Which one of the following is an example of a vect k(/glupl-i9 wor quantity?

  Which of the following operations will not change a vectip e6;g5 oice,w79gl4u xsjd0or?

  Which of the followik3g(omz sxk1 ,f00a egng is an accurate statement?

  The resultant of two vectors is the smalle sgbb;9b equ+k,:w(n6 qycr4tst when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m4.fz;crz ; wvl, respectively. When these twfwzz4l.;c ;vro vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the .ee0iyh e3. mifollowing is a peie ..3me0 yihossible answer for the magnitude of the resultant?

  Three forces, each havingmh0 -+u zso;9khr) nhu a magnitude of 30 N, pull on an object in directions tha ru;)09+hzuh on-hsmkt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vect,lexm b 20ry/mbq *ejct.-/fp. atq s/or is

  Ignoring air resistance f3h,nqvn1x qig/8t/ozbfk5m t f7*5d, the horizontal component of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at 4;c8lxpx g(bg yvg9s*+ca,uian 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 hc( j8yjeo e1wmy .m: 5qqj.n6accelerationne8j: mmoy.wj5qh61( yqjc .e

  A soccer ball is kicked with a velocity of 25 m/s m2a w ;zkex/ldnm+v+*w3 x.ydw 26g xnat 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 dire 7pwirf 5v*z1kt6x9m(ntrj;6af,zt u cted anti-parallel to the velocityf9a 5*rm,pt f(1uxjvwk n6r7i; t6 tzz vector,

  If the acceleration of an object is always directed perpendicular4jp+ pe.evm;(v -fasl to its velocity, jevav . e;p(4s-+plfm

  At what angle should a water-gun be aimed in order forpro+ 3fbfozx56k 1vw2 the water to land with the greatest horizoz2x5fbvokpr+ 1o3 w6f ntal range?

  An Olympic athlete throws a javelin at four different angles above the horizonvsdkejt-xeuii72w e)6)i81i tal, w e28x7di)tv)eii-uij 6esk 1each 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 balr9 9la m*v x -f(e*20uouqecoll leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would -veo q0lm laxr(29u*o*c 9fuebe

  A ball is thrown at an original spe5: s4jsv8ftjx*se7cz*o mk4oed 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, hobs, b4j/ycm*vb,u2 ypw does its speed coycb bu*mbypj v2s,, 4/mpare to its initial speed?

  A stone is thrown horizontally from the top of a tower at the samewu ,2y.sy9rvd instant a ball is dropped vertically. Which object is traveling faster when it hits the level2 v9w ydry,.us ground below?

  A bullet is fired horizontally, and at the same instant a second bule b5xy00r 1/1fnuic rflet is dropped from the same height. Ignore 1xfy 0un 1 /ib5efrr0cair resistance. Compare the times of fall of the two bullets.

  A plane flying horizo 2k:f5uqo5:ecqd dg8rtmey8:lsv/4 i ntally at a speed of 41.6 m/s and at an elevation of 185 m drops a package. 5.2 seconds later it drops a second pacc m:eq 8:e5r:y 52 d 8/t4ogikdlfuqvskage. How far apart will the two packages land on the ground?

  A package of supplies is dropped fr.xuja r hi5r4v( fu,4 jr7fb+(3zudgj om a plane, and one second later a second package i4jx(r .bhrv7+jzf 4gui j, 35rd(fuuas dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a pla +0vckf:gwp/+ba* ee)f ix ft0ne flying horizontally at a constant speed. Neglecting air resistance, when thbp):fk fgatvix ef0we0+*/+ ce bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is onlvj/94pvmo3ad7 crai dr k:;m ;e5q y2ly one-sixth of that on Earth. If you hit a basek ajv32 r ;ymc/p id:ad45;rqv7ol9em ball 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 +x axis relatghp)d jzxv m(2sd4e ht:bv 52*ive to a straight, level road and pass a car traveling at 45 mi/h. The relative ve2 )dtmjx5(s*bg2 4h vh:pzdv elocity of your car to the other car is

  You are trying to cross a -rk, .rg d0 nea+f/.zvyaf8gvriver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the wevenk z-a. ,rvdg+arf g.0 /8fyst bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Hk+v1uyz-atn/ ekpl ,) ho5.kvow much time will it take you t+/ . ,1 znpuek5akovvh)ky-lto move 12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degr4xjw1a h ;bk/oktuk-4 ees below the +x axis. The y componk/ ;tkx uk4awbj -41ohent of A is

  If a ball is thrown with 8k:za/,fq 6ybag3g qua velocity of 25 m/s at an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in(n yc t 6pgxm6l(r(vuy*fr1sxa c6(5n a straight line in a direction north of east and you end up 2.0 km north5(16 u(6txr(nf g*6yxpymvn(cr s cal 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 co; .xk8zz2gimfmponent of its velocity is 8.00 m/s. The angle between the direction of its motiz.2fx;g z8i mkon and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At 5tzuced n 1(+kwhat angle is the Sun ed5uc1+kt enz( levated above the horizon?

  Two vectors A and B have components .sscy3sc-em0,b3 ynins-+ fx(0, 1) and (-1, 3), respectively. What are the components of the sum of theses 0ce.nicss --f bs +,m33ynxy two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectivelyt.ji( osr3z s mu3kw66. What is magnitude of the sum of these twow33si.msk jrtu(zo6 6 vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + 9ei, tbs 1mst2g6d7h bB . What is the magnitude of e s9misgd6 bt7,bth21 C ?

  A car travels 20 km West, then 20 km Sout*x o1jc -h1pzhh. What is the magnitude of its displacement?1hxc-z ho1*pj

  Three vectors, expressed in Cart+5jmzt s*,p fcesian 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 Cartesian coordi zg/hd j9tv:)xnates, 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 4p:395kgduvm v9jj txw(g/ig = (+3.0, -8.0), what is the magnitude of vector C = A - ug t 5wvigg9/d3 9 vm4jp(:jxkB ?

  A runner runs halfway around a circulfbfj 46i)j4jjq ib)0far path of radius 10 m. What is the displacement of j4jff jj)ii46q 0f)bb the jogger?

  Two forces are acting on lhx*ch i7 q4/man object as shown in Fig. below. What is the magnitude c ih/*hl74m xqof the resultant force?

  Two forces are acting on an obje1n-3 /ii czkmcct as shown in Fig. below. What is the direction of the resul cnkii -z1m3c/tant force?

  Vector A is 5.4 cm long and points along the positive x axis. Vg2o +;k*k-c4 -- oopj 4uykdtlad t8kkector B is 8.0 cm long an-tk+pk8a4o kck; d oo-4t 2*- kygdjuld points at $+57^{\circ}$ 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 79 cm long and points 7 q.9 v o t*jx)6*fwl9mvojtlkat $30^{\circ}$ above the positive x axis. Vector B is 21 cm long
and points along the negative x axis. Vector C is 30 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 w3so6ip h4lf u.0 il5knith an initial speed of 22 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time 5l6f.un 3i poik40hslfrom the top of the cliff to the bottom to be 2.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 14 m/s, from a bridge. zi+*7vs8qa qujjmbb 8;kt+ 9dIt falls 20 m to the water below. How far does the rock trav z b*;dq uq+bsav+mt jij8k789el horizontally before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, strikes the vl zih0ea;2h) ground after20zve la);h ih traveling horizontally a distance of 23 m. With what speed was it thrown?

  A jumper in the long-jump gvlrxw8qhx.8 ( oes into the jump with a speed of 12 m/s at an angle oh8(lx8rx .vw qf $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jum9ne8yz3d7(jhok nne )p goes into the jump with a speed of 14 m/s at an angle of)znnd k8nyh 93( jeoe7 $32^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity 0h0bder;wd**y* sjd v:m i:rnof 42.2 m/s at an angle of $21.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial6z9d cp1jhw f/ velocity of 55.8 m/s at an angle of $24.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an aeiy4yrsnuht+88,/d c9b l 8m sngle 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 23.jd ;q.nxyl*:xnj9ja 40 $m/s$ from the roof of a building 32.9 $m$ 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 ( lt.u9q4ogxw53.0 m/s at an anlx 4wt.ugq9o (gle of $45.7^{\circ}$ 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 ptr25xfhz .4q: at 0hyxn.r9tof 4.0 m/s. If you ran the same race on a day when you hatn. pz9f :t2h.atr4xq 5xr0yhd 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 wind of 50.0 m/s tojrl;ke+(4z sza(k t :j the West. The plane's speed relative to the ground : 4j(zl(jera;s k t+kzis

  A plane is flying duez v9q*5ko dsj: South ($270^{\circ}$) 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 iw rv+1bw:pgnqtbo otj.z3gdvu5(4) 8 s 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 s/dq wicsme,fg8y( ,y9;wfl p7peed 50.0 m/s in a forcyif ,;gmdf 8we p7l/,wq(9ysward 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, itmk9id+e6 rw r,,) ebrs directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crossee i,+w69dbt)krerr m,s the river?

  The driver of a motorboat that can move at 9 m/s in still water wishes to t4fb+ ni7q6n lqravel directly across a river 1.7 km wide in which the current flows at 6.8 m/s. How long will it take to cross the rl +nq4bqfn7i 6iver?

  The driver of a motorboat that can move ad1oq9dca*. dh 3h ozgz1 2sb8st 10 m/s in still water wishes to travel directly across a narrow strait in which the current flozd h2 1zqossb38cdo.gd*9ha1ws 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 t2xc; ed2 c y7;dkcxqm+he opposite bank idd7ccxx k2 em +2qcy;;n 6 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 oppo ia4t1e6drm+0 uz1. kxp-ua xrsite bank in 6 min 40 s. She is swept downstream 480 m. What is the s6rr4a1 au1pi-u.mxk0+ t dxezpeed of the current?

  A boat, whose speed in still water gocp+k2 wm nf;y.u* m b4l3s:vis 1.82 m/s, must aim upstream at an angle ofuy3s *kfpcmmw4gbov:n2 .+ ;l $32.0^{\circ}$ (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)  $m/s$