Which one of the follouh/ wz 2tss+ t;sch)u0wing is an example of a vector quantity?

  Which of the followingmr70ji qgfs*3 8fz1ua operations will not change a vector?

  Which of the following is an accldhostn b4 ps(+7v0.* ku gvs/urate statement?

  The resultant of twotf*mjl62; u;rgm-6qksjn ;fa vectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectiver+ vn12 12j(q.yghso75/e qa whn pxfjly. When thew2yjx/qrnhv qpf5a( 2e1sno j17g +. hse two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followibl o8byw: :bq nm9op;2c(xt6psr5 / wing is a possible answer fo w( b;:m opx:8o9bptrly65q sbn/2wicr the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in bdgz720it 9y;aop -o cdirections thotzp7i-d0go2a;bc 9 yat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, tlgpsu md f;v/ .1tzk-,he unknown vector is

  Ignoring air resistance, the horizontal component of nw 6gy- kp/dz,eg*n 7oa projectile's velocity

  A ball is thrown with a velocity of 20 m/s at anb/ mav1o)ko*13yh;6cv cbpmj 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 q i,3f w4aaa33wvlz 4vhorizontal component of a projectile's accelerationi 44lvavz3aq3w,3awf

  A soccer ball is kicked with a velocity of 25o()ru1 cu-m 0+klfm+up o(v(1 gegxvp 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-parallel to the velocitm oaan m:w)3xb .ug2:ry vectxn.)mg:w am: baur o23or,

  If the acceleration of an ob*km2f3ocn+ tgject is always directed perpendicular to its velocityc3n+ kft2mg o*,

  At what angle should a d (h+hc2p/5kxy+r j srwater-gun be aimed in order for the water to land with the greatest h(rjd 5+p2hr+ / hskxycorizontal range?

  An Olympic athlete throws a javelin 6wum4 n.pd1: nu87nt4(xhhw f fs6bkcat four different angles above the horizontal, easdb 7hnn 4c6tn u fp61kwm fw(u:h84x.ch with 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 pofg61w9cn.clgwq 8tfl + o7 g z:h9-tfor the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (comparedcqg-o zfcno 99 tll: 78wgw6.1g+p thf to your first serve) would be

  A ball is thrown at an original speed of w1gc 13) tahur8.0 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 reaaw z 2ivqd(:u4rel5j1ches its maximum height, how does its speed comparejd 5(1zru: wae vql4i2 to its initial speed?

  A stone is thrown horizontal k d wwz-h0n)63ezxshk2zs87 ily from the top of a tower at the same instant a ball -6n)xds73wz2hh ez8 iwskz0kis dropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same iz1n,,r:vr tdfv ka u-4nstant a second bullet is dropped from the same height. Ignore ,zt u1,k:rv nf4vra-dair resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 63.6 m/s and at an elev/*x r8ika- pd ah)j5+jb5aluzation of 247 m drops a package. 3.8 seconds later it drops a second package. How far apart will the two8d ai*ab5kpa r j-u5+xl h)jz/ packages land on the ground?

  A package of supplies is drw4b4d-.d sargopped from a plane, and one second later a second package is dropped. Neglecting airdsd- brwag.4 4 resistance, the distance between the falling packages will

  A pilot drops a bomb from a plan8g + )etaxog7 ahng(w8e flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the pl(agx8 n7geg ho)+at w8ane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earthve */vrio4y(87v, xw w 2hquh,d/coaj . If you hit a baseball on the Moon with q,x/,wvu*e chyha4vo/owrj 7vd(i2 8 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 +.-bd bsvhn47v x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to 47n.vhd-bvbs the other car is

  You are trying to cross a river that flow4 jvln k6j)ev8s due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west nj8)lv 4v 6kejfrom your starting point. You should head your motorboat

  Your motorboat can move at 30 km/hws ) vay)kbtag 48(4cc in still water. How much time will it take you to move 12 km downstream, in a river flowa)k vg4ccws8a(y4 ) tbing at 6.0 km/h?

  Vector A has magnitude 8.0 m at a66, s(3x* axkb brufken angle of 30 degrees below the +x axis. The y compone(ab* br3k6k es,x ux6fnt of A is

  If a ball is thrown wi77 2ut-qb(i gdx0kwf0r (erdxth a velocity 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 a direction north of east and t 2uk09tq6ig0fc j gx5you end up 2.0 km north and several kilometers east. How many degrees north of east have you watiqfx6jk u50 g9g20ct lked?

  A butterfly moves with a v 2wn,vg 8)vzv ymysj71o*e ,hlo yc6-speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle j27 )vw1 v*oy oyglsy6h ,, zen8v-cmvbetween the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shah f/+ se-bto.vdow over a level ground. At what angle is the Su bv.s te+-hf/on elevated above the horizon?

  Two vectors A and B have components (0, 1 e4eibn38 apmmh9g 5n1) and (-1, 3), respectively. What are the componee3e nb 4hm1mg89nai 5pnts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and mw d5,earsr7)(-1, 3), respectively. What is wr5dmsae7,)r magnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). b4gz4fqdl*k* 8r mce4 Vector C = A + B . What is the magnitude 4eg*8kf*4 mlqrd4bzcof C ?

  A car travels 20 km West, then 20 km South. What is th yhj1(by ntq4mi8)b(wog)d +n e magnitude of its displacedmnbg(o8b) (nj1)it+wyyh q4 ment?

  Three vectors, expressed in Cartesian coordiq)vt9 /ohxel9 o8/icxajs-kv(8q -d vnates, 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, a 29 py a6kvvg(rp)xifo/(ewnwg75k 9mre
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 t*e2jjug;z o/sxd 85rthe magnitude of vector C = A - B/j5xju*d2z;sr oeg t 8 ?

  A runner runs halfway around a circulargd )+ x )t-u*o9bn)j2wkac8 tz,ob cfo path of radius 10 m. What is the displacemko2*8b oc9 )ab+gz )ft)uw,noc-txj dent of the jogger?

  Two forces are acting on an object as shown in Fig. below3ee lcvf ) ;8gqab/ gtu*(9on3sxtpl(. What is the magnitude of the resultb)e/ctqau9ogf ;lxe(n3p* tsl v 83g(ant force?

  Two forces are acting on an object as shown in Fig. below. What is the directi b0b4 h:z(m8i6(/qjcwhoydfd on of the resultant/hhf (dyw(d 8b 6izj0m4:bco q force?

  Vector A is 4.5 cm long x/m8r. : pqbmfand points along the positive x axis. Vector B is 5.7 cm long and.qmf xr8mb/: p points at $+47^{\circ}$ 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 72 cm long an7qellku+ ,vs3xw(+m y d points at $30^{\circ}$ above the positive x axis. Vector B is 17 cm long
and points along the negative x axis. Vector C is 47 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 ofr41:r .2y xph i0y*lwbrqmvq) 29 m/s from the edge of a cliff. A stop watch measures the stone's traj) 1:p *xh qrry.0q2vr4bwlmiyectory time from the top of the cliff to the bottom to be 3.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 11 mmk8xmmd 5b5+0 x4gs9x+uwyl l /s, from a bridge. It falls 29 m to the water bel x9wllu+5m4xkbd m gy0+mxs85ow. How far does the rock travel horizontally before striking the water?

  A ball thrown horizonryzj.) 2r :*cpjliq8v.hcg 9 ctally from a point 27 m above the ground, strikes the ground after traveling horizontally a distance of 17 m. With what speed was it thr.* zirrcq:gh j8l)2.9py j ccvown?

  A jumper in the long-jump goes im+srv6o3tg*8-u a uxjnto the jump with a speed of 12 m/s at an angle of -aguj38 *r oxm6utsv+$20^{\circ}$ 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 *vl;0vi -qgdgc :oq3h a speed of 11 m/s at an angle g cv qg qhl*d;:v0io3-of $27^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with anpaz ywuv,9d i3x v5t4myxk1jlf;1v0 ; initial velocity of 44.4 m/s at an angle of $14.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of *yyi:k,pdkp 3 25.3 m/s at an angle of $14.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofssdzg- -s nq pz7,3rh1wy1 2vs $30^{\circ}$ 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 o0;x 3/t+xpg8z/c e bvdksg 0g 26.5 $m/s$ from the roof of a building 41.2 $m$ 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 speed of 48.0 m/s at an i,k)k im6h c/1rddcu 5angle ofd5h6ui/ ck 1m) id,rck $42.6^{\circ}$ 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 velocbaq p. +dn3o q/;ys7wm61t8tow ep8 ldity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind whichp7/+q8bd yoe;3aq m w.n8dst ow lpt16 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 North, and is in a wind of 50bjy.m. ix.nx52/ud uf .0 m/s to the West. Thed 2 bnxmuix.f uy..5j/ plane's speed relative to the ground is

  A plane is flying du vmaf5*jb--/) fqh:mg dfzt*n p5hx ,le 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 speed of 120 km/h is headelfb urq ohy 98*na)2(naoek 0y5a:as3d $30.0^{\circ}$ 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 wv :b3 --f+7y pqbety4tcxi/hdith speed 50.0 mh +-q d v/tb-3t7yfxe ib:cyp4/s in a forward 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 :am/hq(qpf yijel13mmn,6sf 44r5z g d5q (tnwater is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the b6h4fqp,fr n:lzg ej y35is(tq/4n mm5dam(q1oat as it crosses the river?

  The driver of a motorboat that can j soiday b5)eo-s c9--move at 14 m/s in still water wishes to travel directly across a river 0.6 km wide in which the current flows at 5.6 m- yoe )i5 bsja-d-soc9/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 to 1a u2vhfinuc3 t;,ph 0travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle u puf1u2vhh3t i;na ,0cpstream should the driver head the boat?

  A swimmer heading directly across )bln). w7zkwkqu-dq/tcx- l cd8t5:a a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. H5bd k l7a d/n-) c:w-kcw.8lqqz)xtutow fast can she swim in still water?

  A swimmer heading direc2u cr +,ke zjn9.wgdrpc43ll+tly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstreaznecpjw udc9 r rgk.4 2+ll+,3m 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.u h:nt k6f-wi+16 m/s, must aim upstream at an angle ofi6 n:fkhu+ t-w $26.8^{\circ}$ (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)  $m/s$