -eo7gdu 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 straight line in a directi 2+bqqfinr2v.dkc2; /hv zn h:on north of east and you end up 2.0 km north and several kilometers east. Hfhq v k b+z2nq2:/2hdv .ricn;ow many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is 8(d-lt )cmg7lfyddv :1dvp ,7po 8wss4.00 mt8old p w1d)c -sfylsm7pd ,v(g7:vd4/s. The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. Avv ;qdo v(tb- 9(:o5ya edn6xft what angle is the Sun elevatednq d5(;yv9fa v-6vtxoo ed :(b above the horizon?

  Two vectors A and B have components (0,gng/ zjy ) ikb**sp4m5/u-vtq 1) and (-1, 3), respectively. What are the components of the sum of these two v)yjvs /4g-m*t 5kz nqbp*i/guectors?

  Two vectors A and B have components (0, 1) and ( a)x86nb*v rov-1, 3), respectively. What is magnitude of the sum of these two vn8*v)a xor6bvectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mdu 43 4)osnejjtgmd91t l kc.-agnitude of Cs3t gmn4-j ec4d o.j k)utdl19 ?

  A car travels 20 km West, then 20 km South. z)u2s/ ay xmjgn:- xi8 What is the magnitude of its displa2x8m :ni as/ xgu-yz)jcement?

  Three vectors, expressed*ru2qqsl12r. hy;a hp 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 coordi4t)ame-n ws5ome4 t-a nates, 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 magj,li(xf;f+ tdnitude of vector C = A - Bj tf;,(xild+f ?

  A runner runs halfway around a circular path of radius 10 m. What is the dis l94l ,uqb)0geg0 z,q 9zxgysrplacemenz0ggzy9)qx l ,0 9esg,lrb4uqt of the jogger?

  Two forces are acting on an object as shownfr 4a(n:xwuaci+21uh in Fig. below. What is the magnitude of thea r24inhu+:fu cw1 (ax resultant force?

  Two forces are acting on an objec4 whf+p pcy 6( ozbl(qfib11(ct as shown in Fig. below. What is the direction of the re1b wohpzfcip41(f ((l+6 ycqbsultant force?

  Vector A is 5.5 cm long and points along the poy07 sst5fpsb-52gemy sitive x axis. Vector B is 7.8 cm lse5y7mp25sf- bs0tgy ong and points at $+32^{\circ}$ 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 an*-grl: +dob ;h9npeg8l jyaq; d points at $30^{\circ}$ above the positive x axis. Vector B is 29 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 horizontal3uaf yv dvb641ly with an initial speed of 22 m/s from the edge of a cliff. A stop watch measures the1auyb 4fvvd36 stone's trajectory time from the top of the cliff to the bottom to be 4.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velo.dhqe 8y0e6vecity of 12 m/s, from a bridge. It falls 29 m to the water below. How far does the rock traeq.y v680 dheevel horizontally before striking the water?

  A ball thrown horizonta, n6w7mhdtsas1 bi.i3 lly from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 22 m. Witm wisbt7a . ,snih3d16h what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spesyjz62ml3oku0 ehh8b y,*wd) d v6qb.ed of 12 m/s at an angle of .my od0 sh,hv6u* )jqw8 dbz6k2eby3l $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes uhrw 9c+ 3ztno ul819cinto the jump with a speed of 12 m/s at an angle 9 w+hcu oct981n3lzur of $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an,e5d- 1nsp1b c x:qh1z3+ra svt5rc mq initial velocity of 49.4 m/s at an angle of $18.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of.w(g u+h bobqr2t-uc x ;e,,zn z24onv 54.4 m/s at an angle of $35.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired/ae+8 r ush8mt-vk7ny at 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 horizontapivbgcldx ;jf uil,/p9 )2d +2lly at 21.8 $m/s$ from the roof of a building 61.4 $m$ 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 an in6hf)b0o:f fsn bm z5hepz,j85szb c:.itial speed of 44.7 m/s at an bsz:5e0h)zczj b.p6 hfsn85,mff b o: angle of $39.8^{\circ}$ 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.6ttd ir)2pum3qi: kzfitk e;9b0 6sm 1500-m race at a velocity of 4.0 m/s. If you ran the same race on a day when you had a constant . 6 dtsi 9fbtzqi0 :ure;)kt32mi6mpkheadwind 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/i74(ut bhpod, u4m kg,pts*n -m:fmb*s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relativ,:4mdf s-tpih*m no*tugm ,4bu(p k 7be to the ground is

  A plane is flying due South m/b 8msj7 -bcz($270^{\circ}$) 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 s;/3qx;bjemeyx, +x5nb;ac x xpeed 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 m/s horizontally fires a projectv-w) ru,h7zah y 7a3urile with speed 50.0 m/s in a forward direct a,a-vu7 )rzr7w3 huyhion $30.0^{\circ}$ 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 waterb)b.5lmj 2 0uq )pdtrk is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the.q0))ul2jbdp brkm5 t boat as it crosses the river?

  The driver of a motorboat that can movzb4wfn0.cti; qpp-d bq44u3876 dho8rwgox ve at 8 m/s in still water wishes to travel directly across a river 1.2 km wide in which the current flows at 3.5 m/s. How long will it take to cross 6dq;o0- vw go pd8bht.8 7w4b zpnrq3fix4 4ucthe river?

  The driver of a motorboat that can move at 10 m/s in still wattsr3(8bd0f. *6ain*klz gwpd er wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the blb3pgt.k d6 adf0swi*(*n8rzoat?

  A swimmer heading dir pulz;l;gr/qa ce p bnur25u9f9,,sr9 ectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she seu s,z/f2bp,grlr n9;c9l9upu rq 5;awim in still water?

  A swimmer heading directly across a river 200 m wide reaches the oppovv; *,qem e*awsite bank in 6 min 40 s. She *;* v,eawmevqis swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.12 m/s, must aim upstream at an a b-jnks ++px7ltgjeeie .r9f:eh8 /w0yl*q-sngle of+sft8i-ejk+p- lsn.0e 7:jlw eby*re/9x gqh $24.2^{\circ}$ (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)  $m/s$