Which one of the following is an example of y.q cl*,e0j+c8zgv g ta vector quantity?

  Which of the following operations w m8nfr.;b)yqx ill not change a vector?

  Which of the following is an accurate statement?t q7+vgx (n* jyq/l-ttbxl e)3

  The resultant of two vectors is +mmv afcg0 5d*fg .+px9ont6ethe smallest when the angle between them is

  Two displacement vectors have magnitudes of 5.0 m and 7ngvv -q0f/a 8g.0 m, respectively. When these two vectors are added, the magnitude of the sun/0 -gfa v8vqgm

  Two vectors, of magnitudes 20 and 50, are added. Which one of the follow96tzxfqdqq nf(;9)l n3mheu 2ing is a possible answer for the magnit ndq3 2fq ( etnhmu6xf;9)z9qlude of the resultant?

  Three forces, each havqb7bn c2*; nrbing a magnitude of 30 N, pull on an object in directions th c2b*nnrbq;7 bat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vecto vc:tu wb+x(wz+l(v -fg)gy -mr is

  Ignoring air resistance, the horizontal component of a projec da5:kb 66 wb8 btpo eruxsabk+;,8pr)tile's velocity

  A ball is thrown with a velocity of 20 om z7ue(1u -mdm/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 3xrz0oirs :x*projectile's acceleration*30rosi:z x rx

  A soccer ball is kicked with a velocity of 25 m/s at an angle oa 9si(s2xjlx 7f $45^{\circ}$ above the horizontal. What is the vertical component of its acceleration as it travels along its trajectory?

  If the acceleration jc.i/zyxg 5h+/6rr f.+ f nmwpvector of an object is directed anti-parallel to the velocity vecf/6+pxz +/j.y wfcirhr nmg .5tor,

  If the acceleration of anry yf49yoq-.a object is always directed perpendicular to its velocity f-q9o4a yy.ry,

  At what angle should a water-gun be aimed in order for the wat9ys6eq 2uk9s 4v8f5m1 xnoawger to land with the greatest horizontak2f4w96sq1ney9 v8sgum o 5 xal range?

  An Olympic athlete throws a javelin at four dor s9n 2al9//issfk+mifferent angles above the horizontal, each with the same speedsso9k +lmfs//29 rina: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$. Which two throws cause the traveling to land the same distance away?

  You are throwing a ball for the secongisb p +9y)yjpi )3aki hw:w7*d time. If the ball leaves your hand with twice the velocy+g9 i)j7iwwpay3h:b s kip)*ity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an orig y)2:xrhmzryh1xx 71rinal 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 -;nmhfea pkrcs6+ / *afield goal attempt reaches its maximum height, how does its speed compare to r;+h6 fck/n ama-ep*sits initial speed?

  A stone is thrown horizontally from the top of a tower at the same 4erf:*ix iro .instant a ball is dropped vertically. Which object is traveling faster when it hits the level grounex :*frii 4.rod below?

  A bullet is fired horizontally, and at the same instant a second bullet is qe6o z ql4c (/o.0iodic(uex 55s3pe sdropped from the same height. Ignore air resistance. Compare ueqd(ciooo pqx/ce5 0s34(5l zs ie6. the times of fall of the two bullets.

  A plane flying horizontally at a speed of 92.2 m/s and at an elevationrsk(3tk ,zhp , of 255 m drops a package. 4.7 seconds later it h p3s ,,r(zktkdrops 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 ld ks.1u1bladtucra +c c*461n ater a second package is dropped. Neglecting air resistance, the distance between the fa.+sc1rnd6 acd b1ut* kca4l1ulling packages will

  A pilot drops a bomb from a plane flying horizontally at a cons8kl .jcasc-vk 1 dbjm8z009*yur-k c etant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane rsca0d k yc.vzb*8cjul1e0 k --89mjkwill

  The acceleration of z0 nx 6 .5uyig)podw(n6uxip; m0vp/m gravity on the Moon is only one-sixth of that on Earth. If you hit a basey0pu6zw(gp6duio ivx0/x);m 5npn. mball 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 5 wmb-s.bhls6-ja u /nthe +x axis relative to a straight, level road and pass a car b/65su- hmwa. blj-ns traveling at 45 mi/h. The relative velocity of your car to the other car is

  You are trying to cross a river that flow/7(dbd,kg dlb l*(kt ohu(ms7inqn6 a2 z3te(s due south with a strong current. You start out in your motorboat on the east bank desiring to reach the westlqn76k bdt2*3n7u s amh(eg(l (,bod ikt/zd ( bank 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 w;vjydwh 29uec (t5 . 4yo+wjtp3iy1axill it take you to move 12 km downstream, in a river flowing at 6.0 km4c;hxt.5pyuyyj1dw tive2a+9 j(3o w /h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axihs)7d-zx + sea 5py*8 ko7+kt8oou ycas. The y compon 7opk7ko-xsyd a8o +8e5uyt a+cs)*zhent of A is

  If a ball is thrown w8iisg d 0u*mz)n*h)v qi w+s4lith 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 strjq b;ewp9o7 1rogv*(daight line in a direction north of east and you end up 2.0 km north and several kilometers ;(rp7odo *1wjqg 9ebv east. How many degrees north of east have you walked?

  A butterfly moves with a speed of 12.0 mm2qu,qsf( 4 ch vf3:ip/s. The x component of its velocity is 8.00 m/s. The angle betwe42 , q( qp3csvmffihu:en the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long shadow ovb2se, sypp, cx7xc j8k7s4:ggo 5qs0mer a level ground. At what angle is the Sun elevated above the horizon,k cp57scy 0s2:s7egjbgx 4,x mqso8p?

  Two vectors A and B have components (0, 1) and (-1, 3), respecf d+m :ae0fw6ztively. What are the components of the sum of these two:f 0fzewa6d m+ vectors?

  Two vectors A and B have components (0, 1) and (-1, 3), respectiv5 z /mc4q9f e/qfon hp76)1 nhelmjb7tely. What is )6eq 7 b7q/ /m hft no9cj4lh15znfepmmagnitude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector . k ici0gip/0bC = A + B . What is the magnitude of C k 0 0i/ibgpi.c?

  A car travels 20 km West, then 20 km South. What is the magnitude i(l )xea2v/gbe- e /qiof its displaq eg v)-ii/x2 l(aebe/cement?

  Three vectors, expressed in Cartesian cx-;g 4ipvh5e +w,guc )rk/lh yoordinates, 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, expresm j*p30gi wa3xsed 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 vector B = (+3.0, -8.0), what is tt5h( kqpl1rkhdg4o +3he magnitude of vector C = A - + 31kh rk(thlp5qdog4 B ?

  A runner runs halfway arouu b*wa e6e -7.rkmzg9and a circular path of radius 10 m. What is the displacement *azm wb-ae.u 6r g9k7eof the jogger?

  Two forces are acting on an object as shown in Fig. below. W6;t v7g 4jew.eam9 nqfc1,vfb hat is the magnitude of the resbgc7e4,j f.9t mqf;6vnwae1 vultant force?

  Two forces are acting on an object as shown in Fig. b idt /mgr2(*lcelow. What is the direction of the resultant *m l2gr(/itdc force?

  Vector A is 3.1 cm long and points along the positive x axis. Vector B is 8.1aj/xjr1z 8 5fdxy0yz3 cm long ar03zyxa1d8z5xy /jf j nd points at $+33^{\circ}$ 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 78 cm long and points c+j2t(g 7ksbdptup;py4 ; ag8 at $30^{\circ}$ above the positive x axis. Vector B is 20 cm long
and points along the negative x axis. Vector C is 49 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 initial speed of 22 m/s from the0t ps,yaf s2f:+l c.im edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cy2 pic.m asffls+: t0,liff to the bottom to be 3.2 s. What is the height of the cliff?

  A girl throws a rock horizontally, with-:eso5lz uqt.s2ubb ob)(.fu a velocity of 11 m/s, from a bridge. It falls 17 m to the water below. How far does the rock tq b slb.f:-oes2u(.5oz u )tubravel horizontally before striking the water?

  A ball thrown horizontally from a point 22 m above the ground, stdqe p*idc++ (;ptm9cxrikes the ground after traveling horizontally a distance of 16 m. (t+d+m;c dqp9xi*p ec 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(k2n3/a1ddb frq .ake angle deq(.k1band r2ak /3 fof $20^{\circ}$ 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 12 m/s at g/q6 g alabf )yoe7/.qan angle a )bo qg7ge/ ayl.q6f/of $26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 35.7 m/s at au8;v ti imc9i72ln)9zl e7niyqiji-6 n angle of $42.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial vebd;t71yweset lb 0u 96locity of 50.1 m/s at an angle of $49.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is firx/-h8 xiouvsv/m injc ;6y 7/xed 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 horizont zs vwk-y2k)4yally at 18.1 $m/s$ from the roof of a building 39.9 $m$ 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 frohgdam ./ydkf ;nnl,*. *kdl4fm ground level with an initial speed of 41.1 m/s at an an* a dhkm.gfy;d k.ln*n,d /fl4gle of $41.0^{\circ}$ 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 cal,*dj* utinn, 0wl,f fj8qku4 n 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 nl,8ufkd*,*w luijj0,nf 4 tqheadwind which slows your speed by 2.0 m/s, the time it would take you to finish would be

  A plane has an air spee sxwx kx41yizdc8 c/nr2h4, l233fmhfd of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relahf4 ,c8rd1fk/h 3xcz wx4xil 2mns 23ytive to the ground is

  A plane is flying due Soe4(yw ir c(;s6jxdvy,uth ($270^{\circ}$) 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 1k -3a59b- 9fpsvbvi nw20 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 horizontallylx/sc6 /pli m2 fires a projectile with speed 50.0 m/s in a fo//xpsmlc26 ilrward 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 watenr2gi(dg k05c r is 8.0 m/s, is directed across a river with a current of 6rnc 2 g(05ikdg.0 m/s. What is the speed of the boat as it crosses the river?

  The driver of a motorboat that can move at 17 m/s in still water wishht 7p , lkwv(-acl/+b0whe6 hmes to travel directly ae,plhk cv(60 h twlawh7+/m-bcross a river 0.7 km wide in which the current flows at 7.0 m/s. How long will it take to cross the river?

  The driver of a motorboat that can m+; nr*ym9 zvbzove at 10 m/s in still water wishes to travel directly across a narrow strait in which;m zvn*zr9+yb 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 opposit;undmu fh8/i 4q)d kv7e bank in 6 mnuq;8hikd 74m)d v/ fuin 40 s. She is swept downstream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reaches p /n0ru t+ads1 k1 jz9eqsj*,ihgd-z9the opposite bank in 6 min 40 s. She is swept downstream 480 m. -09qeas +itj * g/,uds1h dp1r9zjnkz What is the speed of the current?

  A boat, whose speed in stilur ja13n9kjugi/ 8:v ol water is 0.83 m/s, must aim upstream at an angle of8uian 1o r3jv :kgu/9j $27.5^{\circ}$ (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)  $m/s$