Which one of the following is an example of a vector quanu8 a mt 9jh6mjah7v(8.p*bkaqtity?

  Which of the following operations will not chang*yv.;;tl). b4lwqgwa gs:sa xe a vector?

  Which of the following is an accurate statementv,cg 5qq)q8 c .56ew8lyzbw kko8n8yd0tngu)?

  The resultant of two vectors is the smalkh, 3p2t k /j;mnkdd3alest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respecth ew99fpbb2m. ively. When these two vectors are added, the magnitude of the subf 929bmwh .pem

  Two vectors, of magnitudes 20 and 50, are added. .9id(p abg,3 iigkub+Which one of the following is a possible answer for the magnitup g3, b (ai+ibgk.i9dude of the resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directio8o c jehwxen5/sbn96 1zzwf79oh9q -gns the9 c/ o 79bojfw5n- 89q6xszzen1hg hwat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectg2 dof3 s6jh5por is

  Ignoring air resistance, the horizontal comg7h+aez.4iv y2h:h k9xcukb *g w v7/dponent of a projectile's velocity

  A ball is thrown with a velocity of80 +jkmavkuoimc b 1l gim- 0:t15st/v 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 projectis ice ms(/,ijb7 -w;cgle's acceleration cs(cg -i,;sjiw m7/be

  A soccer ball is kicked with a velocity of 2sb:9wxu ;j7nq5 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-parallehp/ pf px:hfe 0e9+9utl to the velocity vectop 9 +h 0pe/ff:9ehutpxr,

  If the acceleration of an object is always directed perpendicular to i d2t)foy7 z- j kmdx-(m2.lyfsyh+ab9ts velocity,y j9t f7smfoddhybl )m.ya +(k-z22- x

  At what angle should a water-gun be aimed in order for + eal08dg gbz(the water to land with the greatest horizgdlb(+gz80ea ontal range?

  An Olympic athlete throws a javelin at four different angles aboos hb4suo8q t.l+o8r y*:sl8pve the horizontal, .o8o+qlhos p:y * b88urs4lsteach 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 time. If the ball leaves your hand with *qe:y 2wbi*jd twice the velocity it had on your first throw, its horizontal wq*ieb 2d:j*yrange R (compared to your first serve) would be

  A ball is thrown at an a0k f 90md5)nhhdhoq-ml2)p h w ;rks5original 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 focfp1om*r*o5y3s k g(ield goal attempt reaches its maximum height, how does its spemo5c3rkf * *p (oyog1sed compare to its initial speed?

  A stone is thrown horizontally from the twfm b4-obnuy2:ilp 2 9op of a tower at the same instant a ball is dyubo2l-9f2p mnw: b4 iropped vertically. Which object is traveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at the ev+a8ktrad -(g 4p +h:j .snpgsame instant a second bullet is dropped from the same height. Ignore air tdvppeg: r. ak8 anh g+(4s-j+resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 84.4 m/s and at an elevation o l:( epwhb;9q-teaj /sf 174 m drops a package. 6.7 seconds later it drops a s: ;aw/s 9hlpbt(-eeqjecond package. How far apart will the two packages land on the ground?

  A package of supplies is dropped h.(illkha-x :from a plane, and one second later a second package is dropped. Neglecting air resisk- i lh(lxa:h.tance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant sp xq9 o s5red3woa2o)3w nn3/ukeed. Neglecting air resistance, when the bomb hitsr 3x/swdqkna n25o o9)3u3woe the ground the horizontal location of the plane will

  The acceleration of gravity on the Moon is only one-sixth of yurjop i2vxc.qh3 l105c9t/p+iwhl 1that on Earth. If pxlh hi13l +91yic wrq 5jutcvp.20/o 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 land

  You are traveling at 55 mi/h in the +x axvub8b +4+z;h eyx; enenft8va 8i fu7(is relative to a straight, level road and pass a car traveling at 45 mi/h. The relative velocity of yo +7;uua+4ni 8te enyzhb8fb 8e( xvvf;ur car to the other car is

  You are trying to cross a river that flows kg;lv ;ok ofj *rg/909jysj 7ldue south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from jl;; klgy 0ok*g7 /s9vjof j9ryour starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will imhwe3ak 8rerc1 bk*w 1:+4ej qt take you to move 12 km downstream, in a river flowing at 6.0 km83wbejr + qm*a4e1hcw :kker1/h?

  Vector A has magnitude 8.0 m at an angle .z-w,gne3 itk 7 dxft1of 30 degrees below the +x axis. The y com, zfw1.k7titd 3xegn- ponent of A is

  If a ball is thrown with a velocity of 25 m/s at an angle of myv: 5l s/q4s,cq)uan c; hj6i$37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a str :cx)t t0.2xkpudjob+40w typaight line in a direction north of east and you end up 2.0 km no0j)kto4 + td:.0 ycp xubxwpt2rth and several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s/51qwp:ed g xl. The x component of its velocity is 8.00 m/s. The angpq/:gwd l xe51le 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. At wo x6(kyvtx3906 nfxp mrw3wb 9hat angle is t3 f0xp kr n6w36(xtwmbyv9o 9xhe Sun elevated above the horizon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What arhpqm/a+duf3z,g1i y, e the components of the sum o,fyzg3,m+ had/u i 1pqf these two vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. W . 3u ,icjxfw7s7dhly(hat is magnitude of di,hf 7lc(.xjysuw37 the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the mu/db76*1 ycaun-m ge aagnitude of C ?n/-a 7*ebduya gu6cm 1

  A car travels 20 km West, then 20 km South. What is6/wx4n cds;yy* u,gs o the magnitude of its displacemen*ys ,y;4g6 xo sd/uwnct?

  Three vectors, expressed in Carz avz h7u ,8/ohk.)h ,0z1uj)ifjydubtesian 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 coordinatj x: ame /f)8t(c,js+mpe-re ces, 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), whabzn 7 kmb3np.9t is the magnitude of vector C = A - m79 z3bn kpn.bB ?

  A runner runs halfway around a circular path of radius 10 m. What is the dispx *km:n8/v x;g5db zeulacemxe8/dvx k zgumn*b;5:ent of the jogger?

  Two forces are acting on an object as shown in Fig. below. What is sk0u ) +kr( wte/hfkj4the magnitude of the resultant force ()4s 0jftuk/ewhkkr +?

  Two forces are acting on an object as shown in Fig. below. What +ke1qwoizy.jz 4myq3;.d d m6is the direction 3qq dd yy1zimw jk.;o mz6+.e4of the resultant force?

  Vector A is 5.5 cm long and points along the positive x axis. Vector B is 2o.k5 )wjxibr6.1 cmwokijrx.)5b 2 long and points at $+54^{\circ}$ 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 52 cm long 98kfns+;x jecgacl 1+j m/ ;poand points at $30^{\circ}$ above the positive x axis. Vector B is 19 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 ; 6 3ustkdvde3zaq7u1 an initial speed of 23 m/s from the edge of a cliff. A stop watch meu3zd 17s3akquet dv;6asures the stone's trajectory time from the top of the cliff to the bottom to be 2.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a velocity o db1 kg6;zz znyi8gv-h5y8 d 9rhj3ms6f 8 m/s, from a bridge. It falls 23bg86 is9;rzv58mk6 zz dhgnd yjyh 31- m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 21 m above the ground, strikf mr). jf6jcu5es the ground after traveling horizontally a distance of 22 m. With what speedj5 rjmuff).c6 was it thrown?

  A jumper in the long-ju8ax/awbo1l5h y t6 6wsmp goes into the jump with a speed of 12 m/s at an angle of h8sy1wo6la w/ 5ba tx6$20^{\circ}$ above the horizontal. How long is the jumper in the air before returning to the Earth?

  A jumper in the long-jump fxy3r i12yb(e goes into the jump with a speed of 14 m/s at an angle xf2i3ye1r( yb of $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 53.6 m/s at ann *9xcchv qw2 j;9-qat angle of $12.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an in8-a(xm9 pdew jj l;fva,l q;n;itial velocity of 28.6 m/s at an angle of $39.1^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firedvqz0xxl *8 ;ncil.fh( 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 20.9 v:mq3w:bbxls 9d0 z:w$m/s$ from the roof of a building 42.8 $m$ 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 blrakv .a95 q6with an initial speed of 43.8 m/s at an angle 9lakbv. ra56qof $40.4^{\circ}$ 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.:zrjn0 gaa3r* j vf;0g If you ran the same race on a day when you had a constant headwind which slows youja ;r3n*0 j0rv:gfgz ar 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 dc75i f g644bo7f zqqbhj*v sc*ue North, and is in a wind of 50.0 m/s to the West. The planej gc4cbfsfb *6iz*h7v4qqo7 5's speed relative to the ground is

  A plane is flying du 6ky p:t:v mei, /f2qmo5em+ome South ($270^{\circ}$) 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 s q/ /g/jo3tuj6qbe7ob peed 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 movind pqg m0im;k95ty/ ,gng 200 m/s horizontally fires a projectile with speed 50.0 m/stdg5mg ,;0 9qypmni/k in a forward 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 directed across a2 cx0rs .hcyn7 river with a current of 6.0 m/s. What is. chn2 7rys0xc the speed of the boat as it crosses the river?

  The driver of a motorboat that can mog e/8 iiy5y8nu j3(litve at 10 m/s in still water wishes to travel directly across a river 1.9li n j(y8ig/i8yu3et5 km wide in which the current flows at 3.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at 10 m/s in stp2eh 35sht 8rdill water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream shh 5therd3p2 s8ould the driver head the boat?

  A swimmer heading diwrn2r se/.dvy5v +to-rectly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast c y/o.wsr2-tdrvnv+e 5an she swim in still water?

  A swimmer heading directly across a r9 -l0vv drrp4y4*z8sgx y jyp;iver 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What yyxygl 4jv4rp -8z*d0rvsp;9is the speed of the current?

  A boat, whose speed inf)gu2 - efu0rp still water is 2.05 m/s, must aim upstream at an angle ofgf0) erup-u2f $17.9^{\circ}$ (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)  $m/s$