Which one of the following is an example of ak 6tn x651u9 w-mu8d)pixyuqq vector quantity?

  Which of the following operations will no.t esdn32bsikk 7d0y ef/2xxa,j g:5e gg3e6m t change a vector?

  Which of the following is an accurat2o;tn*it )yia 2)yrrr(z ci8 ne statement?

  The resultant of two vectozqyocnr-n9,ge-s;j- rs is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.h0(nv, 2gag og0 m, respectively. When these twon(gv20g a, hog vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one lk jnu )3y6-rrof the following is a possible answer for the magn- l6jr y)unkr3itude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dire/b./83u , 3 o9bpv nl 1jqovwg0wik 7lejn*vofctions that arejg09l8 kwuno7o,vefvw 3 *.jino3 b/l1bq /pv $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector i gv. /./pifcrls

  Ignoring air resistance, the horizontal component of a projectile'r// dald oe+wh mjjl-2l /:*cns velocity

  A ball is thrown with a velocity of 20 m/siabruf (z 5a-( 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 resistani 7(ued0l x-qjce, the horizontal component of a projectile's acceleration 0j7lx( i-qeud

  A soccer ball is kicked with a velocity of 25 m/s at an anglez64n0ugig9 oe 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 /3+vt s1 ti4lfz q:bsmto the velocity 4t qvt3+ms /1liz:fs bvector,

  If the acceleration of an object is always direct9 y5qzpr ,fxk*u9,te ved perpendicular to its velocity, e,xr 9*9fyuvptkqz 5,

  At what angle should a water-gun be aimed in order for the water to lanhy zoq*)q +z-hf7 xqh,d with the greatest horiyzxhq, hhqo+q) f-*7z zontal range?

  An Olympic athlete throws a javelin at four different anoy1- k vz6hap5gles above the horizontal, each with the same spee zvhp-6k1 oa5yd: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 hansrt3 bl )3(3axla+n tid with twice the velocity it had on your first throw, its horizontal range R stln xt+(a3ibar3 )3l(compared to your first serve) would be

  A ball is thrown at anff kw8c**ra ,hh-1 2p1 zvdzma original 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 reachew 3/o tu:kuc8 6 pl*eqltn4wc/s its maximum height, how does its speed compare to its initial spe8 etlw*op6n uw/u: q3k/c4clted?

  A stone is thrown horizontally from t7.p ox2oilx8.j*fr nn:ai e. ahe top of a tower at the same instant a ball is droppedli. xe 2o. fo*nj8:7x.aanipr vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at thf0mw*al ;x1: srdng,he same instant a second bullet is dropped from the same height. Ignore air resistance. shf x*g;mn lra01:d,w Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 14euvt 0 ez0+m5bi8zrinny.e800.2 m/s and at an elevation of 247 m drops a package. 6.8 seconds later it drops a second package. How far apart will the two paz+e n.zum8 ii480 bnrv5ytee0ckages land on the ground?

  A package of supplies is dropped from a plane, and one second later a second(a8 m+c ;bsxsm9gj r:39qptkq package is dropped. Negleb qj 9m q(:gmak 8s+tprc9x3;scting air resistance, the distance between the falling packages will

  A pilot drops a bomb u2q8ea bfwvg 1q07y0pg-j(fkfrom a plane flying horizontally at a constant speed. Neglecting air resistanj2y w0p qukfqg 1(-fbga7ve80 ce, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of tha jtlc.ziho+6q5r1o 3 2o)jdbit on Earth. If you hit a baseball on the Moon with the same efi ohczlb.r )6jq2iojd +ot135fort (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 straight, leve eli7m*bs/nb m) 27nlhl road and pass a ca)l72 l/mb nimh*b7sner traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flows due south with a stro )lj e7say(-uwng current. You start out in your motorboat on the east bank desiring to reach the y (weaul7s-j)west bank directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. Howh/vhb ) xq6aj70je)b zn :ocy( much time will it take you to move 12 km downstream, in a river flowing at 76 eqzj:vbhhnc( /ya0o jb)x) 6.0 km/h?

  Vector A has magnitude 8.0 m u ofx ,x)pi-38vlnykopvc0zo 5 )+ yw5at an angle of 30 degrees below the +x axis. The y component x8wp)5y0f copn yvoi5 +xz )o,ku vl3-of A is

  If a ball is thrown w :l8w3qyg x*oa 6)zhneith 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 oeit99s;ta yc 2f east and you end up 2 9at;sty ie9c2.0 km north 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 xp9wjuf-- v3wt/rmen- vs-em q7t,* a o component of its velocity is 8.00 m/s. The angle between the direction of-/3uo9*rfjpm mwse -nve t-7 ,aw-tvq its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level groun a i4y+6gsi h y+16ncb3bxv3lwd. At what angle is the Sun elevated above the hori3b +nv3asywxh4yl61 bi6ci +gzon?

  Two vectors A and B have components (0, 1) +8/4uku l8igl5a kcu/2 tt zroand (-1, 3), respectively. What are the components of the suk 8l k t+/tig2czuu85 lro4a/um of these two vectors?

  Two vectors A and B have componentv-px . a*m(c/5lsbvcvs (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these twoc /-(xc. lvvb*a5m pvs vectors?

  Vector A = (1, 3). Vector B = (3, 02 6buuy)e8 huu). Vector C = A + B . What is the magnitude ofu2ybe8) 6uh uu C ?

  A car travels 20 km West, then 20 km South. What is the magnitude of its d ddy/59+p c9xgd 6kjrvisplacem+6d c r9k djy9dgpv/5xent?

  Three vectors, expressed in Cartesian coordinates 63uixnruc;9w jr*lp;m.s o4o9/fdq z, 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 coord- /j)ffffehp+ ; ond2qinates, 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 ipvwc4: kl:o)0xhpb 8es the magnitude of vector C = A -8xw)o4l bph c::0v pek B ?

  A runner runs halfway around a ciroi3j-b 2 ocfoo:/ pka3i 8(wjwcular path of radius 10 m. What is the displacement of 3-ck j 2o/ ofw(3jiiaoobwp:8the jogger?

  Two forces are acting on an object as sh3f v ozvc(v q;ay(3id.own in Fig. below. What is the magnitude of the resu( d(i3aqv3z.yfvo;cv ltant force?

  Two forces are acting on an object as shown in ;lpky-es y 0xd+b.): crb-flz r0 d(vzFig. below. What is the direction of the 0.bvrl;r pdd) lz0 -by+kc:-x(zsef y resultant force?

  Vector A is 5.3 cm long and points along the positive x axis. Vector B is 5.5 colw7-u wv;v9qqtb,;y 1e.ogkvy ;3tq m lwqt l;t9qokbyv 3u,v o1v- ;;ey.g wq7ong and points at $+27^{\circ}$ 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 57 cm lonu7e : e n4xa2)jqh kq (9dwmvphw,-tk2g and points at $30^{\circ}$ above the positive x axis. Vector B is 24 cm long
and points along the negative x axis. Vector C is 41 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 vd ck( fua)pd(fig-x68ie+c5 initial speed of 10 m/s from the edge of a cliff. A stop watch measures the x6u 8e+5c ( cd)-vi(f gpkadifstone's trajectory time from the top of the cliff to the bottom to be 2.1 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity of 7 m/s, from a ,ts l:eq;6oei bridge. It falls 24q,loee: ti6 s; m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, 0 xzj57esgtd 9strikes the ground after traveling horizonta d07g9t5 zjsxelly a distance of 17 m. With what speed was it thrown?

  A jumper in the long- -pxa vwkk1o0(jump goes into the jump with a speed of 12 m/s at an angle ofwxpvo1( ka0- k $20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jo(4t c*/1/.itpogsx +vtvnqua y mm4)ump goes into the jump with a speed of 12 m/s at an angle of ac4s/+n( o mvo/ttpv)mugxiy4.1*t q$26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an inir z2z,,-zitsstial velocity of 21.4 m/s at an angle of $12.4^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial veypo,+k(ly) :8hxwr eqlocity of 24.1 m/s at an angle of $14.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at*pixt2 /fi3 sa 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 z-:6qx /wa(jdvuk 9smat 19.0 $m/s$ from the roof of a building 69.9 $m$ 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 levelg p2j+z+ly2/e3hzlr h with an initial speed of 43.9 m/s at an anglp h+3yzh l/ lgez+2jr2e of $39.8^{\circ}$ 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 15* g,jjb-ld 6j nyck2*i:b9bln 00-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 spe*nid6 bbcgj:k*ljy-2jb ln9 ,ed 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 .d ppjxx7 vyynz) 4)d6is in a wind of 50.0 m/s to the West. The plane's speed relative to x6.y7nd ppyvdz))x4jthe ground is

  A plane is flying due South (oe3se*a: u06 )ecvbea$270^{\circ}$) 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 12v6p-3i cbvc2fq8hnghm1li1 +0 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 horizontally fires a pr p;hvo.hqy o,qyi8q, 3uwoy5.ojectile with speed 50.0 m/s in a fv3qph., o qyuihq , w5.8oy;yoorward 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, is direcdrzn*v) is3:nted across a river with a current of 6.0 m/s. What is the speed :3nrs)dzi* n vof the boat as it crosses the river?

  The driver of a motorboat that can move at 10 m/s in still water 1ca3 ziqit1u+ wishes to travel diiqc za i+1tu13rectly across a river 0.7 km wide in which the current flows at 5.9 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(p5pi1+,cfkqa y;w p-mepu l5 water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/ya ; e 15pwl, fmk(i5+-pqupcps. At what angle upstream should the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the oppost;btyfp75ai -)jr rh 9ite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stir9jaf7 ryb-t;h)5it p ll water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank 1ms g,kba. ugl 8s6(9is(hbrlin 6 min 40 s. She is swept downstream 480 m. What is the speed of th(g1s9 8 m6 bb,arl (gulkhs.sie current?

  A boat, whose speed ior4h g0/bq5sm n still water is 1.41 m/s, must aim upstream at an angle of qh4g0mo s/rb5$28.8^{\circ}$ (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)  $m/s$