Which one of the following is an example of af)h a,sw4,ieyzqy gi6/6pggi*5q3fe vector quantity?

  Which of the following i6 ab4nyb,c+l4fpwa1whsa,m. c73qg operations will not change a vector?

  Which of the following is ax+ rt,2 be*yh8zka*qg n accurate statement?

  The resultant of two vectors is the smallest when the angle between th;8i-sz ;hytmn*b3 t kl73ikdj em is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, resp)fq snj5/tp h5ectively. When these two vectors are added, the magnitude of the su)ns5jh tq/ f5pm

  Two vectors, of magnitudesccj8j. 9 oz: skm8)zplk;hj.0hj6e ok 20 and 50, are added. Which one of the following is a possible answer fojzk9 c8sk)6jm8.k:;eo . h0lpjoj czhr the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directiq diacsx 75k7zp )l1sk z6y46yq+.gb oons that arek+gsopzx6) qky 1q6. lab5y74i 7szcd $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the ul ygqw6/ ycm-1nknown vector is

  Ignoring air resistance, the horizontal component of a projectile's velo:up nc r(ggt)4 al9tg.city

  A ball is thrown with /brc i83,zxvdnknwej a buo+0i2 4y4,a velocity 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 component e+4xd)mytx,03b+bs bb 3 aesnof a projectile's accelerationdn3 0ets)b+eb+m bb3 4s ax,xy

  A soccer ball is kicked with a velocity of 25 m/s at an anglewvf:eo2xc s29pn5uns( jw (4+eg oh6av,y( gf 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 tncs+c)yr p,3. c0bx yanti-parallel to the velocity vec n x0ycc,)sty+ bp3.crtor,

  If the acceleration of an object is always directed perpendicular to its e a(ao2de11dq0ht tf/velocity, feo1(th2 deaqa0 t/1d

  At what angle should a water-gun be aimed in order for qiq xul6upk j1jp5jpu *h9:,4the water to land with the greatest horizontal rangeup:ph5k1l4uj* q6qp i ,x9juj?

  An Olympic athlete throws a javef i/u z* e7;x:k.wsgcb9r 5gg z rw71pdhtp(z.lin at four different angles above the horizontal, each with the same speed 9thzd .5r/zb p. ew:kx1 gcfgurs7i(gwp;*z7: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 ltwtsa pz z7e1*o);mf( eaves your hand with st a(fe ;t )1wzmpzo*7twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an or8+ k() suhxm0qiku9ai iginal 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 goal attempt reaches its maximum height,spi84d/ .c nnp how does its speed compa.pdi/4n cn8p sre to its initial speed?

  A stone is thrown horizontally from tm4u+k g5oyde *he top of a tower at the same instant a ball is dropped vertically. Which object is traveling fayude+4k mog*5 ster when it hits the level ground below?

  A bullet is fired horizontally, and at the same ind6nk 6usa9*v cstant a second bullet is dropped from the same height. Ignore air resistance. Compare the tiau6k9 n*6 cvsdmes of fall of the two bullets.

  A plane flying horizontally at a speed of 40.0 m/s and at an elevation of 157 m 4utbuut ex5--ff-9 qddrops a packagft9 uq-bft5 eu-ud-4 xe. 6.2 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 secon+ewku*ixt8 0gd package is dropped. Neglecting ag k* +ewi8u0txir resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. Neg3z7fuj:: ec acr/gu:* ; gsmpy5wri *zlecting air resistance, when the bomb hits the ground the35:u/p7sz:iwz u*rggy jc f em: acr;* horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on 6;v,vvpnw eis /cqc33 Earth. If you hit a baseball ovv3/qicv;6 ps,w3c nen the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling atd(+q y,s.mjvu 55 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. Thevq (mjd,. +syu relative velocity of your car to the other car is

  You are trying to cross a river that flows dukf62n x eh01vse 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 point. fs0xkh2 1n v6e You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it take - :sps6cpl qutb 1)/2mpxh0qxyou to move 12 km downstream, in a river flowing am6s/) :xqpcp1h0bqu -x2ts plt 6.0 km/h?

  Vector A has magnitudpiqw4:4blntq/ kflx ,: dbn9f-0,g k ue 8.0 m at an angle of 30 degrees below the +x axis. The y component of 0qw 9,bn:nfg:-pd,t/ lkf xui4k4 bql A is

  If a ball is thrown with a velocity of 25 m/s a3x/vvd( 7oqklp 9zo) ft 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 direction north of east and;jnbwb*b- px + you end up 2.0 km north and several kilomet+ ;b-pw*jbbx ners east. How 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 8r m 3nx-mffo/j -eu1)itkit87.00 m/s. The angle b13)tji kx/7ti nfmr-m uf8eo- etween 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. hk se7lyc ld9w +n**8wt2wl+0 mjq.ju At what angle is the Sun elevated above the hlw9 .+*ymwd*nj s7l 08wkut j+ec2ql horizon?

  Two vectors A and B have components (0, - 6h0s1rqbsnrn)5r s h a7cdreg p;)m81) and (-1, 3), respectively. What are the components of the sum of these two vs1 s sh8ceb7mdnrn6r 5r0g ph a-)r;q)ectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respecur+ xp3 o227xtnke yd;tively. What is magnitude of t2pedk rto2xy3;+u7xn he sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is thbhp8, tm+zb v 93xt(oze magnitude of C ? xtzopvb(+9bt m, 38hz

  A car travels 20 km West, then 20 km South. Whaklq 5kj*g -ruz52tma.kle* x*t is the magnitude of its displacej*qkl tze5xg*k52-* .lk armument?

  Three vectors, expressed in Cartesian coordinate k70b7 j l(;k; 9ogabu)pghhdxs, 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, ig*s4l (sq1- uc( db/e dzgq/pare
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), g :wooc/ues 8(what is the magnitude of vecou ce:og/8sw (tor C = A - B ?

  A runner runs halfway around aw5ponmb 9;4gk circular path of radius 10 m. What is the displacement of gowkn54;pmb9 the jogger?

  Two forces are acting on an object as shown in Fig. below. What/wm 5ks-4hz yz is the magnitude of the resultantz/- m4shz kwy5 force?

  Two forces are acting on an ob;in;bxx36 mha5s,i l nject as shown in Fig. below. What is the directionhl36i i;5xnbs ax ,;nm of the resultant force?

  Vector A is 3.0 cm long and points along the q88jcqin u5. 7qn b.rz25in cdpositive x axis. Vector B is 6.3 cm long and points zbdn8c.q2.jn8q5 n quic i75r at $+21^{\circ}$ 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 77 cm lod72e bi- deiu2ng and points at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 20 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 ykljb1657s 0ojc ujx1with an initial speed of 20 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 bo607b yx5j so1jk lu1cjttom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock b ,.oww/iojn1horizontally, with a velocity of 16 m/s, from a bridge. It falls 15 m to the water below. / o,1. bwinjwo How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the e0 rd9xb8gl dt x2vmn,0l3s;k,k; b upground, strikes the ground after traveling horizontally a distance of 12 m. With what speed was it tblkk tx, vnbx;329;ms0e, d8lgprud0hrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angs lug/7 d)dt)tle of tld)g7t)u /ds$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpo1)wuyk6 jaf2 goes into the jump with a speed of 10 m/s at an angle o1foa6 uk)2jw yf $38^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an dpr u3.5b r 9p cprjqvx0b;pa4*ltj;(initial velocity of 24.8 m/s at an angle of $41.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 22.5 m/s at an a c glbyqde:j)6y,z35ongle of $36.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fir+:kb3(n c9n2tz+pdzz 3h9roms dj 6 ased 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 horizontally zdkjk dye 0-18a9xud 3at 17.4 $m/s$ from the roof of a building 58.0 $m$ 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 speed of 52jsyo /si.bgs f37q yti4786v o.3 m/s at an angle osobys7.s8jvf4 tii7 yq/g63of $37.1^{\circ}$ 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 4.0 m/sh uwj3l6qq6;qfc438 gly*oum . If you ran the same race on a dloc 6qqwu *f3q3 ml6yguh;8j 4ay when you had 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 m/s due N2s-vz21zutxpuyt2;( l ) gsgoorth, and is in a wind of 50.0 m/s to the West. The plane's speed relative to t;u2vg12zl2 x- )tg zo(uss pythe ground is

  A plane is flying due South tp.s4e 0,epcgxhg. 2g g. bi2a($270^{\circ}$) 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 cov (,yv z3l9ixv8n;xeaded $30.0^{\circ}$ 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/sn +(5yhm2ms:d dzka*bnlsu ,7 horizontally fires a projectile with speed 50.0 m/s in a forwazn,hdd ( n *u72slmy:k5 bmsa+rd 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/mv*2q4 ;2jju kxght ;ps, is directed across a river with a current of 6.0 m/s*jgj;xht ;2 m4ku2 qvp. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 20 m/s in still water wishes to tr0s6ev/h6 j2s x m28oakvhp;y20tdi qhavel directly across a river 1is8hx2vto22k 6eqv0 0ma6pd s/;jh yh.2 km wide in which the current flows at 7.0 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 wspwh )f-wy)0bci(l/s ater wishes to travel directly across a narrow strait in which the currenh-y/l0bwss c)if)p (w t flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading direc x,*,e*v dxtcatly across a river 200 m wide reaches the opposite bank in 6 mi*exvt*axc ,, dn 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across akb4pf;a sba4tk*7;m j river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept j;7tpafk*s b4 ak;mb4downstream 480 m. What is the speed of the current?

  A boat, whose speed in still wat2 tgvd x yskxv-;9rm)6er is 0.98 m/s, must aim upstream at an angle of -gxrt)vy9d6x2 s vkm; $20.8^{\circ}$ (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)  $m/s$