Which one of the following is an ej 6(yihj6i zhu32)robxample of a vector quantity?

  Which of the following operations wi dlgnzjns7k6giw(sh 55f f7y7 o h73o+ll not change a vector?

  Which of the following is an accurate stag9xz ex 8 5w;2f)pkzc d94vnbrtement?

  The resultant of two vecicev s8xj wc.wb;37 u*tors is the smallest when the angle between them is

  Two displacement vecton ovi(d3 7) mhka 616*twexljlrs have magnitudes of 5.0 m and 7.0 m, respectively. When th6 vwmi(7 x)ektdn* l36l1ho jaese two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are adk * . 2s(np,d.x2imbph.8rsztzbn7t qded. Which one of the following is a possible answer for the magnitud,.x7nqt pnikb.b .t8(z*zs2 md2srp he of the resultant?

  Three forces, each having a magnitude of 3- 5naspfmn7hx crt ..30 N, pull on an object in directions thattapnfc7m..- x5r3snh are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown1(ugj vec/4 zp vector is

  Ignoring air resistance, the horizontal component of a projectile's velwb yupr:s,l81 ocity

  A ball is thrown witqs ui3df( l+*9 all+evh 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 ovv u1+uet gq(s8kf 2q-*lp0yef a projectile's accelerationqv-0p( q8elf+k*2euv1ustg y

  A soccer ball is kicked with a velocity;uxsnfyu+/k0jn 6ua iupf;0 0 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 directed anti-parallel to t (lvl rqbc1 k4)ss2g2dhe velocity v slgrs 4v q22k()cdb1lector,

  If the acceleration of an object is always directed perpendicular to xnz fkk8w4 x q e..92ocl/p-neits velocity,pq9k.c/elw 4z28nf .xox-ke n

  At what angle should a water-gun be aimed in order for the water to land bfg ek160n7mb5 1j59uqo rfsywith the greatest humg s161ffk r yb5n0qbo97 j5eorizontal range?

  An Olympic athlete throws a javelin at four different anglesp)yu0g *n*pwx above the horizontal, each with the same sxu* y* nwpgp)0peed: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secosj-11 gxwa4 vdnd time. If the ball leaves your hand with twice the velocity it had o4a 1dxw1vj- sgn your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original 3p e-udr-ni0sxy 8jbx5/( oodspeed 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 heightf3i74 vy zsrh-, how does its speed compare to its ifi4 h-ysv7 r3znitial speed?

  A stone is thrown horizontally from the top of a ce zuy3g/9 ot m)bd73rtower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level g37gmrecty z uobd93)/ round below?

  A bullet is fired horizontally, aycd1 th0msmb3h6k 3t :e:l+i(9kt zvsnd at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bu tbksvmc6m 1tey :klts3izd9hh3 (0:+ llets.

  A plane flying horizontallre5ot06 se35:t p o6ug eek9lpy at a speed of 86.3 m/s and at an elevation of 271 m drops a package. 3.3 seconds later it drops69pets 5 erue3e 5o06otl:gkp a second package. How far apart will the two packages land on the ground?

  A package of supplies is drj .a(.fcvse) aopped from a plane, and one second later a second packac..f)(e ajv asge is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at46 m+dmzjlz f7 a constant speed. Neglecting air rmd4jz6zl m+ f7esistance, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity1hff;3thd6 8k9a8i -mjwwvzbk g.- g a on the Moon is only 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.mwhgiw dkafkvg --1j39ah 8tzb8;6f you would on Earth, the ball would land

  You are traveling at 55 mi/h in thpeon09zb4s2 u: b3lt te +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your car to the other car l use9bn3z: 2t0op4tbis

  You are trying to cross a river that flows due south with a a2sxet k2 t,xz3 h9j4estrong current. You start out in your motorboat on the east bank desiring to reach the west bank e42ax,ttje39sz 2 xkh 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 iijvnzu/y,okqy* j) (uve8a62b((ikc t take you to move 12 km downstream, in c*u (bq8au )v,6iov/ ( jz2(enik jkyya river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degr+;x5 qy7fyyp v;n92ylp-wm azws kd),ees below the +x axis. The y component of l25)9ma+q dw znpfp7yv yy xs;w-y;k , A is

  If a ball is thrown with a velocity of 25 m/s at an anglu43h 2 llr+3nlsf (s0.tmnwvbe of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line in a dapvrt2z fr1 h/f (hytk63 +em8irection north of east and you end up 2.0 km norz ht1+t38 6 ky erhvmfaf2pr/(th and several 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,kvd3-cne rao5q fgd297dlb/kbl1- f its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis mukn1qvdl3 7k f5 aed,- cfg9rbl/ 2bdo-st be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what a9 r*2bha .o.yy 7mii2x2 apxjangle is the Syxp2 i2 .7xaarh *b m2iao9.yjun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whadwaek)xv qnj,+stf z1n1hb p57w2 b(1t are the components of the wb)bjz1w t5xvq7n hn es,p2d11ka f(+sum of these two vectors?

  Two vectors A and B have c th: 0j)rcql8cf,ga :domponents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectq8 d a)trh0,:gcf :cjlors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + Bmr4y y. -hpr-k . What is the magnitude ofph k-m.yr 4-yr C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its dispf a-o*l ocfk:8laceoao:-c k 8ff*lment?

  Three vectors, expressed in Can8zocxg j4s3yn,xz,9 rtesian 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, expreb2s)nl+ fkyv*q 6:w fkssed in 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), what is the magnitm *rxnd(cr,esehu( )9ja8*iaqze,i66h ht r 1ude of vec )hji,19xrua8 enm* rie66s r(*c,zhthqe(dator C = A - B ?

  A runner runs halfway around a circulao5.zgebm 5(a rr path of radius 10 m. What is the displacement of zrgbeo(55.m athe jogger?

  Two forces are actinraeqa5wdw13c+x 5-i;tp fdc7g on an object as shown in Fig. below. What is the magnitude of wipq5 7+c5 fdewadar- ;tc3x1the resultant force?

  Two forces are acting oit vi61oc gjf3 k.+w1rn an object as shown in Fig. below. What is the direction of the resulta g1ow 3jirc.+t16kfvint force?

  Vector A is 3.3 cm lojxh6ymo 3v,-r)paa i3ng and points along the positive x axis. Vector B is 7.6 cm lpa 3 xm63-r,ayi)hv joong and points at $+46^{\circ}$ 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 53 cm long and icfse 83bcv ) gk3wok c26y)q6points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 42 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 speed of 20 m/s from the edgf0v1l dkuu1j;x w jtca1 e5a(+vca98ce of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff ; 890c(jf1l d1uwxv5k 1vae ua+catjc to the bottom to be 4.3 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a ocpet 82zl /m0velocity of 8 m/s, from a bridge. It falls 13 m to the water below. How far does the rock trav8m ect02/oplzel horizontally before striking the water?

  A ball thrown horizontally from a point 20 m above tf cde:( c5ze*yhe ground, strikes the ground after traveling horizontally a distance5fez cy*d(:ec of 16 m. With what speed was it thrown?

  A jumper in the long-jump goeoy . c 30trsvb7mnx- 6ekb9c9hs into the jump with a speed of 12 m/s at an angle ofr63 9bm.occ0 9n yksvhbx7-te $20^{\circ}$ 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 11 m/s at an angxr 8rx.r+xv.mz) 8n-c sfc+ux le of r8 cx+x+m rsxzr.xnuf .cv- )8$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velod4v ov)/ vd5jlcity of 46.8 m/s at an angle of $25.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocit :d5tsbn+r* nhg7g2sk y of 41.9 m/s at an angle of $43.9^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at/t g6ri(kbrb, 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 at 18.2jaa(oae)c9yft( r 2 (++cwua c $m/s$ from the roof of a building 51.6 $m$ 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 gr:r)2vq orm v)wound level with an initial speed of 63.7 m/s at an angle oo)vmq vwr:2r )f $44.8^{\circ}$ 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 ofs nqlf+ )f/pp+ 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 w/+ lqfp+ pf)nsould be

  A plane has an air speqsh p.g ;pr-*eed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relativ.p- ps eghrq;*e to the ground is

  A plane is flying due Saxxy l7pztl60d0d hgtmk7tt h / 0;)w-outh ($270^{\circ}$) 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;u7:-e pgaiggzplrwdy 8o* u0+ k)os( 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 f 2nr hrh56)bwbires a projectile with speed 50.0 m/s in a forward direcrhrb2)w6 hb5 ntion $30.0^{\circ}$ 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 di p4:87 a4uz6dzzf ksy/vbwtz*rected across a river with a currk 4/uwvfypdz8*a: 74sbzzt6zent of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat a1 +s.jb mc4yothat can move at 13 m/s in still water wishes to travel directly across a river 0.6 km wide in which the currentbj4 y.1s+acmo flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stil/ y +p/3v heicoxjp 38r7;aibzl water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle 3 +7epii/r/x;haz p cyo38vjbupstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppositlfm d/ 2x1i6ukp1e t:8fqb82:y vvkg qe bank in veqq8m6i 2ubp 1vtk:2yl:g/d 8kx1ff6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank t/(ppo u 5kz:i el0ak9in 6 min 40 s. She isk 059 pkp(zua:i/ elot swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is9v/ 5cws4 c, wgrrlnprp7+hs lm+v:b( 1.54 m/s, must aim upstream at an angle ofcn s:pwp ,sh4vl+w(rlmb/v75r +grc9 $30.5^{\circ}$ (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)  $m/s$