Which one of the following is an example of a vecz+ dtnpcuxo 2 ,5g6w-.xx+b wator quantity?

  Which of the following operationspd1 yh u2picgbu6f5e):40mvvv*zkt 5 will not change a vector?

  Which of the following is an accurate statementb9vws3oe.y sp -71wrslg-y*s ?

  The resultant of two vectors / :*nspz li )uf((wxwsis the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 mf51+h u;nn wxo 1hln-w and 7.0 m, respectively. When these tl-nn115ox w +u;fnhh wwo vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followinnj /h;jq1d4r0jvq xkra q jjon89ua3x9+gw3 +g is a possiblkno9n w ;+jj qxxq3r03adj h agvu49j+/1j r8qe answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on4hj39c;jto 4vf abv s997xyym an object in directions thmo xy4jav9b9 hc9sy7t v3;fj 4at are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unkn,/kfx7g u,, ka5uwp2yh/x .v:w s1 n; bxotsgyown vector is

  Ignoring air resistance, th r czmj7z)d9g1z6eizg*x;)i,z3 wx ,a5ipfgme horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s9 or-c;27)hz:qf v *tw +mgw,dvpqmoj 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 cow/ 1mpw02l kcgmponent of a projectile's accelerationw2wg p/1lmkc0

  A soccer ball is kicked with a velocity of 25 m/f2-o am*amdanl j+;b,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 ve gs3mji0wzh, q(p( 5- cax9uzplocit(zq(p0 ,i9xgmc u js5 hpa3wz-y vector,

  If the acceleration of an object isdawkms j).+s q,:5h cu always directed perpendicular to its velocit: a msuschjk), q+.w5dy,

  At what angle should a warg6f dxb/ac f1yd-6 y*ter-gun be aimed in order for the water to land with the greatest horyd 6cf-d*1 rxb6g/afyizontal range?

  An Olympic athlete throws a javelin at four different angle40 zlv0;zz zu 16xdjkqs above the horizontal, each with the same speedz106q xkd0zvzj4l ;zu: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the s,fxqq++jzv58g i.r gm m3-arkecond time. If the ball leaves your hand with twice the velocity it had on your first throw, its horiz5 vjrg mik.+q m8r-g+x3,qazf ontal range R (compared to your first serve) would be

  A ball is thrown at an original speed ofeo4xtnseb42vj 59m9a 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 attemydx,o g20fq ,tm2ew7rpt reaches its maximum height, how does its speed t 7fmy0,xq2,weod2gr compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same i1 ix;g.ivzf rm1 ohn3)nstant a ball is dropi1 xgz31. rivonhm)f ;ped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizl,6 mhdj4t*gzontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the tw 6z,g*h dmjlt4o bullets.

  A plane flying horizontally at a speedh)8ikbrv (kbm+4vhw0zu.rj- of 106.6 m/s and at an elevation of 167 m drops a package. ijhu.) rh( rmwz k-4+0vv8kbb5.2 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped,lqtxga w1c zt :u-;+2szifj / from a plane, and one second later a second package i2:xw ztjt;1cs-g+ulz ,qfa i/s dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontallh nu696nnoh+y0rezrz0yq ai9k7j; 2 ky at a constant speed. Neglecting air resistance, when the bomb hits the gr;6h09z n ura0 zi2qeky nhny k69+jo7round the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-six6nr //uv3yippw p bp(y/j.n l.th 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, the ball w/i.3ju/vn/l yppbyp (w.pr6n ould land

  You are traveling at 55 mp ndd3q.k.0 .x(azqdz*u+p2or6cq rq i/h in the +x axis relative to a straight, level road and pass +pd dnq0zq up.*o.6cz.qr 2 (a3drkxqa car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that fl3e 2wpc1swrhev1 5er 4:tixb0- kvq6 kows 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 pointkerwev5i ek24t 0 -: h1rx6psvc3wqb1. You should head your motorboat

  Your motorboat can move at 30 km/h in still water o;ki;/nd-8ubu m(pgf . How much time will it take you to move 12 km downstream, in a river flowing at 6.0 ku; ;-mu dop/gbi(8nkfm/h?

  Vector A has magnitude 8.0 m at an angle of 30 degreeya+.n hxf s3l4s below the +x axis. The y component of lx3h4+sn. yfa A is

  If a ball is thrown with -3o kf/ fojod9*qw;kgrg+a7v 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 direct5ielj s/0ov+ oion north of east and you end up 2.0 km north and several kilometers east. How many degrees north v0+eooi jl/s5of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocidqhygj1 d( t(q*,p)djty is 8.00 m/s. The angle between the direction of its motio*(q1 d dhgpjq(j d,)ytn and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a leveep2ft 8yd8ku *l ground. At what angle is the Sun elevated above the horizonk82p *du8 yeft?

  Two vectors A and B have components (0, 1) and (-5a7qk5gkx,;u) vyg us 1, 3), respectively. What are5 5kag vxgyqu;sk 7,)u the components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and .n 5pc iz8*:ddryw)tf(-1, 3), respectively. What is magnitudi*ftn rc:8p 5d)z y.wde of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is thg;q*1jo8v( ro d+k qpze magnitude o; jkp8qoqod(zr1*g v+f C ?

  A car travels 20 km West, then 20 kme1yzfv zx jlw/*t6 o5*wwkz-/ South. What is the magnitude of its displacemow61/**z/e5z v -yzxjwwftk l ent?

  Three vectors, expresse i9s hje,rh12a ;9xyh7dh*w5 vrj,dyed 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 Carteoj lesw7jetzu)+ h7h kot4;.7a6f 6eesian coordinates, 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), wha it 0 iwbt g,rfbg2gxj.sf+0:;t is the magnitude of vecxijffi+2: b,r0 bgg wgt; s0.ttor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. yt:pk -wjyh cq* 97a0a What is the displacement j-yp wkty: c09ah*qa 7of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is v o+s2lx3 9 13yxakjffthe magnitude ox lkj3f2xyvo9f+ 31 asf the resultant force?

  Two forces are acting on an oa.fx ;(cyi +d3xhi o0rbject as shown in Fig. below. What is the direction of the resulta.0;rya+ if(xxh 3oidc nt force?

  Vector A is 5.9 cm long and poikc 9g kv9:zib3nts along the positive x axis. Vector B is 8.6 cm long and poin3vi 9k: 9bckgzts at $+29^{\circ}$ 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 67 cm lonhp 3w +8faoxp8g 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 43 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 of 16 m/s n r /l*cbia;hnff:xy)f,*)c i from the edge of a cliff. A stop watch measures the stone's trajectory:,i/fb ;*achf lrnc)fnxy*) i time from the top of the cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 6 m/s,bl* c dk-5zt,c 2rh5kp from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally before stri5 *dcp hztlr 5,2-cbkkking the water?

  A ball thrown horizontally from a point 25 m above the ground, st/i x m+49egdbgrikes the ground after traveling horizonm/4bx dgige+ 9tally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into thqgmi eu8:u14 suri8n7 e jump with a speed of 12 m/s at an angle ofi88gqiure71m n4s :uu $20^{\circ}$ 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 of 13 m/06d gkw9 tejb0xern (0s at an angle of dtk wr(0exbe0g69nj 0$39^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 2 w0d/7kcb-xuj8*bom c/7 hjnn6.9 m/s at an angle of $39.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vz 85+/8qp sf xmx sx1,wotd)pvelocity of 39.3 m/s at an angle of $11.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angltuham / )*6/kjj:yxdwe 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 at konj( j 03)igfcml:ukf:p9/o27.1 $m/s$ from the roof of a building 48.2 $m$ 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 withngw,i6)-dw 9mmy;n o g an initial speed of 47.9 m/s at an ang-md6y;g gi onn) ,mw9wle of $43.8^{\circ}$ 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 1500-m race at a vaz70ah vh+ :vih/p,od2alwcq 0/qiz/elocity 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, thp:vz+/io2q /c0wd lvh/7h0qiza haa, e 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 g b aq)rb4n:c/k 4o2 .mj5dbt v;ks+okof 50.0 m/s to the West. k4b5.ktdnabj2m;q:os+k bog 4v) r/ c The plane's speed relative to the ground is

  A plane is flying due South p k+j.ul46pcc ($270^{\circ}$) 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 gern8 7q5om;readed $30.0^{\circ}$ 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 wit dy.bu+p :vlj*at- vx8bqi0 4wh speed 50.0 m/s in a forward direction:w+b*d yul qt04bv xi-j.a p8v $30.0^{\circ}$ 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 directehxb1f p ideu1oh.4* pg/2,axzd across a river with a current of 6.0 m/s. Wxh2 pz,ogd 1/1e*i pfh.au4 xbhat 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 trme1xcj:* -iv 3a 9lpoo travel directly across rcmj19 *xo pev3:a li-a river 0.8 km wide in which the current flows at 7.2 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 to vzw( g3g/u4 ubtravel directly across a narrow strait in which the current flows at 5.0 m/s. At whatv3uwzg(b g/4 u angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the o2k.6cpluovi 7* 11h zdd2v yatpposite bank in 6 min 40 s. She is swept downstream dh6y*.tpdkvc1 22ai uo71 zlv480 m. How fast can she swim in still water?

  A swimmer heading directly acro )+ mhs+b(.ioult ah5oss a river 200 m wide reaches the opposite bank in 6 mit5(sli u.hmo)+hboa+ n 40 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 2.14 m/sl:*9y9x0sxegn +i u hh, must aim upstream at an angle of +hn 9glxi9xuh:s* 0 ye$13.3^{\circ}$ (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)  $m/s$