Which one of the following is an example1irfo1.3ha pg8.ke kt of a vector quantity?

  Which of the following operations wi,1ig y0iteai /tuf5u;ll not change a vector?

  Which of the following is an accurate statemenylan9699kuip yk gs) d2r jz34t?

  The resultant of two vectors is the smallest when the angle between them isj5 egihh446dq;8 b 4ohr2bjtl

  Two displacement vectors have m.tp, lxtej/kj 4t3t9unrla 5m v85a 5fagnitudes of 5.0 m and 7.0 m, respectively. When ther. pmt 4l 39l/5k u,t5eta5jnavtx8fjse two vectors are added, the magnitude of the sum

  Two vectors, of magnit17pg+h zb 0i9 on8 dxsgw;t.xhudes 20 and 50, are added. Which one of the following is a possible answer fod8pgs; ntb i7 ho+x9. xwz0gh1r the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object ih sg o-l1bfnuxq dq.np7*u*96 n directions tha9 q *qu*ghf .7n-n16ub xosldpt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown veg9 - k4)sm1 alhh-spgcctor is

  Ignoring air resistance, the horizontal component of a projectile's vel i4ydi 3f (rafxtvs (a59 gchn):1hjd0ocity

  A ball is thrown with a veloc7f:pqjeg qqgf3*)uaom/37 j: 0vqsbzity 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 componn)pbx5fd k 5ekln5p4g z/t02zf0bq4u ent of a projectile's accelerationk uez4 4pg02lnfx 5b)505/nzd t qkpfb

  A soccer ball is kicked with a velocity of 25 m/s at3xtagzwa 9if0quq3;k8-fl t4 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;rg3u 5noxjx4teo. i 9locity vectox.ooxr5;3i4 etung 9 jr,

  If the acceleration of an object is always directed perpendics+7oi-t 21tmite.jiw ular to its velocit 1 e7.i+wt 2iomitjt-sy,

  At what angle should a water-gun be an yxphb ;+rl rpxlb1j5/w6 w24imed in order for the water to land with the greawy6bpln1jbr r5 /;+ l42px hwxtest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the horizo*-9va clhhnj/ntal, eac9 hvlaj/n-*chh with 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 ball for the second time. If the ball leaved .q lpc(rd, 5rygne8jo s g2vv-z4(g;s your hand with twice the velocity it had on your first throw, its horizontal range R (compared to yourjgryg2s qz(ocgd ;vd- ,p(4nle.r85v first serve) would be

  A ball is thrown at an original speedp7 cm20 t b(7u*sr,w obyibl8rr rx+:h 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, h0eoou8g dtj) ho2o2 2og16dhs ow does its speed compare thgsh8o2oug eo2)0ddo 16t jo2o its initial speed?

  A stone is thrown horizontally frgd5bz7 n nz-xlc)vv4.om the top of a tower at the same instant a ball is dropped vertically. Which object is traveling f4.d7v )bzg5xnzcl-vn aster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a second bullet is drop )yd,,bcbf4fj0 .rbn hped from the same height. Ignore aib,r,c yh)n0 bd .jbff4r resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally a b-lzaw*wu8y +b4p-faxrp u/* t a speed of 105.0 m/s and at an elevation of 121 m drops a package. 2.5 seconds later it drops a seconl8 r /4-pxy*bzap b*+fuaw-wud package. How far apart will the two packages land on the ground?

  A package of supplies is drk.c +dn/pab:y opped from a plane, and one second later a second package is dropped. Neglecting air resistance, the /:nk+acyp .bddistance between the falling packages will

  A pilot drops a bomb from a pla vo6fbscr b/b-w )u.c-ne flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the p-bwcv/ 6bcbsu-ro ) .flane will

  The acceleration of gravity on the Moon is only one-sixth of that on Earth. Iam(-cuwjrk47 h:mxc (f you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth, the 7w(aurcmxc: 4 j(-m hkball would land

  You are traveling at 55 mi/h in thej0xbg0lk ayr;ludpt 1 36 ;8fx +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of yo6u yla 0xdk 83jgrxf;;0 p1tlbur car to the other car is

  You are trying to cross a river that flows due south with a strong current.xmp94c30lgq h You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should hea0l 3cg4m xpqh9d your motorboat

  Your motorboat can move at 30 km/h in still water. H.dawsa n)-h(lyl d 1e87g7 x-q epy-wa6m7ubnow much time will it take you to move 12 km downn-1alaqle(.e )u8w6dp a- y7ghd7-n 7xbwms ystream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m atpym 3-(;xpxzk an angle of 30 degrees below the +x axis. The y component-yz3pmkxx ;p( of A is

  If a ball is thrown with a velocity of 25 m/s g;s ; rga+n j9x1uci6vat an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straigg 0) (hwsxhb6oht line in a direction north of east and you end up 2.0 km north and severa 6h)(hxowsgb 0l 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 of its jhcq2/k9-kb + yz+p d mkm)q6wvelocity is 8.00 m/s. The an)+p cmbdz6kjkhq+ mw9 ykq2/-gle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. kuofydm5 /ny( (ss(u8( x;lva At what angle is the Sun elevated above l (f; suyan(kv(x /odms5u 8y(the horizon?

  Two vectors A and B have components (0, 1) and (13; lv q0*cl,nwcw)r qpok7ho -1, 3), respectively. What are the components of the sum of t0q73 wv kw1 pl,olrhco qn)c*;hese two vectors?

  Two vectors A and B have components (0, 1) angmb( ih8s lkmd/v.)r- d (-1, 3), respectively. What is magnitude of the sum of these two vectors?bmgh8) /rlmsivk( d. -

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . Wha- j2(2,d7 v.glqb r0u zzobmrht is the magnitude .l,m-zb7rvz jhub0g 22rodq(of C ?

  A car travels 20 km West, then 20 km South.5 k rj4v wc+b3uew5qn/tz4m5u What is the magnitude of its displace 5n45tk bmwcu5wruvq3+ez4j/ment?

  Three vectors, expressed in Cartesikk2jwln y3w e r:.d0c-wc)h9qan 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 Carte ludb/hx fl8of gaoqzh2/ 80+)sian 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 j12axb: xj1ksB = (+3.0, -8.0), what is the magnitude of vecto:j 211axsxbj kr C = A - B ?

  A runner runs halfway around a circular path i7jw-u f:ofg-u*ome,of radius 10 m. What is the displacement u iw:7m-uj,oe*of- fgof the jogger?

  Two forces are acting on an object as shown in F 2 )hbz9 ntyde26bwa*eig. below. What is the magnitude of the resultant f n*2a) e6bw hzt2ey9bdorce?

  Two forces are acting on an object50r6k-8 qk ymtft oh2a as shown in Fig. below. What is the direction of the res6-oay mf20rqk 5t h8tkultant force?

  Vector A is 4.4 cm long and pointms6gfwmmih 1s 9j6wc :1*t /ybs along the positive x axis. Vector B is 9.1 cm long im c1y1:/bjmf 9thw mg*w66ss 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 60 cm long and pointd :dboqc3t l 6 bsvumc1*9k0u-s at $30^{\circ}$ above the positive x axis. Vector B is 24 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 horizontalsgk+ g(jijmuw;8an2tjwuf ,o 2kl++-ly with an initial speed of 21 m/s from the edge of a c22 uijmgw jw,l++ uao-s+jtk(;gkfn 8 liff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.4 s. What is the height of the cliff?

  A girl throws a rock horizontally, w6 c 4, iycy-vsbxmvd/(ith a velocity of 6 m/s, from a bridge. It falls 13 m to the water below. How far doeyd(vy-mc, ic 6s /4vxbs the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 23 m above the ground, stsb5*kqpx4+) iqs mng - dwvz71rikes the ground after traveling horizontally a distance of 12 m. Withs kn)wpxg-5s 1zqmqi7b+* 4vd what speed was it thrown?

  A jumper in the long-jump goes into the j6/.iehnsg r4c9d3 sggump with a speed of 12 m/s at an angle of n g h3/seisd.c4 r9g6g$20^{\circ}$ 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/s at an angle cgk6qlna xa). .x*p9lofpx ).l6*gcaln qa xk9. $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial qu sj0jl;dg9uf 0 l13bvelocity of 48.1 m/s at an angle of $40.9^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 34.1 m/s at an angle+5d isk8fa.znp7t a.b5qmha)g pv9l5 of $15.8^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anw8(c0l5o0 8lfhaw cui gle 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 hori0s;t ggn:- eqszontally at 26.6 $m/s$ from the roof of a building 46.6 $m$ 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 levzz3uq7ruyg q jvc l8(r- 9b,0nx0vj4 bel with an initial speed of 60.0 m/s at an angle of rz4vnrq v(l gjyz80uu, b x3 9j7-0bcq$45.2^{\circ}$ 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 j4w0e o-av.lgq;(mic) 4ib vd at a velocity 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, the time it would take you to finish would b.bmg(;a 4e)l io4wd-vjv0 iqce

  A plane has an air speed- i0hmtd-yo.e of 200 m/s due North, and is in a wind of 50.0 m/s to the West. ti-0y odm- .he The plane's speed relative to the ground is

  A plane is flying due South us i1m53ed0kp($270^{\circ}$) 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 headel -tg2c sd6r6ad $30.0^{\circ}$ 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/t:*yq81 lt*ko.p :ulson0i 4rrihig m/s horizontally fires a projectile with speed 50.0 m/loryq*i.*k:phtl :8 1gion/tr4iu0 s s in 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 water is 8.0 m/s, is directed acrossemu 8p:duybr-r 9z 67i jt2t.k a river with a current of 6.0 m/s. W:-rz2bdu.t6mkp 9t rij7y eu8hat is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 9co bng9-3 x/vi m/s in still water wishes to travel directly across a river 1.2 kmxb/ nivc-og93 wide in which the current flows at 6.0 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 tra(8g0cc no0y vvvel directly across a narrow strait in which the current flows cvc 00vg8(yon at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppbdcum5 dvk 0 g4xb12;nosite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stilldm2 x nkg0b5;4 c1uvdb water?

  A swimmer heading directc -c4g+h+pzwwi hno(/ly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is thhcg( wwo+ /+ z4n-ipche speed of the current?

  A boat, whose speed in still water is 2.01 m/s, must aim up,)c0a qs oia/.al+yjg stream at an angle of al/oas yc.ji +qag ,0)$16.8^{\circ}$ (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)  $m/s$