Which one of the followinwf+dmz*1vh8 kg is an example of a vector quantity?

  Which of the following operations will not change 42ahx1p5 kght a vector?

  Which of the following is8ul+-gir j2ec an accurate statement?

  The resultant of two vectors iss *hvyvk)i27 )h j;p kd8fw1y(vys u9i the smallest when the angle between them is

  Two displacement vectors have magnitude8pl1f65foi xsn (xl(zs of 5.0 m and 7.0 m, respectively. When these two vectorslslo5( pfinx86(1zx f are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follow *wzouvutk48.mnh8 - ding is a possible z8n 4odt u 8khu.wvm-*answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull9dx-zib n hr. vzm1-t: on an object in directions that a.:rnz 9zmbv -td i1hx-re $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, ddqd9fi 2a22- 2bqvs2ho(qg ew/m * qfthe unknown vector is

  Ignoring air resistance, the horizontal component of a projexmuty+/- +*0y mmwyz sctile's velocity

  A ball is thrown with ky a0um6 ams8+:6dug.nss.nf 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 of a prcl- u v2r9 b9xml7or8pojectile's accelerationro2-7lx 9crl98 mubv p

  A soccer ball is kicked with a velocity3luqtr.hg d -q9/l(ka 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 qh3y h-tj9mflag;6 x0of an object is directed anti-parallel to the velocity vec0yhjmftg xq3 h-l9 a6;tor,

  If the acceleration of an object is always directed perpendicular to its velocitv mo.ih*u wk li7lbsy0l)w r6er(va3 t1)t8 e6 hai)706it)6bmwtws 1e8ulvel 3*y(vlko.r ry,

  At what angle should a water-gun be aimed in order for -)ysvchc1 zir.+jknb2n )h o7 the water to land with the greatest horsn.21vo-hi hc kznj )7cb+ )ryizontal range?

  An Olympic athlete throws a javelin uo,eb2h 2zth/e1 8jqrat four different angles above the horizontal, each with the same speed:,he/82ozr1 tuhjb q e2 $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 leaw:l(; dw u2nxfves your hand with twice the velocity it had on your fir;w lu2w:fx (ndst throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/s at an angle fe)ca p9rq 8a7of $35^{\circ}$ 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 attey+ey2(yyv1p,fk/ w b fmpt reaches its maximum height, how does its speed cobykyyy/ f+wef, v 21p(mpare to its initial speed?

  A stone is thrown horizontallyvaihog*6 4qm 8 from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hi 64*oqm8ahvig ts the level ground below?

  A bullet is fired horizontally, and at the same instant a second bult*f;p 1yygu)p yg1o9 qk15notlet is dropped from the same height. Ignore air resistance. Compare the times of fall of the two bullets.onkf gup 1 )51* 9gqyyyto1;pt

  A plane flying horizontally at a speed of 5apw+3-m/iqn+cbe 9m- 5wk cuf 9.5 m/s and at an elevation of 230 m drops a package. 6.3 seconds later it drops a second package. How far apart will the two packfe q3bccm+/ 5+kw-aupw i-nm9ages land on the ground?

  A package of supplies is dropped from a plane, and one second y 7i xhs/v50zblater a second package is dropped. Nbiy/xhzv 75 0seglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a 1s z*kf,7 v *xnu d 8vqnk6wjp0m6c6odconstant speed. Neglecting air resistance, when the bomb hits the ground the horw6 1u8 n n*6ddvj,7fvqx ksc 06mzop*kizontal location of the plane will

  The acceleration of gr q7d 0:imn4jva4 bcj;bavity 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 you would on Earth, the ball wo;7bjn4dcbi0:mjq a4 vuld land

  You are traveling at 55 mi/h in the +x axis relative to jocq4 ykn f-p29yry)y ).f l.ga straight, level road and pass a car traveling at 45 mi/h. The relative velocity of your c n 42f-p)yc.g j9yky)r.oq ylfar to the other car is

  You are trying to cross a river that flows due so( 6cx7 faoskz5uth with a strong current. You start out in your motorboat on the east banko5kzfc 67x (sa desiring to reach the west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move l 2l4 - +ob:qtklxp3ydy c6a8h6h-gcaat 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at q tac6lhoh32p-8y4da gy+c :kx6-l bl6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. The *ynk:ko8n2esusj 86ly component 8nlos 8*ky6s 2jk :nueof A is

  If a ball is thrown with a velocity of vh)66 6, gyvoxn b ww4lq ;qn3f4gxcn625 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 lin ux;bq+2o jyfuk tm43;e in a direction north of east and you end up 2.0 km north and several kilometers easbo4tju+f3yukm;2;q xt. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. Tc/cylpxwun-/r2 h / ,yhe x component of its velocity is 8.00 m/s. Th hpwc,y-x/lyrnc//2 u e angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground*bv z v8o l0n/mulu.4v. At what angle is the Sun elevated above the h unu0. 8om*/vbv lzv4lorizon?

  Two vectors A and B have componv9 0skdm8vsvgdfy. wu(v(3w+ 2z cz 0cfwas07ents (0, 1) and (-1, 3), respectively. What are the components of the s w8+svvaf 3.97zmw0kvc szc 0ud0(sgy2(vd fw um of these two vectors?

  Two vectors A and B have componen bi,x) 1ni(t4y q1sf;hl m3r p :iu3qs;.dyenets (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two v;:)mb x suqnyd1i 3s4hqy1it,r;e . (pef3 nilectors?

  Vector A = (1, 3). Vector B = (3, 09 rz+dnjn2(7un eb( hi.*shi y). Vector C = A + B . What is the magnitude of *nhd+izn . (ire hbs79 un2yj(C ?

  A car travels 20 km West, then / )*rog9yjxre 20 km South. What is the magnitude of its displacem)jyer g r9/ox*ent?

  Three vectors, expressed in Cartesian coo lzop+t3/ ;,sv3 ktprnrdinates, 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 Cartesiacs5 o2a08fr uoy: zqdsa:v) i0n 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 magnitudewjg8d/vf +9 ap*/np/xwq7 y ae of vector C = A p/ey jdw9/a+f wqga7/ *n8vxp- B ?

  A runner runs halfway around a circular path of radius 10 m. What is theqbs-dg 9k go.7 displacement of theg7d.bg -oq s9k jogger?

  Two forces are acting on an object as shown in Fm:dvj 9nni txshj0x)n9q9 6n6ig. below. What is the magnitude of thnn vsq6nd x9 j9ti: nm0x6hj)9e resultant force?

  Two forces are acting on anz yq wq;6u( kqnqc42h4c f:ur, object as shown in Fig. below. What is the direction of the resulc4u6,curzfyw4q2hq :(q ;qn k tant force?

  Vector A is 3.5 cm long and points along the positive twbvu (c44 nl :v-k:kyx axis. Vector B is 9.1 cm long and points at4t wcy:ku:vv (ln 4k-b $+28^{\circ}$ 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 point+e0pkyzjy e:; s at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 46 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 23 hu: +z qml22u9gvt-ldm/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 2.7 +v2:luu ld 92ztqgmh- s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 6 m/s, from a bridge. Igm x7xn97jn yqrre7ah-vt*16t falls 20 m to tyh-9nxern q771gjvra * 67x tmhe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a pointkuw3c+j3 bld5s: jnr0 29 m above the ground, strikes the ground after traveling horizontally a dist3: b+3njld u0jk srcw5ance of 15 m. With what speed was it thrown?

  A jumper in the long-jump goes intnirbem5: n ys/0i m40vo the jump with a speed of 12 m/s at an angle on 0mmi:ibe4/sr5 v0ynf $20^{\circ}$ 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 1rxcflory 5b+k( 33kv*1 m/s at an angle of (kk fr lc+o3 *x3vryb5$17^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocitquqrm 88kt8 1py of 31.0 m/s at an angle of $30.5^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 22.9 mb3ms7 q aqph 0j*fjc1f+v;k: u7srv m1/s at an angle of $44.3^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglnrb02*v/ letj.u c+lhe 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 17.5 thq- k.m.wg:l hbquilk/x0 9)$m/s$ from the roof of a building 36.2 $m$ 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 lidzr br-oqdj8o8 /b-a9-b+k pevel with an initial speed of 62.1 m/s at an angle oraokb-8 -+ /poqbj dir9d -zb8f $39.7^{\circ}$ 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 of 4.0 m/s. Ifrf,o: :9*,kh ylwoa wq you ran the same race on a day when you had a constantaqwlo,9h:rk:wo,*y f 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 to td h4(bork w;f.ktb2( fhe West. The planktr fhkbb24;.o(wfd ( e's speed relative to the ground is

  A plane is flying due Sou y *4,lbbahw+4q9gntww )j6 dwth ($270^{\circ}$) 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 syr ip. 3mem: c..8udmypeed 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 uu-;h s(ndlu xyd; pa3l66rx u2*aq9bhorizontally fires a projectile with speed 50.0 m/s in a forward direction l u6a3;pnqd yu h2a9 r;us6-xxul(* db$30.0^{\circ}$ 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 directed across a rsk j+qj9.f qrpvuu+/7iver with a current of 6.0 m/s. What is the speeku++9sf vur.pqj qj7/ d of the boat as it crosses the river?

  The driver of a motorboat that can move at 11 m/s in still qc2gec a5k3usvm6.w 77p7dfiwater wishes to travel directly across a river 1.7 7sd v6pm5 gc7q caew.fu 7i2k3km wide in which the current flows at 7.4 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 water wishes to tr::/84dmvs(u c yvwmhs avelw:s/m8mh : vu4ydsc( v directly 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 across a river 200 m wide reaches t. ),, s :g5ssgp jjzxf5 tt.gtgxq2jk9he opposite bank in 6 min 40 s. She is swept downstream 49jxgt.jgx:t,)ksz ggq25 sjp5,t f s.80 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide rgy0 d:o++v hokeaches the opposite bank in 6 min 40 s. Sgvd+h y:+0oko he is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.15 m/s4iavd+p n ab8kv,s if+ /tom84, must aim upstream at an angle of okpat a8 viidvs/4 m8+b+4n,f $23.4^{\circ}$ (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)  $m/s$