Which one of the following is an example of a vect6/lv4 jxba fl1rmk h(5or quantity?

  Which of the followinjy -j0; w/g,rpy8xsdi g operations will not change a vector?

  Which of the following ilngn/c4l7pbm+ 9 n n-wjvki*be,mo36s an accurate statement?

  The resultant of two d 1- qj;epk65pa2e5 dvd zyxy(vectors is the smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 p9. +o.bazwg9er;veo h yz:sk-bj //am and 7.0 m, respectively. When these two v:wgahb.yso;a/p - ze.z k eb v9/+9ojrectors are added, the magnitude of the sum

  Two vectors, of magni.p ej0d kst()nd px)*btudes 20 and 50, are added. Which one of the following is a possible answer for t skdn *0b)exdt.jp)( phe magnitude of the resultant?

  Three forces, each hal evcv-0;mme4k: 0sqjn / tqv6ving a magnitude of 30 N, pull on an object in directions that aretv:nl 0kqc- 4qmmes; v60/jv e $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, thef.l e)*ng4yylz ;u7 ul unknown vector is

  Ignoring air resistance, the horizontal component of a proje+-a bm-hy )a86yeb r o5hbw2adctile's velocity

  A ball is thrown with a velocity of 20 m/s at)e)om(u b+ noe+ o0ivph9bx(k 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,c v 6mzd6( zv1,e.zsop the horizontal component of a projectile's acceleration6epdc1(z. s, zmvzo6v

  A soccer ball is kicked with a velocity of 25 m/s at an angle of b 7yz.7m,v(u5cioy+ c k *jqyh$45^{\circ}$ 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 direc5 fs6 /yl,is. uqghn4wted anti-parallel to the velocity vect.s 6wsg5yl,/h 4qniufor,

  If the acceleration of an object is always blq xypozea010n ;+e1-m-yx tdirected perpendicular to its velocityxozn-yby qa;1t xp-l1m0e 0e+,

  At what angle should a water-gun be aimed in udbqege y+s56y5g oruf /)j)-saan71order for the water to land with the greatest horizontal rang+dy/s1uas) qrugbo e nj-55ygf) ae67e?

  An Olympic athlete throws a javelin at four sg p-7vpp.1 en4;ds dtdifferent angles above the horizontal, each with the pednp1ss7-;4 .tvpgd 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 th:gg-) nrpdcy8e ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to yc-g)d:yprg 8nour first serve) would be

  A ball is thrown at an original speed of(5gh6 6 9 1wx o+gir /z+pcbhgrbsn1un 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 maxiqoes l w9t55,qmum height, how does its speed compare to its initial sq5o5tqs,l w 9epeed?

  A stone is thrown hori58 cyqaom4y+fzontally from the top of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level qyy4fm+5 a8 ocground below?

  A bullet is fired horizontally, and at the same instant a second bullet is r6ci9pd9a+1h k lp.bu/ df 6fuc,,khg dropped from the same height. Ignore air resistance. Compare the times of fall c9rapick9. f g 1d+pbuu h,66/hdlk,fof the two bullets.

  A plane flying horizontally at a speed of 44.3 m/s and at an elev0c2cd(q0rjlw w 38 kgbation of 297 m drops a package. 7.7 seconds later it drops a second package. How far apart will the two packages land orj c0w 2cw(8k 0l3gdbqn the ground?

  A package of supplies is droppev:n ikm9f-p v5d from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance b-i km 5v:vfp9netween the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a consj*7l3r qg4hv y4ogghl d+ig5 d1 u7y1qtant speed. Neglecting air resistance, when the bomb hits the ground the horizontal locat3d4l jdqgr giuhh+ly74g7* vyg511 o qion of the plane will

  The acceleration of gravity on the Moon is onlyldq. gxs a5(v0e7/zxr one-sixth of that on Earth. If you hit ae./ rsvxgxd 0q5(a z7l 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 axis relative to a straight, level/hp f ju2z92d*jjb f5:8,bmqc1 gfczw road and 8925chf*b/mb2qz wj1 ,jupgfjf czd:pass a car 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 pf dh76+x6(-jsa2kbev 12g 0n+z4xtn jsuyntwith a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your start6g+f2b1vk-ne xj7 tzu4xn sns djh 6ap+(y20ting point. You should head your motorboat

  Your motorboat can move at 30 km/h in still water. How d;izfkm 5ag/dg0 wn; g8nwh ib,xf-1*much time will it take you to move 12 km downstream, in a river flow i1d gh/nw,agf ;5imw-*fzn08b dx;k ging at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis.xn2,xakpi) pxz0l0x2 The y componexx, 2)lpa0 nxx kp0z2int of A is

  If a ball is thrown with a velocity of 25 m/s at an anx (+ iog:0j/ su ojuin4m pd/2*s/vonsgle of $37^{\circ}$ above the horizontal, what is the vertical component of the velocity?

  If you walk 6.0 km in a straight line 0kmcpe :, f0c bis6.qsin a direction north of east and you end up 2.0 km north an .e0i:qc0 m,bc fsp6skd several kilometers east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 m/:a.qgo z t-8jcomq 2*txhm2 ;es. The x component of its velocity is 8.00 m/s. The angle between the direction of imxtzh2o e2-;o :*8mq acqtj .gts motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow over a level grd8: d(zqgi 2hi92iiubound. At what angle is the Sun elevated above the hori( h 9ig228zui dbdiq:izon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectively. What4ud r7vqn2;x m are the components of the sum of these two vectors?74; m du2vnxrq

  Two vectors A and B have comp-8eeu klo/l8 b+0 jkjqonents (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two lu+-kj8 j/ e8qek0lob vectors?

  Vector A = (1, 3). 48zgp;dyx yp, Vector B = (3, 0). Vector C = A + B . What is the magnitudexygpzpd; y8,4 of C ?

  A car travels 20 km West, then 20 km South. What is the magnitude n uyb7kzu*6r0tvu a9/ rd(4zb of its displactu9uav rzdubr(/*y64 k70nbzement?

  Three vectors, express(1h t.dotbcz)4mr r x 63yw:qzed 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(rm 5y:26qy/zgnyo e. uzvvp; in Cartesian 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 ve.y l1 ey 7kfhkd lglt27v44 7cx,-entector B = (+3.0, -8.0), what is the magnitude of vectotk 7 yevlhe y,71l2l -.dg4f47cxnetk r C = A - B ?

  A runner runs halfway around a circula.s ovkm fv*x ri5ot0n74c:m5ar path of radius 10 m. What is the displacement of tintv0 aom:fvc4 s.xk m o7*r55he jogger?

  Two forces are acting on an object as shown in Fig. below. What is the ma a+e8 tk;*d0:plr nqfsgnitude of the nt0+k:sealfqrp* 8; dresultant force?

  Two forces are acting on an object as showmig0yo qy,c06r5a9 ev *(birln in Fig. below. What is the direction of yy6rgi5rv , 9*c oli0amb0(qethe resultant force?

  Vector A is 4.9 cm long and points along the positive x axis. Vect5felc 3u/yx, wxu ld1+or B is 7.0 cm long and points a l3lw fx1ueyx/+cd,u5 t $+55^{\circ}$ 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 74 cm long and poi91* la;yv pne 3-*sr.mfepyo qnts at $30^{\circ}$ above the positive x axis. Vector B is 19 cm long
and points along the negative x axis. Vector C is 27 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 arbx:)t 59 z8ffhtfe 6fn initial speed of 26 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 2.9 s. What is the heightfxeft:hbz)586ff tr 9 of the cliff?

  A girl throws a rock horizontally, wittn,s e3lah6,x h;jze+v q 2nz/h a velocity of 14 m/s, from a bridge. It falls 12 m to the w3ee, n6 zht2;+ a /lsjhvxq,nzater below. How far does the rock travel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, strikes the groun41dadtw*x s+l 8 kp+yed after traveling horizontall+wx+ k8 edpsa t1*l4dyy a distance of 21 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speedl 9 v 8m8xq7)3z)oxcill 0jppp of 12 m/s at an angle 93mlp8pli plz)0 vc7 qjx)xo8of $20^{\circ}$ 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 speedd/fig)6a o6d)y k n4fw+ia*gq 7xpe 7z of 12 m/s at an angle i qk)wfdfpai4*)66x7n7eg z g+a/yodof $21^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity rj zi jxtv tqr *;p 7)p,g+cliz83 j,jw7:ck7dof 26.0 m/s at an angle of $15.7^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velodo f qol6*y ddtv81lk),1w)ejd5 u y0dcity of 31.7 m/s at an angle of $10.7^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fired at an angf8:jkt,k o +ro xv(oe:x) jt+gle 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 ho 9xsqmyrfh/w;+c;0x arizontally at 19.7 $m/s$ from the roof of a building 50.0 $m$ 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 spe20 v-bjz1 jz ;tzdcz7ced of 41.9 m/s at an angle ofv 1-d tz07;zbzjjc2zc $46.8^{\circ}$ 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 cf;vkvuw,/i(2xt ;j8 wti7 amsan run a 1500-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 speedw7tw;jf;tu /xim v, sak8iv2( 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 (ebcj22;qi 5,xfxh v p8 9rgqndue North, and is in a wind of 50.0 m/s to the West. The plane's speedc2,h8vg eqn;x q( fxi 2j59bpr relative to the ground is

  A plane is flying due South (5*wupt z1 +idq:p.af6za:sdq$270^{\circ}$) 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-x e .hb,yau8w 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 horizonth 2d,+icdxm1rv sq29ha) o1waally fires a projectile with speed 50.0 m/s in a forwi ,+1hwdvrxa)mha1dco29 s2qard 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 watetaffj f+ 1nz7w+:8qi or is 8.0 m/s, is directed across a river with a current of 6.0 m/s. What is the speed of the boat as it crosses the rf j1+q 7f w:i+ztfoa8niver?

  The driver of a motorboat thyc n()vz r:t9gat can move at 11 m/s in still water wishes to travel directly across a river 0.9 km wide in which the vgn:r9)z (cyt current flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a motorboav3mss2d 4 vn4at that can move at 10 m/s in still water wishes to travela2dv m3ns44v s directly across a narrow strait in 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 reaches the oob)g wi5 92no)t.yau gpposite bank in 6 min 40 s. She is sweptib 5y2ntg.9ogw) aou) downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a rivwg4hnw1ogo6g w9 . :uyer 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is .gy: w1on 6wwo uhgg94the speed of the current?

  A boat, whose speed in still water is 1.95 k1s 7n ayvga +sw02),q,hhb lx6y3xu pm/s, must aim upstream at an angle ofn,kh76lx3bgyuya1 ,p w+svsqh)0ax 2 $30.2^{\circ}$ (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)  $m/s$