Which one of the following is an example of a v+7hhrow ,v5g z-s7zd f)cew5z ector quantity?

  Which of the following opepk(vj7ajq4e8e ..2yos5/vr yylpq :m rations will not change a vector?

  Which of the following is an accurate state+p: 2 xo/oun8wimzz . fiws)e9ment?

  The resultant of two vectors is the smallest when the angle between them , *l evvr,hcwzi6zr/5is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, resplhact j5 v7b7co /y/ n+us 6tg3gd7cl4ectively. When these two vectors are added, the magnitdh4a 57 jb+ l7u co/cc gt6v3s/t7ylgnude of the sum

  Two vectors, of magnitudes 20 s f0y2w35vxfj and 50, are added. Which one of the following is a pos wxfv05j3s2f ysible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directions gfjdr2 a ye-tg,ot0kt+5*r(atoa*yr tk -0+(t t, jdr52feagghat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, theg8 z3g0j2vmby unknown vector is

  Ignoring air resistance, the horizontal component of a projectiam ho irx7:0u/le's velocity

  A ball is thrown with a velocity of 20 m/s at a *tb rj.ml;l9dn 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 resistancea( z-.pjj5zs mi 4qpgd*ayr5,/;h 8z4yughct, the horizontal component of a projectile's acceleration .j4u,5 ( -dpt grh i/q8a*czspz4mgj; yh5azy

  A soccer ball is kicked with a velocitb z,f+tna 7 kcs l,(f;7;-;eozbsabuu y 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 4bb 2md2;qf -ollkh m0object is directed anti-parallel to the velocity v0lk;d 2mqh2-f4 obm lbector,

  If the acceleration of an object is always directed perpendicufc:z6ym j4/qdlar to its velocityy jq: 4f/zcdm6,

  At what angle should a water-gun be aimed in order for the wa sb-dtd;*t.lhv a wn/.ter to land with the greatest horizontal range?d -. t*;btvshnal/.dw

  An Olympic athlete throws a javelin at four different angles abov;g5nj1 d q9:8i 0v-q)4bnvtx deepeeje the horizontal, each with the same speedv-n481;e)e v deqxdj5i qt p0neb9 j:g: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 leaves your hand wl,ema,w n(s4 )dov89sc l xne.ith twice the velocity it had on your first throw, its horizontal range R (,.9e,xm n8l) n(ws4adcso evlcompared to your first serve) would be

  A ball is thrown at an or24j- sx+3m ftnx j4o6m5 kmgxciginal 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 reaches its maximum height, ho8 am1h2vg.h syw does its speed compayhvh.ga 1 2m8sre to its initial speed?

  A stone is thrown horizontally from the top of a tower at the samb wpqe8l49u5zs1qc4qk g ;li+e instant a ball is dropped vertically. Which object is traveling faster when it hi 1slpug45qz l4+ew 9bcq qk;8its the level ground below?

  A bullet is fired horizontally, and at the same instan4* 3 6ukzft*wq *q)2izp miazqt a second bullet is dropped from the same height. Ignore air resistance. Comparea 2pi3**qzq)4w 6iquf kt zz*m the times of fall of the two bullets.

  A plane flying horizontally at a speed of 65.2 m/s and at asq0uf0f+6 qa en elevation of 269 m dropq0q f0uf +6ases a package. 5.6 seconds later it drops a second package. How far apart will the two packages land on the ground?

  A package of supplies is ww)12j0tbhg wym38ub :rxcr 5dropped from a plane, and one second later a second package is d80 j2u wcwbtr1 :hgxybm)53wrropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant rq7dq: i s5j m*dyeq/8speed. Neglecting air resistance, when the by8d/ qq : 7eds5*irmjqomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only 91 2-w6wmtyhne,rs4rxxfnf 2 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 would r4s,129 t-e xfh6myn2wnfwrx land

  You are traveling at 55 mi/h in the +x axis relative to a straight, level5 3o0recsx -hy road and pass a car tr yesh5 cox-30raveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cro v)*+w.nxdl+r( hp pyxss a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting poip.+w)dn x *ryxh+vl p(nt. You should head your motorboat

  Your motorboat can move at 30 km/h in stillba7a tr/x c.4blc0xk* water. How much time will it take you to move 12 km downstream, in*l 7xcba kac/x4. rtb0 a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis. The 8zun5 n)nly3ly component nl3 nn58u)zyl of A is

  If a ball is thrown with a velocity of 2::gj9k+fic6crssk ,)tpyu1v q8mgx 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/8nxi -f/c9j8 b v xi:zb2yghl in a direction north of east and you end up 2.0 km north and several kilom-xx8ib l f/yncvg89/:2ibj zheters east. How many degrees north of east have you walked?

  A butterfly moves with a*tqd(1d 5n4 uzegbk1p speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of i4 1kqben1tdug 5*d(pzts motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level ground. At what angle6j 9,jf2 pg,pnho(ppi is,pjhgjonp 2 pif p96,( the Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectcn 4ukv u:w4 azwt49i*m0 gxo-ively. What are the c4mc90 ut awo -4w4k:givun* zxomponents of the sum of these two vectors?

  Two vectors A and B have comq,couvon pn ; w5i2ea4;v8l i+ponents (0, 1) and (-1, 3), respectively. What is magniu5 8w neoi+;2qn;ilpc4av o,v tude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What i0pnwxt o6wqzzxr,8u 5+i:3m n s the magnitude i3 5 0nt6wp+xzxo z:r8,wq nmuof C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its disp myw7*0b:b/* .zteod ,s+ gkokv jmyh0lacm. s* ,omyh yb:vzdk7 ko/0bwej0+g*tement?

  Three vectors, expressed in Cartesian c);p 0vgg,38 hfrsezd jhq80tsoordinates, 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 Cartesim5dnad f 2(f9 ,;jhovian 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 = ohxv/6cesq m7o(h 1v8 (+3.0, -8.0), what is the magnitude of vector C = A - Boqm/8hc1vvhoex( s6 7 ?

  A runner runs halfway around a circular path of radius 10 m. What is the displazq5/rp lgl lvbo66+7e cement of the ov65 g /qlr+bllpe6z7jogger?

  Two forces are acting on an object as shwb8dvgo2)+, wi6 /9 oyha nu btcca8d4own in Fig. below. What is the magnitude o /4 b),9ya ao8htc6d8gnwvc ud2w+i bof the resultant force?

  Two forces are acting on an object as shown in Fig. below. What is 8)u q u yiocc, hq*dhrh8;d+mn,i b)z0the direction of theiczd)8h m h cyqru,nu0b o;8 ,ih)q+*d resultant force?

  Vector A is 5.5 cm long and points along the positive x gi e6x0a + vk5-v6x;gz dzv38ixq3yrraxis. Vector B is 7.4 cm long anvagrvik yxe 5+qgxx3rd6vz 0-i 68;3zd points at $+39^{\circ}$ 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 58 cm long8 +q1)teqxyeo* w ku2n and points at $30^{\circ}$ above the positive x axis. Vector B is 22 cm long
and points along the negative x axis. Vector C is 45 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 21 m/s fj a cead 23km 7l;,p/p1/vtn3fckmy- trom 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 4.2 s. What is the height of the cliffcc3k,3n my;pvat/ /-e 12admjtk7 lpf ?

  A girl throws a rock horizontally, with a velocity of 8 un ,.i(iddkvp/-k0 ls m/s, from a bridge. It falls 19 m to the water below. How far does the rock travel horizontally bed l-un(psik/ v.id,k 0fore striking the water?

  A ball thrown horizontally from a point 25 m above the cz6f5n6awfm u; zwh ag o6*m33ground, strikes the ground after traveling horizontallyfm6m3na3 5w *z6czwuo gfh6;a 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/ 9y:cgj,rnh idw(cv;*s at an angle of c wjc9 ;h,iyvdgrn:(*$20^{\circ}$ 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 sp,lmu apgv338bds 3ax, eed of 14 m/s at an angle ,3da v3 msa u38lpgb,xof $25^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initi r-sis4 cnp. l1zg9m+tal velocity of 26.0 m/s at an angle of $33.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vauteqw3eux(7 v zs tuw,7 v4(*elocity of 54.9 m/s at an angle of $30.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angle ofckem ;ol60cu ;6 zj5yo:ph,vg $30^{\circ}$ 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 24f:nh wfe/ e93e rs/ck3.2 $m/s$ from the roof of a building 37.1 $m$ 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 lfmu2(gq/y; iuwv ;2evevel with an initial speed of 63.6 m/s at an angle of ;vfu/2 ivy 2(q;wuemg$46.9^{\circ}$ 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 run a 1500-m race at a velocity of 4.0u j++-l1d4zb r3u pdbn m/s. If you ran the samdpj +zd-ubb n3+4lu1re 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 spee8z x90l.3zs wy6a0hme:6pd4 ipashy jd of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the groun sylm:jwsh z69x da04eh i.p0z368ypad is

  A plane is flying due South hy-ohm sd872d($270^{\circ}$) 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 idhn ld+slk 0lh c6/q,.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 proc xao/x;9wks wr:,ir )jectile with speed 50.0 m/s in a forward dir)wk/9io;ra x:sxr , wcection $30.0^{\circ}$ 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 acro35pss*ob y l8tvoc8k j o u;k:y/-5gxzss a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the l*5u gtocy8 xoskp: sok/5-v8z;byj3river?

  The driver of a motorboat that can move at 12 m/s in still water wis29q r fp 4kg(.vbnh3cshes to travel directly across a river 1.1 km wide in which the current flows at 7.2 m/s. How long will it take to cross the s2.qp4nvg9 (kbfr3c hriver?

  The driver of a motorboat that can move at 10 m/s in still water wishes to trave1 m c,fu8: 5nltkt;rqcab2di+l directly across a narrow strait in which the current flows at 5.0 m/s. At b5lri :18ct ,f2qdm;k ct+a nuwhat angle upstream should the driver head the boat?

  A swimmer heading directly acrdp 0wjb9ec07 3fbnl/n oss a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swebbwpf7n/jd 09nc e03 lpt downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m 5 o+* v/pc nv *eefrgime,v3u.wide reaches the opposite bank in 6 min 40 s. She is swept downstream 4pve ef+ on*vv3 emgic,ur*5/. 80 m. What is the speed of the current?

  A boat, whose speed in still water is 1.09 m/s, must aim upstream at an angle lp5 ws*,4q76v 1x6p ljq dlwroyu*j d(ofj *,6lx4(1d 7q6ys5jwuoqwrpdp*lv l $21.3^{\circ}$ (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)  $m/s$