Which one of the following is an example of a 5xk-;za 0vmwzkrb 1+l vector quantity?

  Which of the following operations will not change a vectohi tu9b2l c0.(v1wo vjr?

  Which of the following is an accurate statcw bful0x f70a. +bnlt1ia w 19g;j;ntement?

  The resultant of two vectors is the smallest wheexwrvg9 , -yq8p2 upo7n the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respec ),rw54v:mo axmahel1 2dhvyapd 085dtively. When these two vectors are added, the magnitude xdm 0l, h5e)d5paa:vm4w2havd8 roy1 of the sum

  Two vectors, of magnit/3swp,l1bh sn)pgzb9 udes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of thes)bg3hp/sp zlw n,b19 resultant?

  Three forces, each havinj fvnd/b d/)9jg a magnitude of 30 N, pull on an object in directions that a d/n bj/9d)vjfre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vect*ttzysbs-+st )4r: onor is

  Ignoring air resistance, the horizontal component of 7.c8j+1 b)gokgtn(:jgga2palfod h4 a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at zkrshng1el)odeb+g8d :.o fu14;ga) 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 resistaw.9 2nefc20unk2ybj mng1a1fnce, the horizontal component of a projectile's accelerationm2 anf9kngjy1e2f10cwu.n b2

  A soccer ball is kicked withu s;ps4a*rae9 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.w7ruk :t /zew directed anti-parallel to the velocity vekw.7:urew/tz ctor,

  If the acceleration of an obje6+jx9e .2;liuwzb vso 5;uv dhct is always directed perpendicular to its velocityvdi; wsl.z 2+96uvbh5eujxo ;,

  At what angle should a water-gun be aimed i3zb 7 v*mxk7cek,luhb19y)jwn order for the water to land with the great9b,*b) v zx3e khl7jyu7mkwc 1est horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizo6-b64sqn6f2ylies6pkbj. yn 8eoqp ; ntal, each with the p8nno;6 yl6-k .2qis be4jeqsfpby 66same 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-y wrdv:zehf lj(b:dx5x / gi7g**ln4 time. If the ball leaves your hand with twice the velocity it had on your first vxbx jl:w dyfgez gh(n74-lr:/d*i5 *throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an originahw2* i: n9 ,qhb(jhhgkl 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, how does2 ko0-v 1bmhbx its speed 0 2k mx1-hbobvcompare to its initial speed?

  A stone is thrown horizontn./euss5f5c mally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling fas/scf5 s.5eunmter when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a ;ak( wgvogv/ ;gvf/8a second bullet is dropped from the same height. Ignore air r/gg kf ;o;/avwvg av8(esistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a s9 - jp1qjaqzb1d/: pvc hq)sx/peed of 47.3 m/s and at an elevation of 270 m dr9pq/jcv qjpa bzdh/s-)1qx :1ops a package. 6.8 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 s et.vmt gv,;5+wsopc+econd later a second package is droppe .5s+vpoe t gtcwm,v;+d. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speej bhv nj +qa3 db.+j:e,gz3,zad. Neglecting air resistance, when the bomb hits the :v z, abaj3,bz+nqjdj he g+3.ground the horizontal location of the plane will

  The acceleration of gravity on the Mo4 07za rs0cxxu1ay lp8on 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 Earth, t4xpusa a r1c7 80z0yxlhe ball would land

  You are traveling at 55 mi/h in the +x axis relative tocz m42mfcd q: p)3 mx;ccw0kr/* yu8vi a straight, level road and pass a car traveling at 45cw kc ;:mi u*p) dy/qrm4vc2x0f3m8zc mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flowia 8oyyno5bo j(qx o0h/il /1(s 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 startij8bx yn 5/hoa iloyo0(qi(o/1ng point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will it ta2f yrx3 52ca:0y,hvnnr dor y;ke you to move 12 km downstream, iyxcd v:yron ahyn;05 rr f,223n a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30di c.v)g c 4dz4q5odf. degrees below the +x axis. The y componefc cdg4 d45.do. ziq)vnt of A is

  If a ball is thrown with a velocikxr*-g0q v nbj:ze/v.cod1j4ty of 25 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 in a straight line in abd),u w2wjgf) direction north of east and you end up 2.0 km north and several kilometjwb,w2)guf) ders east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x coxuy/hp(2m67fxezb, n 5re- y46wdojn kxe + j)mponent of its velocity is 8.00 m/s. The angle betwen-ero6 jjxe2y75e4 x zwy/n6x+kh )u,dp f mb(en 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. hwall7o 0bgqin6(z5e32tl1 qAt what angle is the Sun elevated above th5 qg6z 1oi0wbaqe37lnlt2 hl (e horizon?

  Two vectors A and B have components (0, +o,g ad1bsg ( qfgb+kvi 2l1g9st71ph1) and (-1, 3), respectively. What are the components of the sum of these two vectohbk1i+gf g7gv bgqo+slt1a(1p, s9 d2 rs?

  Two vectors A and B have compone*s41up4fp5 l .jsh(k8b uqgbi + ztp7bnts (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vecto b*t8 lhppb. 74fss 5qkpu+g1(bui4jzrs?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is th; qf-m icub*.u ir5tkxmw i8t668xc )de magnitude of C ?6b8cfm-u.t q;mkir 5c)u6dt*i 8i xwx

  A car travels 20 km West, then 20 km South. What is the magnspz-lklp0v n5v,y-9 ije9/ yj itude of its displacementn9p, e0l/y95kjv ylv- -jz ips?

  Three vectors, expressed in Cartesian coordinates, ax:c3d2wn6qa*3b vtcuz0)div lehl 5/re
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 coordinate: w 9q7v/kytt8fd: 8b4 zszsgcs, 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 qqews2c3:7rpg iygvu7d 9tiud4x4(;magnitude of vector C = A - B yqvdr7gsupq 7u t4x;w34ic2(dgi e:9 ?

  A runner runs halfway aroundl*q(l 2gzkutn 30hvpw+2ka0 f a circular path of radius 10 m. What is the displacement of the jogge0lq22p *t3wag h fz+uk(0vnk lr?

  Two forces are acting on an object as r6m6/uif+ zy)lm vh8rshown in Fig. below. What is the magnitude of t /lui6)z8y+hm mrf6vrhe resultant force?

  Two forces are acting on an object as shown in Fig. below. What is the dirr0k i3 2jzf9jbection of the resultant for90frjb3i2 zj kce?

  Vector A is 3.6 cm long and prafxf kj**+r;oints along the positive x axis. Vector B is 8.1 cm long anfr;jr* *afkx+d points at $+58^{\circ}$ 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 53 cm long jmt2i,ir 8u obdla j 65c2n7s7and points at $30^{\circ}$ above the positive x axis. Vector B is 26 cm long
and points along the negative x axis. Vector C is 24 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 with9hot6f/aw3y,q(b6*op jzmfy an initial speed of 24 m/s from the edge of a cliff. A stop watch meas/69yfjtqhob(yw,f *oz3p a 6mures the stone's trajectory time from the top of the cliff to the bottom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with aa,xmm0 3vv7lj tz-5i xo r(je1 velocity of 12 m/s, from a bridge. It falls 28 m to the water belowvjx(a7l1t3 r ox50ziv -,mmje. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 24 m above 4wg2 /voy5go,,a/ i w /hciigfthe ground, strikes the ground after travelinwg a5gwc/ i2f/h,/4 o ovgi,yig horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes int+0lsyjv-z mg8 o the jump with a speed of 12 m/s at an angle gl8s+- 0zvym jof $20^{\circ}$ 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 0xbcyo(nma*,0v5 eq cof 12 m/s at an angle o(ym5ocn0 qv,c bax* e0f $39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 59.0 m/kwo8 9ks8)u cms at an angle of $29.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initia 1kfku0/a0cptl velocity of 37.4 m/s at an angle of $18.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at ar2d.mm , tydp xhnlaf1v* d4-*n 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 horizonta lopdy (.p*x9xlly at 16.7 $m/s$ from the roof of a building 68.2 $m$ 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 sks7qw xl0:h +r s7dd3npeed of 47.3 m/s at an angle of rxhk w 7sd3n:0s7 ql+d$38.7^{\circ}$ 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 h65 03m f+o2qxe y.s lt1yki1w gq:ucym/s. If you ran the same race on a day when you had a constant headwind which s1ueghyy 3w+:yf21l0t6.s ko qq5 c ximlows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air spee fz2j(5s9ln cv p(7lckm:w8pc d of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the grv 9c( fzclj5(p mlks78w:2p cnound is

  A plane is flying due Sf9gn-aux s6,oy.u z8 gouth ($270^{\circ}$) 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 12+ .c8zfzap 6dy0 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 projectile with speed 50.6az/fh5cz:i e0 m/s in a forward directz /z5c ef6hi:aion $30.0^{\circ}$ 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 dirk +83l;m9sv1p fhtj/ kun4ehqected across a river with a current of 6.0 m/s. What is the speed of the boat as it crj +4 uhpvkn/3helm98 tf ;1skqosses the river?

  The driver of a motorboat that can move at 15 m/s in still water wishes to td u5wehv/ngz(h3 *hvge 83 2vkravel directly across a river 0.9 km3nwg kh5v3ehvu/dzh(*8 gv2e wide in which the current flows at 7.4 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 wishes toi2x ko;qkb;r0 travel directly acroi;r2xbo 0q kk;ss a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 2 *q:sv:wyx ue900 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stillu9v xsyq:w*e: water?

  A swimmer heading directly across a river 200 m wide reacra mtxnn8oz-jnni ,foi-w9n/;2 .a3v hes the opposite bank in 6 min 40 s r,n mi.-xz jn9tav;oa fn 82wn-i/on3. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.36 m/s, must aim upstream at ey fo , ikjehg6ax7y61u+7s9p s1cj(mk) *ogfan angle of )xm f67k( 1ggcioh7j+fy6 a*1oe, 9y sjpu esk$21.5^{\circ}$ (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)  $m/s$