Which one of the following is an exa-oo+ wgd f)rxk:*hp r)mple of a vector quantity?

  Which of the following operations will not chpw/ t k23lmg .ar zf/q(0u:malcj74zc ange a vector?

  Which of the following is an accurate statement61zgk9upfii6 4q7w 8. w smin c3lhz(v?

  The resultant of two vectors is tn -mm;dl9o6n oc(klbkd3t b 1(he smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, re;5/ vvbm.d. tgipg .uuspectively. When the /pugdmvi g.5;.ut.vb se two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are addo9qpt u)t 59xted. Which one of the following is a possible answer for the magnitude of ttu)opqx 599t the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions*xm,uy-y)f p 5z5wy2 z2mkgkm that auy5)z5fm ,pymzy22km-gw *k xre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectot biwxff-6(p0pc0c0g r is

  Ignoring air resistance, the horizontal component of bn-c1*rumu8v:c qahfr*rq;;a projectile's velocity

  A ball is thrown with a velocwea.- 7ev +intity 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 componentxh2yj 1z(7,p.l+wav5tq4 mg ue .j yva of a projectile's acceleration2z17 j. qyeja,w5va+ mgtlxv4h u( py.

  A soccer ball is kicked with a velocity of 25 m/s atm18xl4-gzs cz:o (ghs 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 object8))dk dfpig7w is directed anti-parallel to the velocity vectowgpd )k if)d87r,

  If the acceleration of an gefjjq2elh5*8,i(s2t4n 7ex y cpr,h object is always directed perpendicular to its velocitp 5,2lh2 rhgn8 x(ycef *,e7qs ije4jty,

  At what angle should a water-gun be aimed in bkn6wan**o;q order for the water to land with the greatesnbwaq*6k* on;t horizontal range?

  An Olympic athlete throws a javelin at four different aq brpz+gf*x.t*,n1 jangles above the horizontal, each with the same sptz*jp*1ab gf +n.x rq,eed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 ha6f + x+gk4cxby k,)we6hugl4end with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would )6fgb,k 4e cky+ w xugxe46l+hbe

  A ball is thrown at an original speed of 8aojr60 d9jtv+o 3m8bk4wjoz 7 : hgic0.0 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 goal attempt reaches its maximum heimuqx +z le38f;ght, how does its speed compare to8lem uz3fx ;q+ its initial speed?

  A stone is thrown horizontally from the top of ayb5hywp7ro 7p 82/cj q tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits tp yyqpr5b /772c8hw ojhe level ground below?

  A bullet is fired horizontally, and at the same inl 8 wnb0-ofdwm9kz m,7d * nd;af0f/o6) olauqstant a second bullet is dropped6 am o*-qlbowk 0d7;/owm0z uflfn8 d 9fn),da from the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a- sd:-h.rcignqv4 s/x speed of 85.5 m/s and at an elevation of 147 m drops a package. 2.8 seconds later it drops a second package. How far apart will the two packages land on thedx r-4cvs q.gi:-/ hsn ground?

  A package of supplies is dropped from a plane, and one second later a second pa nf1t;:0+v7idjklzr uckage is dropped. Neglecting air resistance, the distance between the falling7lruv ifzt1jn+: d;k0 packages will

  A pilot drops a bomb from a plane flying horizontally at a constant ( b0 cxz7 2mgrx2ec.uvspeed. Neglecting air resistance, when the bomb hits the ground te0(rxcu 2vb xz7gm2c .he horizontal location of the plane will

  The acceleration of gravity on the Moon is kkt*kf,a0 z tzy): .kjonly one-sixth of that on Earth. If you hit a baseball on the z0k*kkzy. a:t, k)jtfMoon with the same effort (and at 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 stra5 lh+akh r)vy/t u21cnight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car 5l/nyhvu h)1 t+kcar 2to the other car is

  You are trying to cr 2l0vrw(njho7-g.snrs/pfikc, 4s h2oss a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting p shr4ohfgls,jn20w nc2(r /.p v7ki- soint. You should head your motorboat

  Your motorboat can move at 30 km/h in4ll2llns5 5gf still water. How much time will it take you to move 12 km downstream, in a4ll5nglsl25f river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x a2evfav9/ d v .1gkqvk:xis. The y component of k1vf2qvd9ea/v.k g v :A is

  If a ball is thrown with a velocity of 25 m/s at an angle of .hd j.61bku da 6u6udm$37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a direction no0),h n:u97p7s eq w1b pustmfyrth of east and you end up 2.0 km north and several kilometers east. How many d: umqp,0snu1 fhbsp7yw 97)etegrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its vw )ud2fo2ya *7d lr gi(mm y9zcfd)h43elocity is 8.00 m/s. The angle between the direction of it9fda)i7 m 2l4gowuy3rfd2c *)zdy(hms motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over ax-h4obks(1qo 4wl (c e level ground. At what angle is the Sun elevated abow(ex -s (hqco1lb o44kve the horizon?

  Two vectors A and B tx;g mntb0a,6o * / -hmyvn sw)a7xoj2have components (0, 1) and (-1, 3), respectively. What are the components of the sum of these two v)vyan2mw70 ng- x;/ h6txjot b o,a*smectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectirphsh2 efa: mb * 6m(oc*5 fmg+1hj9uuvely. What is magnitude of the sum of *hj 5h u( 2fs:amuhe+m6fm*obr p9 cg1these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitub56xf0a ajzrdu;4 . zqde of 6.fx 0rz ;ua4zbqdja5 C ?

  A car travels 20 km West, then 20de9iv(h upbg2.czcra9 7(rs x w.6a1 t km South. What is the magnitude of its displacemzt v .cid2brp((1cs h.g97ua9 a6xrewent?

  Three vectors, expressed in Cartesian coordindl g)j: ih6cy:ates, 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,4yse /a*e0f 3ihm fah0ed8xu 1syo9q) 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, -4dvq7fca:c t. 9.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B f9.vqdt:7acc?

  A runner runs halfway around a circular path of radius 10 m. What is the displax8coe l1vq20icement of the jogger0 q82cvlio ex1?

  Two forces are acting on an object as shown in Fig. bc0qda(6vh8qdm96 ,qlwk3d t xelow. What is the magnitude of thdqxt 6q dk6qhclawm9 0dv83 ,(e resultant force?

  Two forces are acting on an object as shown in Fig. below. idsc+ qk )/ v1bnq;t hr0f0na9 What is the direction of the resufn1/t+ dkq a9icv0r)qn h ;sb0ltant force?

  Vector A is 5.8 cm long and points along the positive x axis. Vector og gc* kmb+b gz.aks54/((m w4*tykgf B is 7.1 cm/ggbc fy 4mg kg5awo(** zb.4kksm (t+ long 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 63 cm lowa +0wp+t-.i-byf ncuqs2 dj4vbzj0(5tzy b+ng and 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 kyi g-1gc: rsj; w3ec/initial speed of 25 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to g sykrcw j/3gi1: ;c-ebe 3.5 s. What is the height of the cliff?

  A girl throws a rock horizontally, 0fo/ ode.*t w z9 nbv6z9;bxqewith a velocity of 18 m/s, from a bridge. It falls 17 m to the water below. How far does the rock travel horizon*.0vbzqo ebnx;69o/ztdwf 9etally before striking the water?

  A ball thrown horizontally from a point 28 m abovez 7*o1w /(aa:vthock t the ground, strikes the ground after traveling horizontall ha7z1(avo/c* t:oktwy a distance of 19 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an zf d4ku1 h3q5aangle ofq4h5dua3zk 1f $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes in, lksxr ni5 (pj00yoa+to the jump with a speed of 15 m/s at an angle of ja0s,r ikn x+yp 5l(0o$33^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 37.1 m/s at an +zbljs yplc*60uof53e k jl -0angle of $14.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vq1uowt(nc -2l1w6 18,tkdyvu1 tot 4yso .xsdelocity of 22.5 m/s at an angle of $28.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired sny j 5+n6vx5ucy g(mv-1nhj 0at 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 ad,4kt3g hjx 5 c rk2eba3hj0ae0.nk /vt 18.6 $m/s$ from the roof of a building 56.7 $m$ 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 f v)nt*7+ rxvmlevel with an initial speed of 61.2 m/s at an anmvn + rfxv*7t)gle of $47.9^{\circ}$ 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), y8ac1qgg9la+f ou 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 had a constant headwind which slows your speed by 2.0 m/s, the time it would take q+8 1gcla gfa9you to finish would be

  A plane has an air speed of 200 m/s due North, acua -n8ckhbe mo e/5(8nd is in a wind of 50.0 m/s to the West. The pl hoe(5nuk ac/bmc-8e8 ane's speed relative to the ground is

  A plane is flying due Sout8fwo km;jxci5z+m376td a va7 h ($270^{\circ}$) 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 h-ygx rp7g04qbeaded $30.0^{\circ}$ 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 hoe a9)2scb*u,prs7o furizontally fires a projectile with speed 50.0 m/s in a forward dirbuo*9u2efs), ca7 ps rection $30.0^{\circ}$ 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 waovig9 :cu;o- iter is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What io:;c iov gui-9s the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 9 m/s in still water wishes g5 ogvwd 20h k*b5x0ejto travel directly ac wbg05d2xj0h5o e*gvkross a river 0.5 km wide in which the current flows at 5.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s ib xeak;4q54qn ).txaj.bp/ hg n still water wishes to travel directly across a narrow strait in which the current fl4j/g 4ahq.xb b5a;)pxnk tq.eows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches th0g 41 3ikdsbzz/1zriv/l4h,ef(pnn bd /j tx 5e opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wa/dnb 1e1vt3z5,fslihix4z0 r/d nj pgk(z 4b/ter?

  A swimmer heading directly acros tso.a5it h;2os a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the spohttis52a .;oeed of the current?

  A boat, whose speed in still water is 1.66 m/s, must aim upstream at an anglybc2-4x : 7*egdjbv.(gxq k xbe of e (cbd* : kgx4vj yb-b2q.gx7x$29.8^{\circ}$ (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)  $m/s$