Which one of the followingg6 +.rikhz/ 8l li1dk)b5vj uo is an example of a vector quantity?

  Which of the following operations will not change a vec(/tjgf7hn+y: u( iakg8b2a 7u.ym nvytor?

  Which of the following is an accurate ql/kqzq8/nw*nwg s5; statement?

  The resultant of two vectors is the smallest when the anglsqv(.a slu +)ne between them is

  Two displacement vectors have magnitudes6m :j ,l64umc5w+wa 4bkzre in-snhz1 of 5.0 m and 7.0 m, respectively. When these two vectors are ac4u :4 rzl kzn,wnh16mmaw-sb+i6j5 edded, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whi g+;x7tvhl2r yh,oi6ich one of the following is a possible answer for the magnitude of the resull ghi72x+ t hr;ivy,o6tant?

  Three forces, each having a magnitude of 30 N, pull on an object in dir,w g wp etf4,zkidc:71ections that arefpt1 dwk4 7e,:iczgw, $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the :h /pj0ft)jt/qy eij 4unknown vector is

  Ignoring air resistance, the horizontal component of ok ge21iwc)zs 83w4ao a projectile's velocity

  A ball is thrown with a velocity * . kohvs0 kca0wv0;ovof 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 component of a projectile's acceleration-wfq pw69*y t qgn9v2m 9pnw* fg26qwq mtyv9-

  A soccer ball is kicked with a velocity of 25 m/s at a ,jqtl+8mbnwbct9 zn 8ay9q*6n 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 gac 94 p2h7lz 2ms) )9spwf 2dhbrlwl(anti-parallel to the velocity vector,pf (rdw 9hls)7l4g2slmc 2zbaph) 9w2

  If the acceleration of an object is always dire5.4b d bj 7dmk5lkj8pvcted perpendicular to its velocitykdk j74pbv.ml b8 dj55,

  At what angle should a water-gun be aimed in order for the water to lanw /fr7+em5mdnql,y t+d with the grew,e dm+fn+qm/7y t5 rlatest horizontal range?

  An Olympic athlete throws a javyyrp/j hwb0 279:nnsfelin at four different angles above the horizontal, each with the sy:h7yfbp2n9r0w /js name 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 leav5od2r)0 pld u:4zm; vhmh eaf5es your hand with twice the velocity it had on your first throdvm p)5 0hedur l:54a;zh2ofmw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/:e/k;:nx627d:pbx6bvade n1w e wxo ls 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 attemptcb73 p+p47yrjrdl p.f reaches its maximum height, how does its speed compare tojf73 4drpp + ryp7l.bc its initial speed?

  A stone is thrown horizontally from the top of a:2q yswt15ft-wisu pkww4e71 0 wi0kr tower at the same instant a ball is dropped vertically. Which object is traveling fwu17-pkeikr qt w5y :tww42ss10wi0faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet ismkqr pn-v:ulp si7eu5:p6: ;k dropped from the same height. Ignore air resistance. Compare the timesp:qmknk p::i 7s u ulre5-v6p; of fall of the two bullets.

  A plane flying horizontally at a speed of 112.8 m/s and qz d.+bk*o*:a2vtlrs at an elevation of 164 m drops a package. 2.3 seconds later it 2 *as+:zk .dlrtq*bvo drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a h- 06 nmh9tjpfypdh)5x:.gmq plane, and one second later a second package is dropped. Neglecting air resistance, the distance betwe6h:h. p j9f ymdmqnhg p)0xt-5en the falling packages will

  A pilot drops a bomb from a plane flying horizontally at8dr(qpx/lxj lac, e,/g 3ctl+ a constant speed. Neglecting air resistance, when thex e3xq/ c,r c,tl8plda glj(+/ bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on a7fa9qc.btkq 9;v;tp iz1-j4g ofo8s Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that;v. sza4-9c g bp17af ijfqto o;8kq9t you would on Earth, the ball would land

  You are traveling at 5( stt6*xw5pyrotut xsy7n67: 5 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h.xt:p7*ttntsyyxr6uw 57 o6 ( s The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a stronuc:qc0wado / 4g current. You starcc4wd oaq/u:0 t 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 still water4) uhypvzax47-ed zu1. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 km/hv z4x7-zu1ap huy4 d)e?

  Vector A has magnitude 8.0 m at an angle of 30 degrees bea; u9e86odtqilow the +x axis. The y comptdai 6 8uo;e9qonent of A is

  If a ball is thrown with a velocity of 25 m/s at an (z9 3 iwd(vjheangle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in9b2v bcn; y xj..gdqr4nugsds rr-:46 a straight line in a direction north of east and you end up 2.0 km north and several sq2cr xn49;:gdvbs d.gj 4y6-n.urbr kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component q b+om2w2fjah0j m 1:c;pz9mv of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis musj9bj;2qa: zmphmf1+mo 0w2 cvt be

  A 400-m tall tower casts a 600-m long shadow over a level ground.n b,w+nn37pa 4xjd.f j At what angle is the Sunnnjd7f nx.p,+ bajw 43 elevated above the horizon?

  Two vectors A and B have components (0, 1) aieunpya/y.w k,+a1 x;nd (-1, 3), respectively. What are the compopnay ui+; .axwe1/yk ,nents of the sum of these two vectors?

  Two vectors A and B have componene;8he vj-j sp0h(ngeu m 8)zi;1avb 4tts (0, 1) and (-1, 3), respectively. What is magnitude of the suie80p)s4 e mha-t h;zn1jb v;je8v(gum of these two vectors?

  Vector A = (1, 3). Vecttc/jr,o 2kk1daxjh2jvw 0-y9 or B = (3, 0). Vector C = A + B . What is the magnitude of C ?k-wk/ xcy1 j2d2,0jrh9j tvoa

  A car travels 20 km West, then 20 km South. What is the 3gsrfm-hycdw(hquw10(plo 4 nl y0 . 1magnitude of its displace ygh1p r y( l0n-4cq3d0(olfuw.mhw1 sment?

  Three vectors, expressed in Cartesian coordinates, arh d8tdh q.lm82e
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 i pzf:n db5a-(- eupion p ya/2y:*2ktkn 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, -8.0), ww1htcrbhm j6a/ )cof3gix7 03 hat is the magnitude of vector ab go)crch h0xj/ m3it37 w16fC = A - B ?

  A runner runs halfway aro d5c az o9iryekf,,iin1k6i79und a circular path of radius 10 m. What is the displacement of t iiced r 179ai65n ,okfyi,z9khe jogger?

  Two forces are actin- lzz/ 1-jl mkgi/b2egw,utdwok5 g89 g on an object as shown in Fig. below. What is the magnitude of the resl//tge kg8w-lozu -15 gik d9wzj,b2multant force?

  Two forces are acting on an object as shown in Fig. below. What is the dir krjlw s:7*tcj68ayru* c/4rqection okur4 qj* jc7crwa68slty*:/r f the resultant force?

  Vector A is 6.0 cm long and points along the positive x ax tweq698*bf jyis. Vector B is 6.5 cm long 8 qw6*yfejtb 9and points at $+58^{\circ}$ 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 61 cm long and pointsqy1afcqf yd9kvdt h.-))7w( sx:j x k/ at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 28 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 spendur 0le8(*)dea; nrxyx 8 c-aed of 26 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 be 4d r *)0nl88na;(arxyedu- xce .9 s. What is the height of the cliff?

  A girl throws a rock horkqij 2-uf9d+q0 ,everizontally, with a velocity of 16 m/s, from a bridge. It falls 22 m to the water below. How far does the rock travel horizontally before striking the 0iv-jrf+,9qekd e2u q water?

  A ball thrown horizon19bzlf rd8n.vhfi 3k7 tally from a point 19 m above the ground, strikes the groun1n3 8flk .fbi 7h9zrdvd after traveling horizontally a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump withb.dkr + l1 zqvmwkx*:3k))uthvp. ujss0) qd8 a speed of 12 m/s at an angle of+spq).kzxdvwsd1rl*qm3 kb8v):t.huj0ku ) $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jumpej0 ir-c/nr wrb-p/w,ttp v4x3s11r u goes into the jump with a speed of 11 m/s at an angle of rj-rxwv/uir1p/sb n, p3etr1c40tw -$18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with anq( /kn wb dj7x;:pmv;rvr:qpiqv1)0r initial velocity of 20.9 m/s at an angle of $40.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 54.5 m/s at an a rawniu(.dhah, /xq3/l 3e0, qua ,qncngle of $29.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an amh . qbsq6kf2,ngle 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 2wy*cf77 fth .p6.7 $m/s$ from the roof of a building 51.7 $m$ 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 (9 zedmamr ;1fof 44.7 m/s at an angle oem1af 9(;m drzf $37.2^{\circ}$ 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 44w l(w7 j8sbxf.0 m/s. If you ran the sam7jxfb4(lsw w8e 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 is in a+soo i)58ccmz wind of 50.0 m/s to the West. Thesz)o+8c o 5mci plane's speed relative to the ground is

  A plane is flying due Southy47br dhzr 2kw1i3w6.dk0wg a ($270^{\circ}$) 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 .q -r rrn.1ciag3wu m:q/i/fbof 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 fi qqye1k+xk(uz ,c9ru7.a +bczres a projectile with speed 50.0 m/s inqz,9k au+qc7c.x u+kzyre 1 (b 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 ar9e rcn qr13pz1 /*o5vkpwla ,b.mx7water is 8.0 m/s, is directed across a river with a current of 6.0 m/s. w 1p p/k93. * 7nzqec51l,omrxarravb What is the speed of the boat as it crosses the river?

  The driver of a motorboat thgiqa- c- 4wya6at can move at 16 m/s in still water wishes to travel directly across a river 1.q4 ga-w -6aciy4 km wide in which the current flows at 4.5 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 w f8x srnq5rhkq005u t:ater wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should thenqsr8quxt05h: r 50 kf driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite bz wvvnajm36es*t.ny 4-.;e vcank in 6 min 40 s. She is swept downstream 480 m. How fast4snn6cv *.3etv .zmewjv -y;a can she swim in still water?

  A swimmer heading directly across a river 200 mem0zklf e6pm9o5 i(df 1,uf6r wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What i0f(p1 eo9fe6mulkd, mi6rz 5f s the speed of the current?

  A boat, whose speed in still water is 0.95 m/s, must aim pobd; 1 vm3+fwupstream at an angle ofpf d1ob+3wv;m $32.0^{\circ}$ (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)  $m/s$