Which one of the following is an 4.v0m0fx*csyq 9lea u example of a vector quantity?

  Which of the following operations will not change a vecls-o ms.zq)j gx)s 13otor?

  Which of the following is an ac)k n7 f/+kcy*efkq2r7 q2ur vlcurate statement?

  The resultant of two vectors is the smallest when the angle betwee gwwc of07p8e;n them is

  Two displacement vecth 2q9ilp( 0. v,oev.0nxmhvpnors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magn .0ohplevmn (qxv0h.piv29 ,nitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which h)l6(etl ;ekh30/gj0dydnh2 jwwnz /).zpvo one of the following is a possible answer for the magnitudenhg/t)k zehwl /p jdzleyo32v .0j6dn;h0 w)( of the resultant?

  Three forces, each having a ma3vpcbwv61 r8als47xxgnitude of 30 N, pull on an object in directions tb6as 1 47p8cwrlv x3vxhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the uyji 1gn7 hj2j4cs406,j q yqwtnknown vector is

  Ignoring air resistance, the horizontal component ofwgjl;jw p p-5,u2yxu0:gj *x p c3k(kf a projectile's velocity

  A ball is thrown with a velocity of 20 m/);6kms 1qmbfgs 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 projep; 1ef4d59yu-z;yn y 5,:odn excmzsuctile's accelerationu u5ym ;:e dc,z41 -5xfyp ys;znneod9

  A soccer ball is kicked wie:b 6vsv8 0y0t3edrk ith a velocity 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 the v e ,,mop87grymjpy7 ydi,(su6elocity vectorprm7u(i 8 jp,ys,yge6yd7m,o ,

  If the acceleration of ab 0vdj r,5,i8dn ll6xgn object is always directed perpendicular to its velocity8 ibl,d0 nl,xj65vdgr,

  At what angle should 1zl x.ss pe1i) d5(aija water-gun be aimed in order for the water to land with the greatest horizontal ran pd e.x(jzia)5s11ilsge?

  An Olympic athlete throws a javelin at four different angles above the hf:,ya:i2 9yti3d 1cd8bf sp8uu5a ncforizontal, efduy au1 ip2i,a5:d nf8fc9y3bs: t c8ach 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. Ifz831 t:wzq8* ngz x0upw)dbjyay5f 9w the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to you9ab g8x3 pfw)tu n*81dz:wyy q5zz0w jr first serve) would be

  A ball is thrown at an original,(tl)6ltb8a fja xd tjie7(h2 speed 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 reachrqw- y p7zjeoc+ i8 c2ez(s5r0 o.hl1ues its maximum height, how does its speed compare to its izwop j2e( h rc.y8oz0e1 q lcisur5-+7nitial speed?

  A stone is thrown horizontally from thego 8jt6xg i eu98 bl-eznm9ofw2skf1s)q ,g5* top of a tower at the same instant a ball is dropped vertically. Which object is traveli6n91u)oxlkwm fz8e5 8ji*gtf- so9b ge, 2 gsqng faster when it hits the level ground below?

  A bullet is fired horizontally,* jf aiy2(icl3 and at the same instant a second bullet is dropped fromicf a l3(*yij2 the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontarq1gegi+xe2*nsote 8/pmbg 0vtj99 +lly at a speed of 62.6 m/s and at an elevation of 204 m +t+gi2b*rqv 9 x og g0jnet1s/emp98edrops a package. 5.2 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a plane, and one second later (9zcld jf9 pzpvi70+q8obmcc -et :h2a second package is dropped. Neglecting air resisvczqct(:279h8-0 fpebc jip9ld+zo mtance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontalbeg9wnq (w 9lsl dm-v(9il)p(ly at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locatiw) dgblpil(l-neq (99 wm9(vson of the plane will

  The acceleration of gravity on the Moon is only itn8po.*ef lofd qb8p .5 3mh9one-sixth of that on Earth. If you hit a baseball on the Mdto m 3p8 58eo9fi..nhf*qbl poon 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 t hoqmb6q)eu ucg7m42z9(8etraight, level road and pass a car travelhb8)4u7ec( ueg tm62mqt9q oz ing at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a ri(hpl81s ym5k; ,spwbgver that flows due south with a strong current. You start out in your mo,5gmp y wlk ;b1(sp8shtorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still waterpc+ -t3 0wngmu. How much time will it take you to move 1c n-m0gup3+ wt2 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at iw z.dudw8a 90an angle of 30 degrees below the +x axis. The y component oai.dudzww 0 89f A is

  If a ball is thrown withsc9iys d. w/c. a 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 a straight line in a direction north of eass cj5osb-q3a.x8pg 3 st and you end up 2.0 km nos8xosjq3a-b 35gps c .rth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. Tk6 maxg:y0rct+,* b 2/kjihbvhe x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis musy 0xhmb2k bt:ra6i/* +kj c,vgt be

  A 400-m tall tower casts a 600-m long shadow over a les5 hpmwvmvec.;2 w /4(dv*oj xvel ground. At what angle is the Sun elevated above thsx mhv4j dcw/5om ;*2vv(w.epe horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What axw v1m-bxm / *jb:dbe(re the components om 1x/*vxmbjwb-( d: ebf the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3),ynx3 /1(-loilbvu eh 42ni4nbw t.t8o respectively. What is mwi4/hn-(.o1lt iub8o vlnxte ynb23 4agnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magnitjqnbm5 wh6p : 6huowk (9ev45iude (566kw5q mpih v9 wjohb:4eunof C ?

  A car travels 20 km West, then .bb7 zf*xri;i(he9ew aq 4mi;20 km South. What is the magnitude of its displacezwfbbrhxq;e .79;i imi *(4ae ment?

  Three vectors, expressed in Cartesia7bb hza )g,kd5r7ij e.n 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 Cartesp2:v 3jcsw p i7y/7zgrian 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(yhfg:s3 p1x z.0), what is the magnitude of gzyxh s:(3f1pvector C = A - B ?

  A runner runs halfway a hhhfur*v0g +tjq()t8round a circular path of radius 10 m. What is the displacement of the joggvq 8h(0h*u thf+j gtr)er?

  Two forces are acting on an object as shown in Fig. below. What is the magnitudchs) 8, zcna3 d08hof )dr7ncxe of the resultacc)8xha3 8c)nos rf0zddhn 7, nt force?

  Two forces are actin7z:y1 sjhzt(9ysasiy+rg 8 d( g on an object as shown in Fig. below. What is the direction of the resultant for yrsd1(itjay9 zh:s7( y+szg8 ce?

  Vector A is 4.9 cm long and points aloyz ; egls.;/tgsixa2v( yfm(4 ng the positive x axis. Vector B is 9.2 cm longfa( i;e/ zy tgslvy;(4xm 2g.s and points 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 75 cm long and poi3cdb 0qswur49 0rfz:ants at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 39 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 24 m/s from t5b ;-ar+dsl ji/qlsebw-1nv+ he edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 2.9 s. What is the height o-5rn;/q1wjs b + -isabv+ldel f the cliff?

  A girl throws a rock horizo2; *z5e r2di4yqgnqatntally, with a velocity of 16 m/s, from a bridge. It falls 18 m to the water below. How far does the rock travel horizontalld4 ;*2qzer5gt i2yqna y before striking the water?

  A ball thrown horizontally from a point 28 m above the ground, +bbgn,ss82 jc+otp + i)oi,l vstrikes the ground after traveling horizontally a distance of 22 m. With what speed was it thrown?b sojvot s2i,+ )lpn+gci+8b,

  A jumper in the long-jump goes igrnv0 2*/1l i8 pwaebznto the jump with a speed of 12 m/s at an angle 2ezwibp* an8vrg1 /l0 of $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-ju1o2ql;i9 e1ug :snsa g ek7wh4mp goes into the jump with a speed of 11 m/s at an angle of 1ow7;he selaki14n s2:u q 9gg$24^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 49.8 m/s at an angzs-t(u8q*h *u 1 ig-kicv- vaule of $48.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vel 5ad,zw* evzqn4u:h 3docity of 58.4 m/s at an angle of $48.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an annr7 d2yal+;h a-wwz b8gle 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 shotuf03 .vh+c8xq fnq;vz c f+5ie horizontally at 17.7 $m/s$ from the roof of a building 42.5 $m$ 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 an0p 3d,pejm hsis)1ie / initial speed of 50.6 m/s at an angled p,siih )/0ejs31mpe of $38.6^{\circ}$ 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 ym74bz9 6-i vkhir jts nt12j7can run a 1500-m race 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 its hyj49tii zk7m162-7jrnbt v would take you to finish would be

  A plane has an air speed of 200 m/s due North, and is in a lm9+ zu (t+kzkm+xaw+wind of 50.0 m/s to the West. The plane's speed relative to thel zk+uxawz+ m++k9 (tm ground is

  A plane is flying due Soutk nj -t4 v4giuz8t46pch ($270^{\circ}$) 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 spmb 1scuhy: 1q5 (v+gc (xb3avdeed 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 / *odr+cihk )a.ri3 dnhorizontally fires a projectile with speed 50.0 m/)ra+h.ndi 3ci r*dok /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,*aif+u ) est k2*mc5d5namm0m is directed across a river with a current of 6.0 m/s. What is the speed of the bu )5sdm2menikaft*m5 cm+ a* 0oat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still water wishes tbxwq 92f vb2;)ganf7i o travel directly across a river 1.2 km wide in which the current flows at 6.5 m/s. How long will it anv9qbg2x7 bfiwf;2) take to cross the river?

  The driver of a motorboat thhnek ov 3q*: :1 e.v)qri96r kayuf8gjat can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstreajr1 fr3vhg 9kn*qie6 a.k v8 oy:)uq:em should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppoh )q( jqkv:bd*f0p7i 7 amxhg,aq6j-ht 38bbosite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still wat h3t-mf)hbk*07bg8dqoqj v bxhj:qa6ip(7a ,er?

  A swimmer heading directmes we d16g2l0ly across a river 200 m wide reaches the opposite bank in 6 min 40 s. 10 eelg 2wmds6She is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.95 m/s, must aim upstream at an angle tmaj+ il.)r( ns+ wk)kof sa)inltk +( w.krmj)+$19.4^{\circ}$ (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)  $m/s$