Which one of the following is an example of a vecvo9d *,jv) qmetor quantity?

  Which of the following operations will not changv+ zvyv ej42x)e a vector?

  Which of the following is an ac+yvyu f+9pu*ccurate statement?

  The resultant of two vectors is the smallest 4 9r3 /*mo )i-cm i*ahrd bips2hng2(wznpe3k when the angle between them is

  Two displacement vectors have magnitudemho+v sn zlgbq 38s01iai(+ c,s of 5.0 m and 7.0 m, respectively. When these two vectors are added, the la3nq+i8+ z(c,mbh1 0svgo ismagnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follot5 q/6hg ,y -9j(-(v(yrh5jkksxky w :moro dbwing is a possible answer for the magnitude of troo w(tjd ( - r:kjm,s55/ q( 69-yhhgbyxvykkhe resultant?

  Three forces, each having a magnitude of 30 N, pull on an object in directio5+,nkkn5u gzyo3qj o )t/uw c9ns that aretwnu 9) /+ kqcng,uz5y5ojok 3 $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vectowu3n4s99e jw8qv ( tprr is

  Ignoring air resistance, the horizontal component of a projectile's 6 qgfxvew1fc0b5:myy m8+9xo 7rfcp, velocity

  A ball is thrown with ar d- *x2ztqge; 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 projectile's acceleq sey1y2ola ;/copwms10i - 2:iux wg*rationi u1sog : e2 owly*a-qs/2yp;i1x0m cw

  A soccer ball is kicked woj7 oed fi46k*ith 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 ojipq(q (1gj- to the velocity q(ojjg- 1 q(pivector,

  If the acceleration of an object is always directed perpendicular to it,*z r pxqy+j5hs velocity,yhxzp,j*+ r 5q

  At what angle should a w bmki hfg7 7xden-nnw/.85t.iater-gun be aimed in order for the water to land with the greatn5-ximhe /n fbgtin.wk d7 .87est horizontal range?

  An Olympic athlete throws a javelin at four different anya y*q+l+9u)eb9ejfd gles above the horizontal, each with theyfab+d* euejl+y9)9 q 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 secopp;xye v b(+rw54a7gm9 m lrz,nd time. If the ball leaves your hand with twice the velocity it had on your first thro+x,e4z 7a;m bwlp y(r9pv m5grw, 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 and04ma5,;qc ,dsuek cmgle 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, how dn) z s)uoc5ck05g6b usi-fo 6noes its speed comparenf0 - s5s zun)6c)cog6 uobki5 to its initial speed?

  A stone is thrown horizontally from the top of a tower at th(8grj5w(e;fcpmm n8pe same instant a ball is dropped vertically. Which object is trap5mpc ;(jw8(ngm e r8fveling faster when it hits the level ground below?

  A bullet is fired horizontally, and at /ac 74 ld7t,x rct4zwkthe same instant a second bullet is dropped from the same height. Ignore air resistance. Comk47czdtratwc4/7,x lpare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 63.7 m/s and at an elehqpl/ 7xag q7.j s02jpvation of 267 m drops a package. 2.9 seconds later it drop ja7g x0lq/.qsppj 27hs 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 latelcmis71t 4h- qr a second package is dropped. Neglecting air resistance, the dis qstm7c1li -4htance between the falling packages will

  A pilot drops a bomb from a pm,jq k0i1afq- lane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of0 ijfmqa-,kq1 the plane will

  The acceleration of gravity on the Moon is onlibman*+elo:dnd7c9l u r40 z ,y one-sixth of that on Earth. If you hit a baseball +edrn ,:*9mciz bnldul04ao7 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 axis relative to a straight, level nn5wn.)q* *j(ysk ear2dba1 lsma ;+8fyvr(o road and pass a car traveling at 45 mimj.r(e;2nrfa+andn8(a*y*5v)k s 1 l wqso yb/h. The relative velocity of your car to the other car is

  You are trying to cross a river tzq0+) xm5 h d0upmvvy0hat flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west ban00d z+qpm y v5vumh0x)k directly west from your starting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How much time will itk:x e:/mcpb8etzefn, c3 +oqe 75b;v q take you to move 12 km downstream, in a riverbev ceem;/o tp+kf bex 8qcq,35:nz7: flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degree mdvjw(0jzd+( s below the +x axis. The y c(d(djj v+wmz0 omponent of A is

  If a ball is thrown with a velocity of 25 m/s at uiz u5;n.y-cl4 5flqr an angle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in nn.wgy9 thh;4zv(wvns l2kk;1h. 3mva straight line in a direction north of east and you end up 2.0 km north and senw kz9nn3lvw;.(h4hhkys1 ; g .vv 2mtveral kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x compon tux u7k05v8lkent of its velocity is 8.00 m/s. The angle between the direc5k 0l 78uktvxution of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over aq 89r8 ibi9wzq5wx32+ amk4lzg fre7x level ground. At what angle is the Sun elevated azzkxrw298gi4abi rf+ q9 lx7 w5emq 83bove the horizon?

  Two vectors A and B have compone;qqy;car: qz8 /yo;j vbyc2b ,nts (0, 1) and (-1, 3), respectively. What are the componvqc 2;c z ;b8boryaq,y/q;:yjents of the sum of these two vectors?

  Two vectors A and B have components (0, 1) a,)x lgilqy5eje, 5zt/nd (-1, 3), respectively. What is magnitude of the sum of these twozl5q,i,ee) xjg /5ytl vectors?

  Vector A = (1, 3). Vector B = (3, 0). , ldan7q9ap33wv q*.eh vb.ui Vector C = A + B . What is the magnitude of3.b 9ew ad. 7aqvq ,hnipvul*3 C ?

  A car travels 20 km West, thenk6d jc(+ug69w5pwve tf2fs- u 20 km South. What is the magnitude of its displacemenkf+sucg66edt j w9vup2f-(w 5t?

  Three vectors, expresslv, kp2vn6stp,+36cau p3l zhed in Cartesian 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 coordinsq hy vxe+l1(0ates, 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), wha(6w u(lmu + o ugb i:9*a()hylp 1gsru4r(lzynt is the magnitude of vector C = A - B ?*gn(uy1ugab)sr lwl4 :z ( oh (yiu(+96ruplm

  A runner runs halfway around a circular path of radius 10 m.6y9gc bm vc8)pc0,a fp What is the displacement of t9cg60yv8pb mpac)c, fhe jogger?

  Two forces are acting on an obl,v4( .xortq oject as shown in Fig. below. What is the magnitude of the vq o4lt(, xro.resultant force?

  Two forces are acting on an object as shown in Fig. below. What is thbi1-wu tzm lud 4l,,s5e direction of the res s-, w5ubzl,1ml dut4iultant force?

  Vector A is 5.4 cm long and r wn)/jkbn,pkkb 6f5b l41 u+ipoints along the positive x axis. Vector B is 8.0 cm long and point p4,)n nw ibk6fk5/rbj 1lkb+us at $+55^{\circ}$ 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 60 cm long and.o e8ggslr m21t4x.q1z shg2 m)55a xlf)ycxk points at $30^{\circ}$ above the positive x axis. Vector B is 18 cm long
and points along the negative x axis. Vector C is 29 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 initit .)7t8pduv z:civu/)flad-kal speed of 14 m/s from the edge of a cliff. A stop watch measuret)l- uv z:d ivc.f)k7adu8p/ts the stone's trajectory time from the top of the cliff to the bottom to be 3.8 s. What is the height of the cliff?

  A girl throws a rock horizontally, with a i-mhiup,y*0vwc 5rp*u +p2y9 e0icw yvelocity of 12 m/s, from a bridge. It falls *y5vp- pw0iy0c pwu2imy+9h ,re*cui23 m to the water below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 29 m above the grznff1ki/:;8(joek s 3 ur7gkdound, strikes the ground after traveling horizontally k7dz8es/ i1; k3f (f jgkun:roa distance of 12 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jum kf j61kzh.yih m**u2z5mc5 u)7mkenvp with a speed of 12 m/s at an angle of ju2zmkfkn.ck 6ui*m5h e*)y 1hz 57vm$20^{\circ}$ 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 8 m/s at an angj + kzjht6csv+t/;.q nle o./s;cqnt h+ tj+j6v zkf $29^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial veloc; cvblu i(rnoae4+,.qity of 58.4 m/s at an angle of $17.2^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of8l0(5p, h s/jqoa0l li ymbpj. 44.8 m/s at an angle of $39.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angl+o+pp 0 atwiv8 y.y-w: nikla)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 hoxh +.wxgdidu8lu,3ky n .*6qorizontally at 23.8 $m/s$ from the roof of a building 41.5 $m$ 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 with an initial speed of 42.4 6x luu q*x,lfcxh-s5z y.d8u r:l.v 7sm/s at an angle of ,xx-u r8 6l5dhuu.*lys.l fq:zxv7s c$44.7^{\circ}$ 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 d18ogd b6.grl (sn r(rvelocity of 4.0 m/s. If you ran the same race on a day when you had a constant headwind which slows your speed b. db(6r( ng 1osdr8lrgy 2.0 m/s, the time it would take you to finish would be

  A plane has an air speed of wyksmk5oyu) j1* n: ux7 ns 6m5-qyjv(200 m/s due North, and is in a wind of 50.0 m/s to the West.: ouyv sj n( -n7y*k )5mqkwjs5m6uxy1 The plane's speed relative to the ground is

  A plane is flying du ;ssevs9q-t x:e 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 speed of 120 km/h is headed )b3 pgkqb.pyud:--l t$30.0^{\circ}$ 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 fx8cd97 -iw( meu 1w- zfbvrid2ires a projectile with speed 50.0 m/s in a fi 7fbxz2 198d -wm(v e-duicwrorward 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 y77adf ; 3wbzeqygu57 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of tzfewa;b 77uydg7 q3 y5he boat as it crosses the river?

  The driver of a motorboat that can move at 8 m/s in still water wishes rm.ty;s fc4y6bku3pt 0y6h;h to travel directly across a river 0.5 km wide in which hfc64 tum ;p. ksh;rt603ybyy the current flows at 7.5 m/s. How long will it take to cross the river?

  The driver of a motorboat that can move at +rewq/ex6jbq(hir5 s vo/0)a10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. At what angle upstream sh6s5ej+eah qvrqxr/i w/ ob0()ould the driver head the boat?

  A swimmer heading directly across a river 200 m wide reaches the opposite 4 azq-k2f +p3e.t ;8ejkrkh x8shs a;pbank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in stil;84tzkr eh+.;a f- exaps kspj8kq32hl water?

  A swimmer heading directly across a riverlcr(/p4mb y, x 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the currentbp myr4lc,x/( ?

  A boat, whose speed in still water is 1.53 m/s, must aim upstream at an anglen5ei5/dgq 3x/hme7 ss3j buw* of s5/ wjdqbhmxi353e7e/sgn u* $20.1^{\circ}$ (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)  $m/s$