Which one of the following is an example of a v 5pc.g(vn0 euoector quantity?

  Which of the following operations wia7 bt dmjaz8:s2zu4 2qll not change a vector?

  Which of the following is an accurag-6 dk gt6ba;eb0 yud:ksh5c,w6 ct0kte statement?

  The resultant of two vectors is the smalleitx5j c5iz*j10zy1q /5.5y cm5pcmybk 5 f gkyst when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. W l5kmr5 (e4mduhen these two vectors are added, the magnitude o 5( ud54ekmlmrf the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the folqo c,1,niy( aslowing is a possible answer for the magnitude of the resu so c,(ni,yqa1ltant?

  Three forces, each having a magnitude of 30 N, pull on an obj*nzk ;z s-/z7ix lq0iiect in directions that arezzilq 7*nk-zxi/0;is $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown,* 8y3ki8axek,zj) j rl the unknown vector is

  Ignoring air resistance, the horizontal component of a projectile's vu2jjt5;pv+ko elocity

  A ball is thrown with a velocity*ilz ; knn u23b71n hojc8g+ci 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 componentz.j9n c2 pb 5c7d(qcqy of a projectile's accelerationcc(q5d .79n pcq j2zyb

  A soccer ball is kicked with a velocity of 25 m/s (4vf pnr;m; 1+rsnaix7 qfw*a 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 vwr :rj:d1 b0kl7:cz zdelocity vector:dlzw 1r70k::jbzcr d ,

  If the acceleration of an object is always directedjc7 /rwj q;*he perpendicular to its velocit 7jwreqc/;*hj y,

  At what angle should a water-gun be aimed in order for the o 3:fb mip;we6water to land with the greatest horizontal ranwib:pe 63f;om ge?

  An Olympic athlete throws a javelinahy1))jlld(-c grs ,/m,blvr at four different angles above the horizontal, each with the same speed rl,-sv ,r1/h(dgj myac) l)bl: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secondmn f uhu7p78nw5/ /mg2gku,eo time. If the ball leaves your hand with twice the velocity it had on n72upw 5g7 muh,e /m/n8guofkyour first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at aor5f7w3 hq6w5aw) i/r yl7;hqkmjq, .*kwa hgn original 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 go v5dwr)di m+3bal attempt reaches its maximum height, how does its speed com53iwdr)dmv+b pare to its initial speed?

  A stone is thrown horizontally from the t-igs 8-v 0,ecgnbcw19 fyshs 4op of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level grou-gh4108-e,bc9 in scwyf svgsnd below?

  A bullet is fired horizontallyh6y:fz 2;h+pi smepu6g(jls1 , and at the same instant a second bullet is dropped from th:zmlheg(p2 jyhf+ s1uisp6 6;e same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizo i9;cku)bwi*jntally at a speed of 73.1 m/s and at an elevation of 148 m drops a package. 2.2 seconds later it drops a second package. How far ci)jw9uibk*; apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second la5nrl f ib1 +zrbjoe;+4/k*hfjter a second package is dropped. Neglecting air resistance, the distance between the falling packages wirrij/n*;jl+ekfb4 z5b +ho 1fll

  A pilot drops a bomb from a plas6noj/1)wnkb /dnu f* ne flying horizontally at a constant speed. Neglecting b/)wnoj/6fk dn n*1su air resistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on t4bmbgn9ino0 p )ffv*sp-ss cd gi -x-0u6;(ti he Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (anp b-nu;0m*s oi)ts 4icxs9i g-ff(v6-0gdpbnd at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the +x axis rc/huqi9c-7,+v4 vgwse ad it2 j,g 2cselative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the eiv -g+a/vs47dhqc,c 9is tg2u ,wj2cother car is

  You are trying to cross) hvuk1yd mi1:to:q7n a river that flows due south with a strong current. You stakqyt d o71uvmh:1:)inrt out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stil) h5+(s.vz*mxyd jxi hl water. How much time will it take you to mov*ijvx()mz sx5h y+hd.e 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. f3 sj twj-i;0o The y coi-j0owt;3 fsj mponent of A is

  If a ball is thrown with a velocity of 25 m/s at an anvf4+v 0 5os4fv0d drnp3dft4jgle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in ul iyw-yo w ,imyh9.,(a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees nuo9yil,-h,wy( ywmi .orth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its y-2m j6lr-k8lrxp - g7n1pzagvelocity is 8.00 m/s. The angle between the direction of its motion and the x axis must bezpy8 xa- mk7pr1g 26nj-g-rll

  A 400-m tall tower casg t7 ).3ya-s1izdvve q b:+ohrts a 600-m long shadow over a level ground. At what angle is the ogdbv7+e ia hty13r :qz.-sv)Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) anu )e,,s3hw/ed(cflf od (-1, 3), respectively. What are the cwud3,f ,ce(sfol e )/homponents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and bp6d 0ob0) idw1clbg t,n1vg5( 8cd 1 mby0zyx(-1, 3), respectively. What is magnitude of the sum m1opvng10c)bct018bl(wy0 6d x5bgdziy, dbof these two vectors?

  Vector A = (1, 3). Va3jbv;bp5 6juvt64e rector B = (3, 0). Vector C = A + B . What is the magnitude pbjvtjb e6 r;a546 vu3of C ?

  A car travels 20 km West, then 20 km S0., 7oupiqd2l4z) ms:el (xups ac xw9 +0oaqnouth. What is the magnitude of its displacemeq.(u)pxi9l2dm7+0 n0aao,s ezuwo x lp4qc :snt?

  Three vectors, expressed in Cartesian cn7zzl go1 ew73d71cmz oordinates, 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 ly8jq/p82b 4 kvtkif0in 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 = (+f:v k:gj s+yprh,q;d; 3.0, -8.0), what is the magnitude of vector C = A - Byh pj;f,qrv;:+ : kdsg ?

  A runner runs halfway aro2 v kf2e:bifx n .mgaw udu:3kcx09y(7und a circular path of radius 10 m. What is the displacemen.am :n2 (0eyu gdu:xv7i2xb9cfw fkk3t of the jogger?

  Two forces are acting on an object as shown in Fig. 0 n r7lu5rb3jgbelow. What is the magnitude of trngr0l5 3bj u7he resultant force?

  Two forces are acting on an object as shown in Fig. below. What is y*//w c7dqsm 9tzmym*s-+pubthe direction of the reswt/z-c9d7m+pmsb s y/q*u * ymultant force?

  Vector A is 5.5 cm long and points along the positiveusvn7e 3n+i7g q7c.f o x axis. Vector B is 9.2 cm long and points aicg77n.uv f3os7+enq t $+55^{\circ}$ 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 70 cm longuv7k 2ab6lx 3j and points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 34 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 inixmitle t + vcj(+8ve 6tr;ojl1:*:mvrtial speed of 13 m/s from the edge of a cliff. A stop watch measures the::x ttt*; 18mojleei+ vrvlr+6cmv( j stone's trajectory time from the top of the cliff to the bottom to be 3.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocgvjz.hvuf4+ nc +2t+rity of 14 m/s, from a bridge. It falls 27 m to the water below. How far does the rock trave+.nrhj z2+ug4vc vft +l horizontally before striking the water?

  A ball thrown horizontally from a point 27 m above the ground,ei9 qqswt -2si1;i 6rfj5cv6w strikes the ground after traveling horizontally a distance of 11fw9wqqt ;si6jr csie56 -i2v7 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed anlvac8b 1s1 hto764 y+dlu(l of 12 m/s at an angle y1a l64+(17v8tl du slnaboh cof $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump ecy 1cnc -b/;x61i.z9vdyx mwgoes into the jump with a speed of 9 m/s at an angle of 6.emi w/byy xxv-n1dcc9 c;1z $19^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an iay/xav4 wdr 41nitial velocity of 30.6 m/s at an angle of $26.0^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 5751by9b4fef 3dkg7sl f.6 m/s at an angle of $43.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an an fainavu/ 13p0gle 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 horizon9;yvg 2s *isut o+pw5khg7vq 2tally at 24.8 $m/s$ from the roof of a building 35.8 $m$ 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 46.9 m/rto;1m thr kilw);z ; -*vte/as at an ana; rz;lkrv* o;-)/h1 twimet tgle of $42.0^{\circ}$ 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/)j7+p 9uhkgnn0el v,gs. If you + en0)v n7,9 glguhkpjran the same race on a day 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 speedczw:d -o 4vyo) 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 cvdy)w-zo o:4 ground is

  A plane is flying due South1 ,q fb d: gcc lz/+rvsmcq0ov+a*,eb- ($270^{\circ}$) 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 12cdx 4u exc4c06j6,z nu0 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 phj*f, vivab4k5 j t7)krojectile with speed 50.0 m/s in a kv 4j*j5kbiv,af) 7htforward 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, is directed acrossa72 0r:golw*xr 1 uthc a river with a current of 6.0 m/s. Whata71t 0ox2rl hwug:c*r is the speed of the boat as it crosses the river?

  The driver of a motorboat that can movba++gd to i hol) ii*wr+./,sge at 14 m/s in still water wishes to travel directly across a river 1.8 km wide in which the current flows at 5.0 m/s. How long will it ta,ao/g*+ srdi.gtw++l oibi h) ke to cross the river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trave6:uyduanl zpz-m;v :5tn v*0z90op hpl directly across a narrow strait in which the current flows at 5.0 m/s. At what angle 90ltp:5uo*-u;hv nyzp6z anpv 0 :zmdupstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite ban1ww5:/r* s c zlgxbj.tjq e gtf/)p3.yk in 6 min 40 s. She is s)*qecpwg y5 ztfrgl bwx/j/1tj .:3s.wept downstream 480 m. How fast can she swim in still water?

  A swimmer heading dihxcfig 8yl 980 i(r:qarectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. Sheg(8lcx8ifr q0h 9i y:a is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.29 m/s, must u mr 2v6b0zbb sn0xyk04+w8bp aim upstream at an angle ofmbb 0+zv60 p0 ubk2sx 4yrbw8n $28.4^{\circ}$ (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)  $m/s$