Which one of the following ismu cs8z wg qk88my:e;z0tbi82 an example of a vector quantity?

  Which of the following operations will not change a t), s an.l: +t;xjq -5eisoveavector?

  Which of the following is an accuratettxbi rzlc s;q/tlir995b-9, statement?

  The resultant of two vectors is the smallest when the angle b p yz2 kld02q::xdsy:r w7dv7metween them is

  Two displacement vec* 8bka.l hvl,l tjma mcgsccgu: 271,2tors have magnitudes of 5.0 m and 7.0 m, respectively. When these twlt,l2 7kg*sh1gmj luc2vbc8 m:,.aca o vectors are added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one obg at;e3xjja18oc)w; 6/ f kcbf the following is afc/) bb8c3wk ox6e;taj;a 1jg possible answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in dipo)npk -h9.uf1 ho -ehrections that o)-kn - eh9h.hfopup 1are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shownb;zoxpqif2u70 nn;p:w1 )zdk, the unknown vector is

  Ignoring air resistance, the horizontal component of a projectilef zh.cx2y touxb+2:rpr x-l)r * fgw6:'s velocity

  A ball is thrown with a velocity crq(znsy(b 6( 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 horiz41-gr +swy f ,h2mcsgjontal component of a projectile's acceleration rwhg4-1j 2+ fsyc,sgm

  A soccer ball is kicked with 9qyfx;nk 3y,wcof/ p;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 velo xd50v v;twxo0 k2jsn5city v0wx vn 5 jk02xv5t;osdector,

  If the acceleration of an object is always directed 1 o5jcw qb99xm7-xhjzperpendicular to its velocity,5hj7mzbjo9 x 1cwq-9 x

  At what angle should a water-gun be aimed in order for the wa 0 g3q-cy2kjt/weq .;l5fxd. mcpsbl0ter to land with the greatest horizwlm0qg..kqsjy2cbxcep/fd 53 l;t 0-ontal range?

  An Olympic athlete throws a javelin at fo: fi2 0t*us-g4bmfiakur different angles above the horizontal, m0af-: *ts giufi24bkeach 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 t qqxf1)vh4oivo by ,ri,*0 1rfime. If the ball leaves your hand with twice the velocity it had ib*y v1 fr ,qhfq0x,oi4v)o1r on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an origin4ny oil:oq1- tal 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 g y(s:lhu.a+-aouz 0 vreaches its maximum height, how does its speedg( s.+:auovza0uh - ly compare to its initial speed?

  A stone is thrown horizontally from the top of a tower alr; 7jyye-h/r(b. rws3)pdu at the same instant a ball is dropped vertically. Which object is traveling faster when it h7ad ) yu(slye-. w3rp/jr;r hbits the level ground below?

  A bullet is fired horizontally, and at the same instant a s. 5l0xp qs7y1 pljmhvu90kn+s econd bullet is dropped from the same height. Ignore air resistance. Compare the times ovm0s.j+5nl7 k 1yspx 90lphquf fall of the two bullets.

  A plane flying horizontally at a speed of 60.0 m/s and 19hr9 m3b+u bu15h0qhs o,tb.mwknus at an elevation of 293 m drops a package. h.r,0bw h um9s b51+om 3uhbu9k1qtns 2.7 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 a srcg;hia86z.;1 jlze ,c ujua8econd package is dropped. Neglecting air rzi 8;a c6auzue;hgj1j.rc,8 lesistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constanehh pprcop,: lqj1u;75 bq8 v0t speed. Neglecting air resistance, when the bomb hits the ground the h qjchbpp,v:5l8oq u r7;p01ehorizontal location of the plane will

  The acceleration of gravity on the Moon is only ofejves-xyw /mf8 c9(,ne-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 / -cexfje(yvfws 9,8m land

  You are traveling at 55 mi/h in the ug xy,s nvm4/:/lp9du +x axis relative to a straight, level road and pass a car traveling at 4ym ,p/ 4nudg/9x:lus v5 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 gjh3 u1ni98cf strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You shh ju31fgc n8i9ould head your motorboat

  Your motorboat can move at).lpi+r,0jxwl8oh y ldt 3xv i067iiu+uxd*v 30 km/h in still water. How much time will it take you to move 12 uy lioj+x 8x0d*u3h+7dwt rpv,lli.i6xv0)i km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees be6 fpmmd8w.hvfoq.-wg+.l l*5net8xalow the +x axis. The y component gxwf n l -o*6t+mq .5hfve dw8l.mp.8aof A is

  If a ball is thrown with a velocity of 25 m/s at an angle ofr7-z) 9sngp74yalmfpr8 7st+lpc 2ab $37^{\circ}$ 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 dc// l9wg7ipbgrx 5 f.of east and you end up 2.0 km north and several kilometers east. How many g .9wl7 bcixp/rg5 d/fdegrees north of east have you walked?

  A butterfly moves with a speed oa2 :u -on7kwehf 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of it: wakue- 7onh2s motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a levelx*j/ qf 0-wbgx ground. At what angle is the Sun elevated abojw 0b-fx g*qx/ve the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. Whaah6uf. qtevek.y12o h ( :ipd7ovur -*t are the componenoe hau:ipt 6krqfu 12.ov dey-*v .(7hts of the sum of these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively l11urx-bm.we . What is mxr .u1elm-b 1wagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mp4b:4,goy:ml(bi i msagnitude of gl 4(ipso b,:bmi 4my:C ?

  A car travels 20 km Wesd x9 )uw09jzhane*x) zt, then 20 km South. What is the magnitude of its displacz)newx9d hjx0)9 za*u ement?

  Three vectors, expressed in x : prbf531-l. bdieinCartesian 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 coordinates, am: ueg 2jjnszr 25d+4are
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)itc9 ht8mqhfi0 ceqf*s/ 5 (m- and vector B = (+3.0, -8.0), what is the magnitude of vector C = A(f 0fq8chs mii ehtmqc t5/9-* - B ?

  A runner runs halfway around a circular path of radius 10 m. What ( pf6 ohpbj+jp7ukf2)2p p7gn is the displacement of the joggerh7fopjpppku7 gbnf 6 2p2+(j)?

  Two forces are acting on an object as shown in Fig. below. Whatmw qrqgm-:py+(yw :nbi-( np / is the magnitude of the resu:n/pyqmpy-wb+g:-iw m n (qr(ltant force?

  Two forces are acting on an object as shown in Fig. below. ns)vglu s6ts8l6ps lc lh + 770msbgd;vpa,6 : What is the direction of the resultant pbl s)cs8s76d+ :gp67hl; ulv0asnm,6vg tlsforce?

  Vector A is 4.8 cm long and points along the positive x axis. Vector evzzpa 2/+v+ r +esec7B is 8.3 cm long and poi/zs7a+epz v +crv 2e+ents at $+53^{\circ}$ 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 82 cm long and pointsy3kx y .7(xfuf at $30^{\circ}$ above the positive x axis. Vector B is 27 cm long
and points along the negative x axis. Vector C is 35 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 aw 0b+eih0 p, l+(ztbtkn initial speed of 21 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 4.8 s. What is the height of thehwi +eb(pbkl+ 0tzt, 0 cliff?

  A girl throws a rock horizontally, with a velociv lu / eajdcf)s* **lh3dthq9+ty of 19 m/s, from a bridge. It falls 29 m to sq **d3)d9*hf etucal+l/hjvthe water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a poi1l 5qxselzn m:f *-r7x,7 a,yzkgfr:gnt 29 m above the ground, strikes the ground after traveling horizontally a distz,f:fm,gx 5r17:qa lx-ezy k7*g n lrsance 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 at an )jp ga.zg/ ;pu8pz/x eangle of up 8;j/ gga)expz/z.p$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump goes int4d0vo8e3fpl i60ty nmo the jump with a speed of 14 m/s at an angle ofdo4nfly0tmp e3vi680 $34^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 47.-1lrov tb3 kp*6 m/s at an angle of $33.6^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity onzh:v 2orm81 b3a2lm4hxcxw*5yww ; m f 26.3 m/s at an angle of $49.5^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an anglecz6y xm1hq;*e 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 horiz/qufq 1:kngskhmik3m.e5 1p s7 su5f*ontally at 17.8 $m/s$ from the roof of a building 53.2 $m$ 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 level wit 6pbcooj/b.rv+5r hmzu6 js9: h an initial speed of 59.4 m/s at an angle o/ rpj:m+5v 6hcbb ujor9.szo6f $42.1^{\circ}$ 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), yov eorvvv)vt )+ 8h6b/v- 3win9wagin8u can run a 1500-m race at a velocity of 4.0 m/s. If you ran the same raor)g 8+)vvnvi38 vhb tvia -6/e9 nvwwce 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 speed ; zfdt1szd5t p,yh+y1of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relat s+ yd tfz,zd1th5y1p;ive to the ground is

  A plane is flying due Sgrcu w h*46:dqji a7;uouth ($270^{\circ}$) 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/+tnsb- *gct2alc u:da 53ta e*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 projectilemh ;gu2z ofo:7 with speed 50.0 m/s in a forward do m;hugoz: 7f2irection $30.0^{\circ}$ 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 o*i7 yr9x c 2*45yx sqkxrspn8river with a curreq5opx9 ny4ix rss 78rk*cy* 2xnt of 6.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that cz(i9f)y+m v. rdmtb,zan move at 20 m/s in still water wishes to travel directly across a river 0.7 km wide inzitmvr ),yd.+(zf 9mb 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 water wishes to travegm3ede45 qqp*34r) ba)eyqo vl directly across a narrow strait qpqae4 3b*g)mved3r5 eq o)y4in 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 reac6 wxv0b b2dpo,rnz i*wg+nd 33cyi.u1hes the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fasud2 1,i3.p6nw03w igbd z+nb*rxy ocvt can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches the opposite bank 8psv8 5nj.nbi, xf (qain 6 min 40 s. 8j,n pfi(5sb8.qavnxShe is swept downstream 480 m. What is the speed of the current?

  A boat, whose speed in still water is 1.41 m/s, must aim upstream at an angle p itde4 no65qvzl d.a1tt+;p3of ep nt.t +ta1pd3vd qol ;iz654$22.2^{\circ}$ (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)  $m/s$