Which one of the folle jau hz5g0dht8e-fk2:c z:clc .)m;iowing is an example of a vector quantity?

  Which of the following operations will not change a vector?6 -i bdwf/ ,sgj,q0bnw

  Which of the following ik0vr/lv xk (l8s an accurate statement?

  The resultant of two vectors is the smallest when thec0 ,jym uan+y9x lm: x,ywh.j; angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively 8a je0zz;*g*hmex.8sol/urb. When thesj*l/.;x 0o8 uhbm*8ez az regse two vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, an8 zq w:)k )-wwwk7whur 1v*gare added. Which one of the following is a possible answer for the magnitudvqkw*k)ww-a)h:z 8wng7 r w 1ue of the resultant?

  Three forces, each having a magnit)v6h-1*7z7cwuk v mly njh s(p2tt,vrude of 30 N, pull on an object in directions that are h m7z61y)-jsvu*rn2 pk 7,lvcttw(vh$120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vewus1- -zrakh99bp7xv ctor is

  Ignoring air resistance, the horizontal component +x5iv g(1,j llj*e0kt h bjg:9kccuf)of a projectile's velocity

  A ball is thrown with a velocitu9.sg czt+ n(r a,.edcy 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.0 ex7wd6hp0rewh. gx horizontal component of a projectile's accelerationhdh.0x.pe76 wwr 0 egx

  A soccer ball is kicked with a velocity of 25 m/s at an angle of(.e*1p)iverkil w)ov $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration vecte mvfbli9p9u) cv: /1tor of an object is directed anti-parallel to the velocity1ct9 )fipl /: euv9mbv vector,

  If the acceleration of an object is always directed perpeo)2b6 p g-hy-8nicppf ndicular to its velocityochin 8g)-pfypbp- 26 ,

  At what angle should a water-gun be aimed in order for the wxtuxn:fp e r15z:rjcq3 d (+ ete6(pa2ater to land with the greatest horizontal ra +rpj:qp6 5edxt3 :1c(tafne xez (2runge?

  An Olympic athlete throws a javelin at four different angles above the horizonta,3snr1 kx 7hhil, each with the same speed: rksn hx7,h3 i1$30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 leaveln 9;w*ckpvnkitc6/ c 1x*3iz29 eo tns your hand with twice the velocity it had on your first throw, its horizontal range6t*kewnp31v;i9l nc x*c /kco z29 nti R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.v8vy ko vyn+l29s+iwy al2/p3 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 reac .q7virr;u1 ;7zcfvlb hes its maximum height, how does its speed compare to its initial speedb rr;;vu7.cz 1f vil7q?

  A stone is thrown horizontally from the top of a tvzm-m: qmp, q3ower at the same instant a ball is dropped vertically. Which object is traveling fas-m3zpqvmq: m, ter when it hits the level ground below?

  A bullet is fired horizontally, and at the samez 1wdxza))6vx instant a second bullet is dropped from the same height. Ignore air resistance. Compd )) 1xwvz6zxaare the times of fall of the two bullets.

  A plane flying horizontally at a spz6u *tbq*bgin9jg67p 4ut k 6eeed of 51.5 m/s and at an elevation of 223 m drops a package. 3.8 seconds later it drops a second package. How far apart will the two pacb7u9gb qj4 **6ekuzit6p ntg6 kages land on the ground?

  A package of supplies is dropped from a plane, and one second later a seh5 fdk1y)uxo-cond package is dropped. Neglecting air resistance, the distance between the falling pacy 5k 1)fo-dhuxkages will

  A pilot drops a bomb from a plane flying horizontally at a constant ffd(an rkohw8+1t5( aif4:mnn vc1, sspeed. Neglecting air resistance, when the bomb hits the grounfatri+m1svnh4( ,f fnco (w:kn851d a d the horizontal location of the plane will

  The acceleration of graviro,zkb.7wnzv j8 x4.s ty on the Moon is only one-sixth of that on Earth. If you hit a baseball on x4vzbj w .,k8sn7.zrothe 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 +x axis relative to a st z 3sprtkw176a jomb4v+ ,wdg.raight, level road and pass a . ts+d zj r16wb4w7,pvagmok 3car traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a stronq+u)np7m ff +-)kgu t0x nhb*cg current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your + )xt)7qnunb p fhf +k*-gmcu0motorboat

  Your motorboat can movefr blj8gy0w5 2p// dnp h9r*izob ek*( at 30 km/h in still water. How much time will it take you to move 1r0lbrgyf8* pij*b 9o pke2(/w / nzd5h2 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of5(a/7s(h7ogx nj 1 s0iqfinnl 30 degrees below the +x axis. The y componenjo7ln g7sqxnah i15(nf 0s(/ it of A is

  If a ball is thrown with a velocity of 25 m/ jrcewu)p va+ig-o gi.82,gp2s 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 straightxw ho; (,:zkk9vuwo.e line in a direction north of east and you end up 2.0 km north and several kilometers east. How.:kkw vzx ;h(o, 9ueow many degrees north of east have you walked?

  A butterfly moves with e;mh-c ,2fc)j*zh /ov/z gr mda speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction ofj o2e,f*hh/ gzr/;)cdmz -mcv its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shad/f8l) 2 ffe;vpg bce0iow over a level ground. At what angle is the Sun elevated above the horip/c2b;0efgvfi 8lf) e zon?

  Two vectors A and B have components (0, 1) and (-1, 3)zxz3gx:t8 ;d8znok+ b, respectively. What are ktgd;zxz+88b : 3oxz nthe components of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3po-uhybmcq 5 .cooa) u 0l00b+), respectively. What is magnitude of t 0 .hba-u)+bq yocc5u0olp0mo he sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitudd2 f6x)wiado f)y*t)ye of C ?w2oa))fti)d dy6yf x *

  A car travels 20 km West, then 2r euv.s . jrgm9; hbjtll8t,.* w*ecx60 km South. What is the magnitude of its displa9jlv.lte..s*c ;u ,hjm 8b rx*tgrew6cement?

  Three vectors, expressed in Cartesian coordinatespi(a*e7p,dpv4e,3vkh ng , az, 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 coo f13cuhfb 91b6obb qps*56bnqrdinates, 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 ,1-e ni-k) o/yebtr5l6dpm lethe magnitude of vector C = A -mlp,6eer-l5od-/)b ek1 ti ny B ?

  A runner runs halfway around a circular path of radius 10 m. What is lgg2e/kh,zl ,: eqo (pxr27qqthe displacement of the /eo(k l q7:,qxr,zh2pegg lq2 jogger?

  Two forces are acting on an object as shown in6. uvh/2zhb(aej n h2z Fig. below. What is the magnitude v eanz .hb26uj2z/(h hof the resultant force?

  Two forces are acting on an object as shown in Fig. bev*9vxoj t+z7 *xu ys(plow. What is the direction of the result o*7 uvx*y v9jxt+zps(ant force?

  Vector A is 3.8 cm long and points algsmm;8oi(n9hnw : y km,l;5c2.sp w eoong the positive x axis. Vector B is 7.7 cm long ak2gws;wn y(mi8: o9c ;pm.5em,l oshnnd points at $+55^{\circ}$ 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 86 cm lo,l)x axa c4)umng and points at $30^{\circ}$ above the positive x axis. Vector B is 17 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 horizontally with an initial speed p+ pgivoqo:d )g-hg-+of 28 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 3.8 s. What is the height of the cpg-- gih)vq opod+:+gliff?

  A girl throws a rock horizontally, with a velocity of 12 m/s, from a bridgeja33v0ait 9 oj. It falls 21 m to the water below. How far does the rock travel hojia oav9 t303jrizontally before striking the water?

  A ball thrown horizontally :7f; ez9jbxx++b drvgfrom a point 21 m above the ground, strikes the ground after traf e+z97jbvbgxx d:+r ;veling horizontally a distance of 15 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a sptjo 83p2n-d-5j;rqovrh q n7i i5 0uebeed of 12 m/s at an angle ofbe- rqoihtjujo2q8 r07v-5dnp 5i 3;n $20^{\circ}$ 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 9 m/s at + / vuma0+s9wf 5pkcuuhc4r9 san angle ofsrhwc+as 5+/u0uu9m 4 vpkfc9 $18^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 39.3 m/s atyf (*1x m6xom9 *f.ivfd9j tgl an angle of $42.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an init ypc9,5ns0h hbial velocity of 57.9 m/s at an angle of $29.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angw7facz: u9l*mle 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 apnj-ks qo3 3b(coak;a*: dy b1t 18.1 $m/s$ from the roof of a building 39.9 $m$ 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 of 4 y9cmsu:2r ,4dn8qptufpb 9e97.8 m/s at an a,tq 9fd : 4u9b8pc snpm2ey9rungle of $38.1^{\circ}$ 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 .fd,t(w8ys5 y8gl nza4.0 m/s. If youz8dt85 an.swyg lf (y, 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 be

  A plane has an air speed of 200 m/s due North, aa )kv+lnkjm2*oj) k, ind is in a wind of 50.0 m/s to the West. The plan )2kmkvk,jl)+in j ao*e's speed relative to the ground is

  A plane is flying due Souif,lf a/9vym. th ($270^{\circ}$) 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 speewleo 37 (:glmed of 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 fires a projectile with speed 50.0 mr;8-a b61 ul uvwar:w6hgcsk 73dy/egon1-u p/s in a forwarw-1y3ua 6d6rg-18ucp ahu:vgnws;r / kle 7bod 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 8ygn17 r9yma x6pn1x p4r ga0( d*y)n+ftba5t f.0 m/s, is directed across a river with a current of 6.0 m/s. What is thet1 )(fmtfrarg 5ngxp n0p ab*7yy6xn941ya d+ speed of the boat as it crosses the river?

  The driver of a motorboat that can move ato+7 wo totd0 x+xs,4ia 9 m/s in still water wishes to travel directly across a river 0.7 km wide in which the current flows at 4.5 m/s. How long will it take to cross o7t xotod xwa+4, 0i+sthe river?

  The driver of a motorboat that can move at 10 m/mee ojw09:3w rs in still water wishes to travel directly across a narrow straite mwr:e3o0 wj9 in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acro8//s bpq5buq2an9d(w s ss s c4t(+eeoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream qo8 eess(c(u4 /5/nd2bp qs+b9sawts480 m. How fast can she swim in still water?

  A swimmer heading direb xt+pk;ahr . /s34(unvv2ae uctly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 44 pes; kuvvt.rn3/aa+u2(xh b 80 m. What is the speed of the current?

  A boat, whose speed in still water is 1.71 m/s,(52xux ,zykejl q:7 vtu+.ja s must aim upstream at an angle of 7.:z, a+xesuqukt 5yl j2jx(v$14.6^{\circ}$ (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)  $m/s$