Which one of the following is an example of a vectord6zua m i70a8:)l tgog quantity?

  Which of the following oper3g q4w., 0pj fznb,oibations will not change a vector?

  Which of the followiyts/ p qctewixku9( ,61u (ry7ng is an accurate statement?

  The resultant of two vectors is the smallestc tqx ls7:.:bj)re5ljq sl6 fef3;pqu 1d *p8k when the angle between them is

  Two displacement vectors have magnitudes of 5.0 mco s00w1vq hn(u(9bk w and 7.0 m, respectively. When these two vectors are added, the magnicw1 0(0uh o vqks9(nwbtude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Which one of the followingh-(m.i*5x r3f hy3hjihslno 0 is a possible answer fhi.n 0o*h53h y3jislhxr fm-(or the magnitude of the resultant?

  Three forces, each having a magnitude of 30 No c87k kxpa4rb uefx.33 sk8q8, pull on an object in directions t 7e8ou8.38q bk4k srxaxf3pckhat are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, w0px-pe vb.-*cyyur5y ihk+ 6 the unknown vector is

  Ignoring air resistance, the horizontal compo)ww/rqchal ( 5nent of a projectile's velocity

  A ball is thrown withj,,4gmv(yyu 9(s mwlj a 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 resistanceh 37hzr6mmruh+ex1nh jgx *:m9-kj / n ,slvq9, the horizontal component of a projectile's accelerationh3q :n,zjxr/ v x7e9 h*kh 61gmujhsr9-+nlmm

  A soccer ball is kicked with a velocity of 25 m/s at an angltt3q3ago) n/t odc.q: e 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 objectr, b u efshl/h+28yce8 is directed anti-parallel to the velocite rch+8 /u hfbey28sl,y vector,

  If the acceleration of an object isyb camk4/ em29 always directed perpendicular to its velocity, y/m94kma2bce

  At what angle should a water-gun be aimed in order for the water to land with4i33b;y-;b sdux jhby the u j;sdx4- 3b3b;bihyy greatest horizontal range?

  An Olympic athlete thror.funo-- rgj8tm9 y/ d,blz3tl i 0:ryws a javelin at four different angles above the horizontal, each with the same speedrbng dl8o3j-9-t,y fur l/rmz 0y.:it: $30^{\circ}$, $40^{\circ}$, $60^{\circ}$, 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 hanjbu z)mmz f q1d+)/y.xd with tymz z+dm1 u fj)q).xb/wice the velocity it had on your first throw, its horizontal range R (compared to your first serve) would be

  A ball is thrown at an original speed of 8.0 m/bq m t/86sk-e fr *hjnm19guk: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 maximum height, hoyq6 ke5l jnen;e*r+t /ha*4xwy;lr2gh a; l*aw does its speed compare to its initial sph 6 wxr* e y;ajnk*l/l;+yth2;ega4e*qn lr 5aeed?

  A stone is thrown horizontally from the top of a towe7athemg6 e*wfay5h cia 5) /1ir at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level ground belo c)ai1w iag 65t5 hfa/yhe*em7w?

  A bullet is fired horizontplbdvg1jat e )7 1zh80ally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare thgh0 7teb8)dl11 v azpje times of fall of the two bullets.

  A plane flying horizontally at a speed of 112.2 m/s anmm)0(yhu+b wod at an elevation of 233 m drops a package. 2.5 seconds later it drops a second package. How far apart will bo hy(m 0u+mw)the two packages land on the ground?

  A package of supplies is droppedbtdcei*cz3* 1(4qnviz 7y 2oa from a plane, and one second later a second package is i*a oiv3z*d4 b1z(n27cyqe tcdropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed 0;usoggt kn;*. Neglecting air resistak;0u osn *ggt;nce, when the bomb hits the ground the horizontal location of the plane will

  The acceleration of gravity on the M75w o cv:chafn98jxe8z6o;h uoon is only one-sixth of that on Earth. If you hit a bajchhewu9n 85oxo 86fvzc;7a:seball 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 rej;j )9.bhebf-ecluv+lative to a straight, level road and pass a car fu-bbjj).9ce hve; l+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 with a strong current.; bxqf55q f*ds8es(;hg hc kr1 You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head yg1kfe8 hsqb;cq x5rh*(df5;s our motorboat

  Your motorboat can move at 30 km/h in still water. How much time wit/g 7*l e+ycq,x-mke+d+pi c pll it take you to move c+e-*gd+, xyp/letc+7kp i m q12 km downstream, in a river flowing at 6.0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 dj;; 85tjilddgt5wf 1e egrees below the +x axis. The y componetdtw;e15;i f j5lg8jdnt of A is

  If a ball is thrown wi*ok )fz1gbwe; th 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 straight lipe5kfk:.u/ 6.eyu )o/z hs ,o lw:giolne in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees nz g o ,f)ukhwsy :eo:pl//k56ul.io.eorth of east have you walked?

  A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is2bvy l hvn*p9s+78n uf 8.00 m/s. 7u pyn2v+h9vb*s8 l nf The angle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 600-m long c 4 +2tkj0mkl(fl roe.shadow over a level ground. At what angle is the Sun elevated above the horizol(r+k4l 02jfekt . mcon?

  Two vectors A and B have components (0, 1) and (-1, 3), respectkmdxaq iv 95y 8t8y9 d r-gmy344h5tymively. What are the components of the su4t8m-v9tyah9qi5y4 8yx m mkg ryd d35m of these two vectors?

  Two vectors A and B have components (0, 1) and (:5rl6wijotv9 *j 9 hgx-1, 3), respectively. What is magn56 hgr:oj9xj*vt9wli itude of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is the magni( btcmv-+ k w-jx; mh xjdhnjr;/m6+7jtude h+tnmj-dj;7c xj (/-j +b;k mrv6hwx mof C ?

  A car travels 20 km West,:ms- e,9 knd t6+kj y:kmomkii,hh ,l; then 20 km South. What is the magnitude of its displacemen;6k - hmimky,:skn t :mi k,hl+djo9,et?

  Three vectors, expressed in Cartedh7 -u8l c:6i njqwh*jsian 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, eu51fp :g e8zjare
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 vecto22puo .wi6ec nohc7 3br B = (+3.0, -8.0), what is the magnitude of vector C = A - B ?u 6oicw p 73co.enhb22

  A runner runs halfway around a circular path of radius 10 m. Why vztt )94zr4uat is the displacement of the joggv4 t) yu9rz4zter?

  Two forces are actingf mdse h*um +az,i3x*/+ec7735 )p tqddvykke on an object as shown in Fig. below. What is the magnitude of the resmm3dicf**+e,z ad/+)7v kpk75ehe tuqdxsy3 ultant force?

  Two forces are acting on an laqyu5 m/pb;r k 9;k;; zb:.vvj2abxdobject as shown in Fig. below. What is the direction of the resultant fk;/ maklq;b:xd.95 vv;z;juapbyb2r orce?

  Vector A is 3.5 cm long and pjo9n7owy nh9. oints along the positive x axis. Vector B is 9.9 cm long andow9.yh 7n j9on points at $+29^{\circ}$ 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 87 cm lojt;q1 ltd.;hung and points at $30^{\circ}$ above the positive x axis. Vector B is 28 cm long
and points along the negative x axis. Vector C is 26 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 14 m/s from1eiy k97 a+iubno*kq6: hw9fp the edge of a cliff. A stop watch measures the stone's trajectory time from the top k7 91ypuo+6bn qhw ii*ea:9fk of the cliff to the bottom to be 4.1 s. What is the height of the cliff?

  A girl throws a rock honv-n pz ikqx 32ii0xy3* oo1,g*g it4irizontally, with a velocity of 10 m/s, from a bridge. It falls 13 m to the water below. ik txxo*y -z 230 gini*v3,4qpio1 ngiHow far does the rock travel horizontally before striking the water?

  A ball thrown horizontally fromom14if;k- vol a point 24 m above the ground, strikes the ground after traveling horizontally a distance;v4omi l1of- k of 20 m. With what speed was it thrown?

  A jumper in the long-jump goes into the jump with a speed ofcw)(thxr+-eo 0if1 swtfhu 8- 12 m/s at an angle o8-owt h-ce0 i)h+ wrx(suff1t f $20^{\circ}$ 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 w,r o dt5m.zn8sith a speed of 8 m/s at an angle of rtd s.m85on,z $28^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with an initial velocity of 50.1 m/s at au,y9ty 7t.xc8 ntaau9 n angle of $47.1^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 58.3 m/s at tk) rx v, -67nhe6wuy)bb:vn fan angle of $20.4^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fir p )g7n5ig*jw6b+p(t6l in gaied 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 horizontmmdl2 xc5 6rr,ally at 25.4 $m/s$ from the roof of a building 62.6 $m$ 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 lsnr3zaq2 g;cm ig8e1*evel with an initial speed of 62.2 m/s at an anqg2*;1m 3gaec izn r8sgle of $47.2^{\circ}$ 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 wirgxt(; bge6: 7d9hlqwnd), you can run a 1500-m race at a velocity of 4.0 m/s. If yo6 x ;g7(qlwegbh dr9t:u ran the same race 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 of 200 m/s due North, and is in a wif 8rd bh711qghnd of 50.0 m/s to the West. The plane's speed relative to thedh87fh g1rq1 b ground is

  A plane is flying du5 wr8c0m/czucf/ ,*q7nlt vzme 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/hqp0:d7kwe6fsn q i0z9 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 horv .w,28 cmzxki8ex21 dltuxlmcm.sw**87kw eizontally fires a projectile with speed 50.0 m/s in a fxw.k8m.7dx ecwls1*mw 2kz mi2txl,uv8 ce8* orward 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 stillcpdd- ,*,y/f/ ou7f5blutlha water 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 cr, ylh*b7cfda,u/-plu t5/ fdoosses the river?

  The driver of a motorboat that can move at 9 m/s in still watc99cf s,zpb7 ,zz :zicer wishes to travel directly acroszis,9cb,p zz zcf :c79s a river 0.6 km wide in which the current flows at 3.1 m/s. How long will it take to cross the river?

  The driver of a moto6+oti bx: u+8)e pmlqprboat that can move at 10 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 should the dri 6b:ol+et+ )pxm8upqiver head the boat?

  A swimmer heading directly across a river 200d ((swyeflksln g6n8d, 2q:-g m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still w6gkd,y((:8snfs -nl 2 wg dqelater?

  A swimmer heading directly across a river 200 m wide reaches the opposite zr 9rgg y-f gwc.71b+ns82wdyl 2 7ebabank in 6 min 40 s. She is swept downstream 480 m. Wggb -.w8 1y 27a+wg7sfzce 9r2bydrnlhat is the speed of the current?

  A boat, whose speed in still water is 1.79 m/s,3dq09x; w ifmnbxs h.* must aim upstream at an angle ofnm.;xd sqi3f xbw*h09 $13.9^{\circ}$ (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)  $m/s$