Which one of the following is an example of a vector quanti3/i-er-tst e ity?

  Which of the followingjyj jlrxm :/(ub9; 1sp operations will not change a vector?

  Which of the following isj , e+sku t4t zc):d8ne,oyp(s an accurate statement?

  The resultant of two vectors t pvo0:jtz5f6is the smallest when the angle between them is

  Two displacement vectors hav*:hq n1cd5wuu;v7by u3d xe:z e magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the ;q5dn d uz:v cu*b1ux:w7h3eysum

  Two vectors, of magnitudes 20 and 50,,64jaibxw muad gyg0n- 6j) ,h are added. Which one of the following is a possible answer for the magnitu,)ud4wn g -6 b06ia hxj,majgyde of the resultant?

  Three forces, each having a magnitud:cxg7 k.0 3 rklv+dr *bq:/ ,opgpmulz0yr:h ve of 30 N, pull on an object in directions that a.qy:h*xk3vulp7/prd 0cblo0gk r+ mv g,::z rre $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the22m+ vip z1r kxtjo1m0 unknown vector is

  Ignoring air resistance, the horizontal component of miv6u 0byi,9 7se7hl/img /qja projectile's velocity

  A ball is thrown with a velocity of 2:sw e0+8pcxm,sw5io pk (r+g 2tlx2ww0 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 horizontahasbjteo;e z h(3 a/4rfy. l1x v3+j2kl component of a projectile's accelerationeaka;13/ j(+ys2j3v.xhl4e frz bo ht

  A soccer ball is kickehm4zr0xbj,b 9n1e / 7pdhd.aed with 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 directe d1v;mx;8hspl 7 lt2ntd anti-parallel to the velocitmvh 8l sl1t2;xn7tdp;y vector,

  If the acceleration of an object i oegv .kn:boq1b. a+y5s always directed perpendicular to its velocity,.+vbobeqon1 g:yk a5.

  At what angle should a water-gun be aimed in order for the watu9yh(y) /ozy ger to land with the greateygh/( oyyu z)9st horizontal range?

  An Olympic athlete throws a javelin at four different angle7 bw1g,ohxj isfl 3:v8s above the horizontal, each :,ofv1ix lg 38hj 7bswwith 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 ball0 e:dc:ta(b al for the second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve)elb:0(d:aatc would be

  A ball is thrown at an originspj4r7x*( n btal 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 does i/cnnk0serl 2 +ts speed com snlc/20n k+erpare to its initial speed?

  A stone is thrown horizontally from the top of a tower at thx9wasl+;e syn( 7*rqne same instant a ball is dropped vertically. Which obj s9 7ewns*l;r+xaq(ynect is traveling faster when it hits the level ground below?

  A bullet is fired horizonta mg-a;;sxuj3z lly, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times ofxgz us j;m3;a- fall of the two bullets.

  A plane flying horizontally at a speed of 41.0 m/s and amk.mvhy5g- h.ba tx4 :t an elevation of 168 m drops a package. 4.9 seconds later it drops a second package. How far apart will tmbg.m a x:k5-thhvy4.he two packages land on the ground?

  A package of supplies ig o+riaw7xd,p7 gjc me (1(tv.s dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance bet,7 r iad(j.ocwg+(7p tv xm1egween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a consl ww*jpv5hb:*tant speed. Neglecting air resistance, when the bomb hits the gr*bph wj5v: wl*ound the horizontal location of the plane will

  The acceleration of gravity on theg4/ mto y6h/7:okvy7.wlxvg b Moon 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 wohwymvog 47/l :6kg.7 ob xt/yvuld on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis relative tor , r9vj7c0cva3sq*ds a straight, level road and pass a c*sds q 7rc v0jc,v3ra9ar traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river thak-xn 3fz un2t)t flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach thuf2ntkxn -)z3 e west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in sv *.e9hes o;7hypds,0fewgr 6 till water. How much time will it take you to move 12es*v;fs ge9hdo h6 p,.ew70ry km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an(ve4mjqe 2h2 sq(fkc: angle of 30 degrees below the +x axis. The y component of (s42v(q ehmfk:qc 2je A is

  If a ball is thrown with a velocity of - h, ke2d/mu1ey6z egi25 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 5few l5fx sy eh.1q-/weast and you end up 2.0 km north and several kilometers east. How many degrees north of east 5.flqs1/xfy5-h ewew have you walked?

  A butterfly moves with t4yegnds )v3r2 . nz(7xq1us:0ofm exa speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must bexs s qnz2my(1r7)tg :0.u3 fdnoevxe4

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what an84m.huk+x hkb gle is the Sumxb 48+uh.h kkn elevated above the horizon?

  Two vectors A and B have cnd zqtw,ovh s -3(rzya*gt w51mmr-h9+f+ zt*omponents (0, 1) and (-1, 3), respectively. What are the com*zh1atgvfz-drz-wm h+y t,5*ots+ mwr (q n93ponents of the sum of these two vectors?

  Two vectors A and B have components (0 u 9/;d4-qyw 8muerktc, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vq-cyrudu8;kt/9 ew4 mectors?

  Vector A = (1, 3). Vector B =wn my,7.;jzj1 ih9jfl (3, 0). Vector C = A + B . What is the magnitude of lnj y,1;.fmjzw9i j7h C ?

  A car travels 20 km West, then 20 km South. What is the magnitudfev/lb ok 895oe of its displaceko9 olve 5/8fbment?

  Three vectors, expresse.aiqpbjwpi h5- 6m h.7d 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, express crx,2hioz:sbt u 1(y+gr7l4red in Cartesian 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,oju 4aa dhvm,e)tq.6oj/q )i. -8.0), what is the magnitude of vector C =6 )jdqa) .ouqoje m,.a/4h itv A - B ?

  A runner runs halfway around a circular p/2l 8yl: fap9n ayr71vodq-c path of radius 10 m. What is the displacement of the jog7ona1ypvp2 yl ra -:c 9dlf8q/ger?

  Two forces are acting on an object as shsd j-p(tai(i*oqt2 od6t ,q4ro94 kudown in Fig. below. What is the magnitude of the resulqa,*di sdk(4(o4i pod ut92o jqt6tr-tant force?

  Two forces are acting on an object as shown in Fig.upa9jtc 6texyo em.b74u ;76d below. What is the direction oe c.7y6uet atu;dbjx7opm96 4f the resultant force?

  Vector A is 5.3 cm long and pokhek9j2cacr 8n5)dzm )w22d pints along the positive x axis. Vector B is 7.0 cm)8)r cjacp5wn hem2 d2zkkd2 9 long and points at $+31^{\circ}$ 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 52 cm long and polpbmsa( f,f:6 ints at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 21 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 horizon2 5 /o)bxd e bf6z3ud3,wf9vmdf ,jbeep./yehtally with an initial speed of 20 m/s from the edge of a cliff. A stop watch measur eeo, vef3yx f)293h5,bdb /fdjw.6ub/epz d mes the stone's trajectory time from the top of the cliff to the bottom to be 3.5 s. What is the height of the cliff?

  A girl throws a rock (-/qeu6ukj ds yf 60dmhorizontally, with a velocity of 15 m/s, from a bridge. It falls 12 m to the water below. How far does the rock travel horizontally before striking theuku 6 6/q(0ymjd-sdfe water?

  A ball thrown horizontally from a fk2a;w oocc1if.r g;e,vwi 9 -point 30 m above the ground, strikes the ground after traveling horizorwf. oe;oc2f k;v9 1,i-giawc ntally a distance of 20 m. With what speed was it thrown?

  A jumper in the long-jump goes into the rttt 9aqc g* 8 4v4lnbv-;gpv2jump with a speed of 12 m/s at an angle cgbn4pvvq 4 ;atg8 tl-t2rv* 9of $20^{\circ}$ 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 jm 5tj4,m -j/ *ejvld(9un hze xc,x.ghump with a speed of 15 m/s at an angle /*x.gj,x mjl(e5t9,nj4-e hcvu dhmzof $22^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial vg9d m v iv1 /f*kgv ;9y;vrdr:rtg;qx9elocity of 43.0 m/s at an angle of $42.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an injpy7j4 :m v)w25*zqd amav ec8itial velocity of 24.9 m/s at an angle of $37.0^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired auszt 4lcoxw w p4s:/t)rc:) t9t 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 aep-8b h3./a4vux flrh t 18.7 $m/s$ from the roof of a building 64.5 $m$ 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 firedm pqg2zk/)4y g 7mg5ug from ground level with an initial speed of 45.8 m/s at an ang72gu qkg/zmgy) g4p 5mle of $46.5^{\circ}$ 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 wr.l;g gt9r*9q zox7zbv *,k,ft1us,rs iwv/ 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 7wg9k*f*x ,i vqt 9rb rz1svzs.wt/r u;,g,ol would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a wvw/7c 5 i9dzuvind of 50.0 m/s to the West. The plane's speed relative to thc79u vvw5i/ dze ground is

  A plane is flying due Sout bf3 tv 6-e.da+es/twwh ($270^{\circ}$) 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 msva/1w jzx38er9qk :120 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 7l b7f;e ai+fnprojectile with speed 50.0 m/s in a forwal;ib a 7nff+7erd 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/s,ff1:jy qgag, .f6g2 2np ms/se is directed across a river with a currents:n.fy, 12/ 2efqjga 6sgfm gp of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 *g/ c8oxyzrf /8y haw+eq-+hzm/s in still water wishes to travel directly acrosx -r8+c+z z/f/*yhey ahwogq8 s a river 0.9 km wide in which the current flows at 6.5 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 wisxpo4zfwx z32nu0my, imv .z*vv7;z, jhes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head ,yi3zxv2, u zvpnv 4jmoz7f zx0 .*mw;the boat?

  A swimmer heading directly acrdjcjl07r4u3w8zr0b poss a river 200 m wide reaches the opposite bank i0z7 0l8c rdj3pbr ujw4n 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches thehen; zi/u n c5vwb1*;l opposite bank in 6 min 40 s. She is swept downstream 480 ni 5nbzwu vle1;*ch;/ m. What is the speed of the current?

  A boat, whose speed in still water is 2.00 m/s, must aim upstream at an anglfem:ej9x1t41p eld m 8l2u2hwe of j9eep1l8e hud2w t fmx:1lm42$19.6^{\circ}$ (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)  $m/s$