Which one of the foluyhi- p421jns lowing is an example of a vector quantity?

  Which of the following operations will not change ))nvs-, :gq3d3hhw p h oefy*ca vector?

  Which of the following is an ajumf i)z6 t:)rccurate statement?

  The resultant of two vectors is the smallest when the angle between t8h dy/im.hoo-hem is

  Two displacement vectors have magnitudes oa:t -i*la rxu)u0myy40 vwv0mf 5.0 m and 7.0 m, respectively. When these two vectors arxt y0u ulav )maw*0:i-0mr vy4e added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follotz c3(;j pq41xlo3.tgs zs 2ldwing is a possible answer for the magnitude of the resup3.2 z;zlxq 3dtt1cgl(os j4 sltant?

  Three forces, each hac4kps7bh te3an 7+rp /ving a magnitude of 30 N, pull on an object in directions tha /p7ncr e7hat34 s+pbkt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown4h.f+6t *imz0t nbicd vector is

  Ignoring air resistance, the horizontal component of a projectiwrrxukr i ;8-2 y-qtihs:mw94le's velocity

  A ball is thrown withl( /k6zfe15xllq)cr q 5-cm7k. z zzz*axz5eg a velocity 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 component of a projectile's accel h:pfloix (6i(erationi(6x o(fp:ilh

  A soccer ball is kicked with a vj+.ix:.)b- wko ; *rhfbiw3cgj(zx k relocity 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 d0 40 bde4kb o66 0vao0yhy )reveo0rpgirected anti-parallel to the velocity vey 4rok46 e0py e0dgo0hr)0ebv 0ab v6octor,

  If the acceleration of an object is always directed perpendicular to its veloh,5pn 0 m2ikc)t smiglx 9/ e/vr+a3udcity2k l+api9 ir,u)/dvms ntm5gc03/x e h,

  At what angle should a6t+bdx;k .ze c water-gun be aimed in order for the water to land with the great x6tkc;d.ezb+est horizontal range?

  An Olympic athlete throws a javelin at ,qyoqn (*fu63ie cv.s four different angles above the horizontal, each wino,qf(i3 q.yce 6s v*uth 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 seconi2(+h g(heggnz1,rao : hy4w qd 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):zo (4 graenq(h1 ig h,g+2yhw would be

  A ball is thrown at an original speed of 8. ;9odntxb;e 0t0 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 fiel y5l(+ bk2fjehd goal attempt reaches its maximum height, how does its sf(ejky+b5l h 2peed compare to its initial speed?

  A stone is thrown horip( -h ndyvmtr1d zl6l0 *v9a)zzontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level groualzhm0p9 r -zn6)tvd* (yld1 vnd below?

  A bullet is fired horizontally, and at the same l 58 ,xh xjwbxcmx4g++instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the tw8b+h+xx xjlmx, 4g5w co bullets.

  A plane flying horizontally at a slyodyx)t d q:f;5t g0 ),k+ikcpeed of 82.2 m/s and at an elevation of 271 m drops a package. 5.1 seconds later it drdtdqyg5fix tly:ok)+c);, 0kops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped flm qpys 8t 0tk8e47idgwo xg: ,d*;h,crom a plane, and one second later a second package is dropped. Neglecting air resistance, the distance bet: pg;skg,i* ymox47, chq ddw 08t8telween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed.r1:foy rt(c 3r Neglecting air resistance, when the bomb hits the ground the horfc:3(ro1ytr r izontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that on Eartq2 /of/o pcj3qh. If you hit a baseballoj/q/of3 qpc 2 on the Moon with the same effort (and at the speed and angle) that you would on Earth, the ball would land

  You are traveling at 55 mi/h in the nnij+2b*fk8 z +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your c n*bj 2fnik8+zar to the other car is

  You are trying to cross a river that flows due south*e jf mzffjqct* )h996b4mdu2n k(id4 with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. 2fz4m*i jtuf(9 hj6bn q4*)9mf dce kdYou should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much td7gih pzq4v) 6ime will it take you to move 12 km downstream, in a river flowing7id 64 zhvq)pg at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle zbj8 ) q oyjx2h3oj;gm,2ogz: of 30 degrees below the +x axis. The y component ozqg y,gm jzjxh2 ;)ojo38:2 bof A is

  If a ball is thrown with a velocity of 25 m/s at an angle of /rw+2pjrpl au,f1hp + $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a sqt5yn4a-zf01uhun t7traight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east haq5u 0zht t1n f7yu-a4nve you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component ofxw26qu z9 (whd its velocity is 8.00 m/s. The angle between the directwh wx(962u dqzion of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what ango(xnu ,k5wepw5k 8n2ble is the Sun elevated above the xuk, p5wkn2(w e5b8n ohorizon?

  Two vectors A and B have components (0, o-),nn yd;gm+.ayoke1) and (-1, 3), respectively. What are the components of the sum .e;-dy a ymon ko,g)n+of these two vectors?

  Two vectors A and .qogk4pphpqm2 a 7f+2B have components (0, 1) and (-1, 3), respectively. What is magnitude of .p+ 4o7p kg2afqhmq2pthe sum of these two vectors?

  Vector A = (1, 3). Ve4h 1mst bxa7jsf: (v-i :v/ih1ug)jptctor B = (3, 0). Vector C = A + B . What is the magnitude(hgia-b i1:px :vvts4 m)f7t/uhsj 1 j of C ?

  A car travels 20 km West,yp*jvt.9z u id4v ejofu (8+y6 then 20 km South. What is the magnitude of its displacem i68j4 .uvu*yeyvd+(t f9jozp ent?

  Three vectors, expressed in Cartesian coordinate*vfy2zr( i-t hs, 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 cp5weox kk2) 2soordinates, 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 wc,h(,qyv * 4dtpd6 lp= (+3.0, -8.0), what is the magnitude of vector C = yd *4,6vwpqd (tp lh,cA - B ?

  A runner runs halfway around a circular path of radius 10 m. Wh;jvf+tfhe +h3 at is the displacement of thev j +hf3ef;+th jogger?

  Two forces are acting on an object ap2ox. a0bz:l as shown in Fig. below. What is the magnitude of. zo l2xaa0:pb the resultant force?

  Two forces are acting on an object as shown in Fig. below. What m2/ za en5s /fw+mo4oiis the direction of the resultant force?e+2 a5n /wozos4/m ifm

  Vector A is 3.4 cm long andwq5y *(9vu hx: cf*owdb:tmj0 ne7 nn: points along the positive x axis. Vector B is 5.1 cm long and pfwhbw*d(9 :x:v e ytu oc* :7njnn5qm0oints at $+44^{\circ}$ 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 64 cm long and points d+m+hw1 g4ndtat $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 46 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 initialf6rxv t0,7 35 ;kz mkcq yqu/.dv:wktd .zct,k speed of 24 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 3.0 s. Wr57mcd.x z,/:d.t c ,kfkqvk03 wtzqtkvy u; 6hat is the height of the cliff?

  A girl throws a rock horizbpo8 .oxb1g8n1nz( og ontally, with a velocity of 5 m/s, from a bridge. It f(o1. b z xbgn81opn8ogalls 11 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a pointtb7pa vapk(rm5+f 7u* 21 m above the ground, strikes the ground after traveling horizontally a distance of 1pvrt7 bfua+a(m* p75k6 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a spe;f) juu al1q:*wi gxi,ed of 12 m/s at an angle of i:x qufuj1,a);* iwlg $20^{\circ}$ 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 uub4a tb9f w4lzp3oic-):k .i speed of 13 m/s at an angle of bf ki-:uz) .bo acwt9lip4u43$17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched withoy in b od;sg-o+kgmgx,6 0q.+ an initial velocity of 59.4 m/s at an angle of $34.3^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an)4n*p f16fa p fiqi+gy initial velocity of 26.9 m/s at an angle of $41.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angro+nzphyub; i /+25 bile 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 g;hmv6xrbd-7 ul5; 0ybyirc517.7 $m/s$ from the roof of a building 62.0 $m$ 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 levgmhnqt1 lu:m 3-(ee.mel with an initial speed of 46.3 m/s at an angle of .ule 1hq3-tem:nmgm ($46.2^{\circ}$ 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 nfgu(sq .w9/lj6:m upcan run a 1500-m race at a velocity of 4.0 m/s. If you ran the same rac/f:snmw.(6 glu 9uqj pe 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/nt9o0rn; gr smbi r18/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relativersg8i9 ;no0 1nbr/rmt to the ground is

  A plane is flying due Souzzx+ ) :cn9y +uujse5tth ($270^{\circ}$) 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 hecqf08 kura6suk4 / n31ihpgf 9aded $30.0^{\circ}$ 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 witnegx;njs: u,xkw,j3em h +o (-h speed 50.0 m/s im+,ku 3ejjhx x ,ns-:o(gw;nen 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 across a river with a0b.ad7m3 ; xrw phpl-t current of 6.0 m/s. What is the speed of tha-0hw.b3 d pr;7lmp xte boat as it crosses the river?

  The driver of a motorboat that can move at 14 -pxqbcze/ xcs 3+--le2a,toxm/s in still water wishes to travel directly across a river 1.3 km wide in which the current flows at 4.9 m/s. How long will it take to cross ttxb - 3cxc q- ls,pe-x2aezo/+he river?

  The driver of a motorboat that cabw.6 hdgyr9v -ieml2/ n move at 10 m/s in still water wishes to travel directly across a narrow strait in which the curreeli9b.mvw2 dr-h 6g/ynt flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200ey8h;).1h/ l tyagzlf m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast egy 8.lh;l)ay tf/z1h can she swim in still water?

  A swimmer heading directly across a river 200 m wide rew0.nn-+ukue41hju us1 l 5(u 0wurqbkaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current-e u04 0bn(n w15k.lhur+u1j uuqus kw?

  A boat, whose speed in still wate+2ncy vplb, f+r is 1.65 m/s, must aim upstream at an angle of v,n b+y2lfc p+$27.5^{\circ}$ (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)  $m/s$