Which one of the following is an examae6dlxj2q sk2,+ exzv)m g 96sple of a vector quantity?

  Which of the following operation./t t hd(n8bdkmv*qz+s1m y .ps will not change a vector?

  Which of the following is 7nenoy ki4/ik9x,ft bu;9 gk*an accurate statement?

  The resultant of two vectors is tht7oip+qe9c 6ze smallest when the angle between them is

  Two displacement vectors have magn uxyva9i7xp 2d +n(r2v: h/p.fhaq (iiitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the suxi +fn2 avqxpd y(i: u./(9hpr2ahi7vm

  Two vectors, of magnitudes 20 and 50, are ql *y*d4qw z3iadded. Which one of the following is a possible an* i3q*zdw lqy4swer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N,c1,ts 6v s f*mnn14n0 jzplb3b pull on an object in directions t*p tsnms3 b106,znf1 c4blvn jhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown*mjj.o y;8 bhr, the unknown vector is

  Ignoring air resistance, the horizo9t5 ;y jqz8ybpntal component of a projectile's velocity

  A ball is thrown with a velocity of 20isn7eiw/i7o6 ,pi2zb 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 comp )p71emyzx ,tp-t fnp(onent of a projectile's accelerationnpfey- t)z p(p m1t7,x

  A soccer ball is kicked with at5 ccr*v5bsa1wqr ec km44wv5o; o0b( 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 in ;uhm8o/jto 9s directed anti-parallel to the velocity noju 8;9mo/thvector,

  If the acceleration of an object is always directed perpendicular to its velo:9:uw ffpkz4bcityw f k4:uf9pb:z,

  At what angle should a water-gun be aimed in order for ,rb15fnokv,ul/g mf 6the water to land with the grflok u/1 n5b6,fgrm,v eatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the hdpcklv4, 5hm9orizontal, each with the dc54vmk,9h lp 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 for the second time. If the ball leaves your handhd6e v.g7bj( x with twice the g 6jexvb(h7.dvelocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at ancuw du:6*m4uo 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 goal attempt reaches its maximum heabch c.0*n;h sight, how does its sp*nc 0;hsac.h beed compare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the same instahvn c +u+j(i*c;sm j2dt/- xn7xtc9mx nt a ball is dropped vertically. Which m7c 9stndx(vj* /;n+hmuc x -+tcijx2object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, a53dx 8 s da*ivvtjz7w3nd at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bullz8ad*v3sdwvxi 5 3tj 7ets.

  A plane flying horizcbx iel ig(9 l)1,s7:unm2vnfontally at a speed of 117.1 m/s and at an elevation of 230 mxif,uv)inbm7n1l se(: 9g lc2 drops a package. 3.5 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 second later a q* )mqig7yxjtft l5i2/s.k 5isecond package is dropped. Neglecting air resistance, the distance between the fal)ij* 5kq gitst7mq/2 5fxl y.iling packages will

  A pilot drops a bomb from a plane flying horizontally at a conbea*h7a5/rixw3. -inf(x mr rstant speed. Neglecting air resistanfa*mr. ir x(x7nh/w-35 erba ice, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only gkg4ve+jhn4 imi*m0/ 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, the ball would landhi/i04jmgvk * ne+4gm

  You are traveling at 55 mi/h in the +x axis relative to a straight, level iasxeo8,i;baa-pf:2ny3r 6hqz .7 mr road and pass a car traveling at 45 mi/h. The relative velocity of your car to2r-rzyphn qmixi,6 ;:f.8aao7bae s3 the other car is

  You are trying to cross a river that flows due south withaxeyar af7p s(s1isjj)/)( ;r a strong current. You start out a7)srx;p(/f1ae)ras (jys ij 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 still water. How much time will iz1nc b:fy: n1)yk ejir*ht2 x xs.2hu2t take you to move cx:.* h12kyzihej tub:2s) 1ryn 2fxn12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30om kjioe/)b 0/ degrees below the +x axis. The y component of A isk jb//oem o)i0

  If a ball is thrown we,g.t44bg 7sz) bo czz 9z9briith 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 line8+grca4: m*7ilg ip8evb+t dc in a direction north of east and you end up 2.0 km north and several kilometers d+t vcpi8ir7gm48+g*e a:blc east. How many degrees north of east have you walked?

  A butterfly moves with a speed omryms4 wv42n6 f 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 m ymnrs244w6m vust be

  A 400-m tall tower casts a 600-m long 6qbhd kb2dy7pq3 57xoshadow over a level ground. At what angledp7652kbyodxq 7 h 3bq is the Sun elevated above the horizon?

  Two vectors A and B have components hfewjx 74 ;-aa(0, 1) and (-1, 3), respectively. What are the components of h-x4a awe;f7jthe sum of these two vectors?

  Two vectors A and B have comua)c1:*kjux go2cc q+n5 rdv :ponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vecto1cavcg+2 *q) o5xu: ukjnrcd:rs?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What i;bzii/1tk nt- s the magnitude ofn bi/1tk-;itz C ?

  A car travels 20 km West, then 20 km South. What is the magnitude3+ l6cwcz: mhf of its displacement?m3 cl6ch+z f:w

  Three vectors, exprestirj+0e.s+ u x o,) zbs706wvii+ eatrsed 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 Cartesian coordinates, arsacg0 :x1 7kz bzf 2wan9wp )xs7t,q.je
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 qvk0n9lp1x0y:u 8hpf.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B 0upfh nkpv81y9l: x0q?

  A runner runs halfway aroundpq:+ c7x ddd6 o9hvpy. a circular path of radius 10 m. What is the displacement of the j h 7dyxp+6p:9qc dvo.dogger?

  Two forces are acting on an object as sho,-3ezrln xyq6 wn in Fig. below. What is the magnitude of the resultant force?xnz6 r y,3-lqe

  Two forces are acting on an object as shown in Fig. below. What is the directiaq f aa n qg*0gk*))hf wy8vy5rvm((r6on of the qa f* )vyga(n(m8 yh0qr5kr)gwv*af 6resultant force?

  Vector A is 3.7 cm long and points along the positive x axis. Vectopm95 su6vfvc8 r B is 9.0 cm long andf865vvcsu9 pm points at $+56^{\circ}$ 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 79 cm long and points at .aqju1./n x7zbpm+h 0v) qdgj$30^{\circ}$ 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 initial sp )fv-ym 6xk(oteed of 20 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to bevtk)-m(o 6x fy 2.1 s. What is the height of the cliff?

  A girl throws a rock horizon13n ves;oebqaqb /hf; n9 .ea8tally, with a velocity of 10 m/s, from a bridge. It falls 22 m to the water below. How far does the rock travelfeqa3.sb;; eoha8 e9n/1 nbvq horizontally before striking the water?

  A ball thrown horizonjcdz,ks yl: l*70h1 -f;zjwk atally from a point 29 m above the ground, strikes the ground after traveling horizontally z:s1jl;hwdy ,lf*c 7zk0ka-j a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s at awo hq7/pa0. qen angle oopeaq/ q.h07wf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goeh: zz:6f tjk-us into the jump with a speed of 9 m/s at an angle of f zh::ukt6-zj $18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 46.5 m/o- /2s u.utods,/9y emd bayn7s at an angle of $29.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launccs)hk,tj/q2 qmy+boixk );:ihed with an initial velocity of 44.9 m/s at an angle of $46.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired atmk /e ars0i9v3 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 az ch;j.w krf54 fkb1c2t 26.1 $m/s$ from the roof of a building 49.4 $m$ 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 szdlswb- 2k f yyx;8 ;hdcy7)w,peed of 53.9 m/s at an anglew,;);k d72fc-bxy8hwdlyyz s 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), yo epv3 6896xl qlar1xd.ixh qg+u can run a 1500-m race at a velocity of 4.0 m/s. If you ran the saxx l9 gaiep8rvq3l dhx16.q6+me 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 speed of 200 m/s due North, and ich12,/5ik:zlar jahy2vq d *zs in a wind of 50.0 m/s to the West. The plan*,:hzd2hzv a/1jalykq ir 25 ce's speed relative to the ground is

  A plane is flying due South p.)p-wy*sika. m +ouj p)8r wc y8wvh;($270^{\circ}$) 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 t5i dej2 ;sr7u120 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 5cfismu*0x5j(k)/ ) 4pc qbefg0.0 m/s in a forward direction uxffi 0*pgc 5)4 )k(/ sjeqcmb$30.0^{\circ}$ 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 direcbl zr2pek0p1g j84ck:ted across a river with a current of 6.0 m/s. What is the speed of the boat as i4pkr p 8b2:1 z0kjclget crosses the river?

  The driver of a motorboat that can move at 16 m/s in sti m r(74b gxtq8(zm: ,cbbdf3apll water wishes to travel directly across a river 0.9 km wide in which the current flows at 6.4 m/s. How long will it take to cross th zc m(b3mbfrba(t:q4p8 g,x7de river?

  The driver of a motorboat that can move at 10 m/s in still water wishc8ceop 47mz 6qes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should4e8cp mo 6zqc7 the driver head the boat?

  A swimmer heading directly across a ris sq3cuc:z3: over 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wate oc:zssuq3 3:cr?

  A swimmer heading directly across a river 200 m wide reaches tw 8)5qhtr6aaw +z9 7lyouuv yy0j ez3.he opposite bank in 6 min 40 q9zu z8auwjrwo0l6hey3yv at+.y)57 s. She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water ip1(,tl.v i sg /rbs1n pb55odcs 1.43 m/s, must aim upstream at an angle of55i ( brs./b g,po dscvt11nlp $15.8^{\circ}$ (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)  $m/s$