Which one of the following is anv1mfwf 0uo.-7 w0jik x example of a vector quantity?

  Which of the following operations will not chang:flus rj s 8u7q3:4lx-dp*mkie a vector?

  Which of the following is an accuxfqqklz)ez)i h s8/*8 rate statement?

  The resultant of two vectors is the sd-g7uh y.4k* m2hk:s s,chor hmallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m 4phdwmyq2 :-v ;iiu s +* w21vpd6pn )dqpnf.nand 7.0 m, respectively. When these two vectors are added, the magnitude spi;y p2u1 . nq :h4p)v2*- +wnwpqddm6dfnviof the sum

  Two vectors, of magnitudes 20 and 50, are added. 0zznct-; 5ua,7k2w ylzync b *Which one of the following is a possible answer for the magnitude ofu-c7by; nyz*c20a 5z w,nk zlt the resultant?

  Three forces, each having a magnitude of 30 N, pull on an b7y:6 pvm;k nyobject in directions thamby:pv;k 76n yt are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the uz yj p3mk;75afnknown vector is

  Ignoring air resistance, the horizontal componejsp9/ teo; hlh2hnn1 7nt of a projectile's velocity

  A ball is thrown with a velocity of 20 m/s at an ang)i6l ch)f gmw1m3ol+ dle 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 comp(uw9qblx1twk -vv+w ,:1 toxponent of a projectile's accelerationw1 x9pw,wou:( lvqv1+t-bxtk

  A soccer ball is kicked with a vtwwgii414 mjfc)+f /ielocity 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 toh2l;nkhz)/a cvp, g:u the velocity vectorc;az, n pu )l:kvh/h2g,

  If the acceleration of an object is always8xj) d0tpt-6ktls ,va directed perpendicular to its velocit-aj8s 0dtl6t,t)xp kv y,

  At what angle should a water-gun be aimed in order for the wat z6(g( ucs2dduer to land with the guz(c(d 26su gdreatest horizontal range?

  An Olympic athlete throws a javelin at four different angles above the s qsj8:+nvw.s pl*rbll*w2x7:guodpn 8 .n- bhorizontal, each with the-p wnn g.2sl* 7:qw.8p*xndl ru8 +bjsl:obsv 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 t8je 6g wg4dob)t0ure 7ime. 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) wo67et)b0gud4gej 8 ro wuld be

  A ball is thrown at an originar :p9l tkq(0p pnjs(6gl 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 attempqqq*)ygrooyn /z:v(* t reaches its maximum height, how does its speed compare to its initiayqoqyoq/gvrn z): (**l speed?

  A stone is thrown horizontally from the top of a tower at the same instant agzw az(;bs4:w ball is dropped vertically. Which object is t(:wag 4 ws;zzbraveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the same instant a yxjw6fx5e *xmw27/s w second bullet is dropped from the same height. Ignore air resistance wfw67m/*x5exyjw2xs . Compare the times of fall of the two bullets.

  A plane flying horizontally at a s/:/r ,nsm h9ba4uxtfpv(ti t ;peed of 61.8 m/s and at an elevation of 177 m drops a package. 6.5 seconds later it drops a second package. How far apart will the two packages land it:9 nt4rb;/h(/a vx,pmf stuon the ground?

  A package of supplies y+qn.y ,crk b:is dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, try:qy .nc+b, khe distance between the falling packages will

  A pilot drops a bomb from a pe:q)d8l u*k:trm bz *blane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizonl *)btdbzemur q8 :k:*tal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of that ont okg3 j-7n-ns Earth. If you hit a baseball on the Moon with the same effort (and atstk-ng37 j-no the speed and angle) that you would on Earth, the ball would land

  You are traveling at 0 l9usk pq(8np55 mi/h in the +x axis relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velk (np s809puqlocity of your car to the other car is

  You are trying to cross a river that flows due sgl-tmx0)ak8 ,5lg(7 p cc d* fc. 1tyhjbn3vcoouth with a strong current. You start out in your motorboat on the east bank desiring to rea )gkxnc0b8chm5-t .o1ajv dftlcp 3cyg ,7l* (ch the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in stil5sg8k:i 7m hasl water. How much time will it take you to move 12 km downstream, in a river flowing at 6.0 7mis:5gk8 haskm/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below fe292twqf4a b the +x axis. The y component of A w292 4bfeatfq is

  If a ball is thrown withdxd zf8a0.* l7jv jgire1 nw8) 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 zn.pjwkqc,3+h .fhjtx3 9b4 ta direction north of east and you end up 2.0 km north and3 ftn .h+qk,4j3jt. h zpbc9wx several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. z gg vuz88*ro+5irdg ,The x component of its velocity is 8.00 m/s. The angle between the direction of it+, dizg5 8r zg8rvugo*s motion and the x axis must be

  A 400-m tall tower casts b r2tnrl-8wr 1 4gjhf;a 600-m long shadow over a level ground. At what angle is the Sun elevated abh1 r lgw4ftr2;n8r- jbove the horizon?

  Two vectors A and B have components (0, 1) and (-1, :kgoty5oo:(vuslvo h,+7 wh/,zg0hz3), respectively. What are the components of the sum of these two vectors?, hklz5/:(o7,sy:huow0 gt+vv ohogz

  Two vectors A and B have components (0, 1) anx byc 63qva(,vd (-1, 3), respectively. What is magnitude of the sum of these two vectors?(36 vxayv,c qb

  Vector A = (1, 3). Vector B 01y;hbl blw wgd,z+y)= (3, 0). Vector C = A + B . What is the magnitudegyb ;yh0)l1 dw, l+bwz of C ?

  A car travels 20 km West, then 20 km South. Whk4f1v)b ysm7 bqn ;.joat is the magnitude of its displacemen7jb f mvknsy 4ob;1.q)t?

  Three vectors, expressed in Carte8k.nb+3tox bt v *tr+tsian 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 coordar be/s t/zgr;pswth07;k6-nft2/u ninates, 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 magnitude o ;3ux5srs id2af vecdu 2a35r;xss itor C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What is the dd(3+jeif sh) q aw.b1uisplac wh.bse3j)1 u qidaf(+ement of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is the magnituxd/ozu 1gq ./bde of the resultant forceog/.b1u/ x dqz?

  Two forces are acting on an object as shown in Fig. belirlwb.2 h v6y d j6:ej3drl+x3ow. What is the direction of the resultant jj2b3hv6l6r:er +w 3y.ddilxforce?

  Vector A is 3.0 cm long and points along the positive x axis. Vector B is 6.4 cf-.sc)l+c nlu he;ey2rs ),u qm .,+2l;ch u)eyseqn-rs cu)lflong and 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 75 cm long and poin2d-xrh iq-dg)ts at $30^{\circ}$ above the positive x axis. Vector B is 25 cm long
and points along the negative x axis. Vector C is 37 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 27os6 5ir.wtq k,a m0hm- 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 2.5 s. What is the height of the06o kiaqsm-rh .m5w ,t cliff?

  A girl throws a rock hori u +kdu5*h/twkfe 4w8izontally, with a velocity of 19 m/s, from a bridge. It falls wtif* u8 kdwu4+/h5ek12 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a g0k kgx( v.2iadw2e4xpoint 23 m above the ground, strikes the ground after traveling horizonta2 e2.ixxvdg 04w(kkag lly a distance of 17 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed of 12 m/s 3.jhv1ao11uhq*.wy b1o mn r nat an angle of mqj.1*11y3wnbuo vho 1anr .h$20^{\circ}$ 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 a)e v9c ilfj5/of 10 m/s at an angle j )laf9i5v/c eof $37^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 57.6 m/s at an ck:+-a;qsd 8 wtn*ry rangle of $20.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 44.9 m/s at an a6z qb xcubcq;r;3 -3gx;y,bo xngle of $46.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fi inw (2s*ej0mvred at 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 fxmn wslh3*x.,04obg 1b6 aqd 20.3 $m/s$ from the roof of a building 49.9 $m$ 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 inihveu2c( 0-vvdq*1 e iotial speed of 37.9 m/s at an angle of02hqveovve1 ( c -dui* $45.9^{\circ}$ 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*y41yzy)rr,h zc; *p* r4jay qrq dtfb1 4ip*y 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 bzdq *y 4*yfr,j1)*;1*rby4y4tr r apqich zp yy 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 w1 wswj0x yl*-kv;9rx+aqd4 q.0 m/s to the West. The r;q xdl+-qw0 yjkaws1x9 4wv* plane's speed relative to the ground is

  A plane is flying due Sou-)cna/emwzu 9dd:+g ,eul 0x bth ($270^{\circ}$) 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 33p8t 5x3nje ssh2sb .,xjpet 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 2d9ehld 5va2oq 6div,.0 m/s in a forward directiv v2 a eih6qd5,dlo2d9on $30.0^{\circ}$ 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 2:tgtb 8 oe12fltb(endirected across a river with a current of 6.0 m/s. What is the speed tlfet8bg1e t2b(:2o nof the boat as it crosses the river?

  The driver of a motorboat that can move at 13 m/s in still water wishes cqg:ea)h9zvve/oa7na/ w7. ato travel directly across a river 0.6 km ena7ag:h acqvvzw/.e 9o/a) 7 wide in which the current flows at 3.6 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in still gkfixw- au;j6dhh1 8h0/ gu1w water wishes to travel direc 8xhu gh1-i/h0j6ga ukwd;w1ftly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream should the driver head the boat?

  A swimmer heading directly acrf4hm6 m5t u+zfoss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480tfm+6mzfh 5 4u m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank.2pfupu3 pj 8d in 6 min 40 s. She is swept downstream 480 m.. 3pdfpuujp2 8 What is the speed of the current?

  A boat, whose speed in still water is 1.11 m/s, must huhs-*w .+cqc2 5ekpi aim upstream at an angle of 2wsh+qkc *hu5ei .pc-$29.8^{\circ}$ (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)  $m/s$