Which one of the following is an examwnv cl r)q t*ds).c/a*ple of a vector quantity?

  Which of the following operations will not c, cbz4o83ihk xhange a vector?

  Which of the following is anm9kdk ,k() hmx accurate statement?

  The resultant of two vectors is the 0oqg 9ca(f; /x ksg)unx iesdj578u4esmallest when the angle between them is

  Two displacement vectors have magnitude(h:dwo:k1ob stfarw3wqei5 n. e: z* +s of 5.0 m and 7.0 m, respectively. When these two vectors areo:e+ 5swwkdr*zehi:o q3n .f tb(1a:w added, the magnitude of the sum

  Two vectors, of magnitudes 20 and 50, are added. Whqr,3pwp8 eoq. ich one of the following is a possire8w.oqq 3p,p ble answer for the magnitude of the resultant?

  Three forces, each having a magnitude of 30 N, ogvwe.-*/ uyypull on an object in directions that ov y/yuw.-*eg are $120^{\circ}$ apart from each other. Make a statement concerning the resultant force.

  In the diagram shown, the unknown vector dhoa(z-ust3vr p7tp zh+2 + e2is

  Ignoring air resistance, the horizontal component of a projez5ose6 r *3:xe:.56g x bnjbmajdse0tctile's velocity

  A ball is thrown with a velocity of 20 m/s ats3 sa .qksel gairlu84r:/0 b* 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 componerzujzk-dgsv54g0i b z,h)trh) +t s13nt of a projectile's accelerationuz sbi)h v 4z03 5rdhrgjk -s,)1gtz+t

  A soccer ball is kicked with a veloc m7 vzfm:;sly, :ayl4nity 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 to thnnd;vm2frj 78a,w4 wie velocity 842 rnn;md vfi a7ww,jvector,

  If the acceleration of an object ic30kq1t ch 2mgs always directed perpendicular to its velocitc13c0h 2g mtkqy,

  At what angle should a water-g( vc6w-s 0ovrpun be aimed in order for the water to land with the greatest horizontal 6vs0p crw (-ovrange?

  An Olympic athlete throws a javelin at four diffmnc8g- vu;)ijd;* bndtzt,5werent angles above the horizontal, each with the same5*,- tumd)vjdcbi; wztn;8n g 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 tqamn( +5nhrl* he second time. If the ball leaves your hand with twice the velocity it had on your first throw, its horizontal range R (compared to your first serve)lr+ah nnq(m5* would be

  A ball is thrown at an original speed of 8.0 m/s.cllmdmw fpd/ 4euq9o: n51q6 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 reache7pwb 47g;rk fqs its maximum height, how does its speed kp77f rb;q w4gcompare to its initial speed?

  A stone is thrown horizontally from the t yd *( fl6n3lrmgfs)v/mi w8. w6s:hrqop of a tower at the same instant a ball is dropped vertically. Which object is traveling faster when it hits the level gss vl3.m 6f) nlrm6(g/d yfwi8r*h:qwround below?

  A bullet is fired horizontally, and at the same instant a secpe oxg7(oixs f 2pgsb*27:x9pond bullet is dropped fbg e2g*o:7p xp2 s 7oxsi(p9xfrom the same height. Ignore air resistance. Compare the times of fall of the two bullets.

  A plane flying horizontally at a speed of 105.0 m/s and at an elevation o 0.hisseyw)p 8scv3 l-f 232 m drops a package. 2.6 seconds later it drops a second packagewesi y.-hp03l)s8cv s. How far apart will the two packages land on the ground?

  A package of supplies is dropped from a po, vozqf6pqh7a 2r p)p pr 6qo 9po.l:p.xd:+qlane, and one second later a second packag q9p+ppp6pfz,.lord qa2h: r xopq7)q:.o6ove is dropped. Neglecting air resistance, the distance between the falling packages will

  A pilot drops a bomb from a plane flying horizontally at a constant speed. phz(6(:0n +fsem dr; p;gxd eu Neglecting air resistance, when the bomb hits th nu ;me+gpdhdx6f( 0;(rpezs:e ground the horizontal location of the plane will

  The acceleration of gravity on ( ,ug)o-gfbih the Moon is only one-sixth of that on Earth. If you hit a baseball on the Moon with the same effort (and at the speed and angle) that you would on Earth,igo -b hg,u(f) the ball would land

  You are traveling at 55 mi/h in the +x axis relative to a straight, le8 )si2wtm af7qvel road and pass a car traveling at 45 mi/h. The relative viw ts2fam)78qelocity of your car to the other car is

  You are trying to cross a r*gonllt q*lc3 1ny9 /miver that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting pointntnlq1cog3ml y**9/l. You should head your motorboat

  Your motorboat can move +xvw qj6swzmhu;;: 4yhbt7:tat 30 km/h in still water. How much time will it take you to move 12 km downstream, in a river flowing at 6.wvhbh; w;stz+mtx:j7u q:4y6 0 km/h?

  Vector A has magnitude 8.0 m at an angle of 30 degrees below the +x axis.62k i tjbbx*3kmkdiim8s7 l13 The y c ki kxm8ms3 ti3j62i7k*lb bd1omponent of A is

  If a ball is thrown with a velocity of 22 ejkzvpq4o.7 5 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 line in a direction north of ea pci*wuj:imoe+m4 44est and you end up 2.0 km north and several kilometers east. How many degrees north of east have u* 4o eeiic:4wm4p j+myou walked?

  A butterfly moves witj 5hpn u9is2*a 4gv4hhh a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The ansu25*a4 9n p hvjih4ghgle between the direction of its motion and the x axis must be

  A 400-m tall tower casts a 6u .*iuctahr* a.7 8vol00-m long shadow over a level ground. At what angle is the Sun elevated above the horizon? 8i ochut*.a.lra*uv7

  Two vectors A and B have components (0, 1) and *q1a:cdv2 n,1tq wl+n :m jvrp(-1, 3), respectively. What are the mn1jrl::tv dap1c,wqn+2qv *components of the sum of these two vectors?

  Two vectors A and B have components (0, 1.iqh6ivmi/;e ) and (-1, 3), respectively. What is magnitud ie h/m6vq;.iie of the sum of these two vectors?

  Vector A = (1, 3). Vector B = (3, 0). Vector C = A + B . What is a59yts. ,z5zxxl 2nsmthe magnitude o txm55sz ly.9axn ,s2zf C ?

  A car travels 20 km West, then 20 km South. W qi-if 3vcmw*+ )q*r) t7oegqjhat is the magnitude of its displacementgjq-3t mriq7 fe))i*cw o+*qv?

  Three vectors, exprergus qd( pa+c,zuo8:8l/ifhux, vh ldo9:, a 7ssed 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 Cartesiaykqpk uzw;:8(w+d /hin 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 t-j -wz; ow6o ,yjtrc5:v hjh nph.+2 nvtj*h0the magnitude of vector + o0 - * hv:tjct5;phwv nz.thywjnjh-jr6,o2 C = A - B ?

  A runner runs halfway around a circular path of radius 10 m. What qeuj .n9yj,g/is the displacement of the j,n9je /j.y uqgogger?

  Two forces are acting on an object as shown in Fig xdloay48,4rg . below. What is the magnitude of the resultant fo 44ryoa, x8dglrce?

  Two forces are acting on an object as shownoa.k 5(9(dx-h +p lhzx8ze iye in Fig. below. What is the direction of the resultanzkh(5ox 9+i h.eyxzpda8e l-(t force?

  Vector A is 5.9 cm long and points along the positive x axis.;b/ zmn61rb5 uw;cly*p q ;zsl Vector B is 5.8 cm long and bw;lz;1;y5bs/um *pn lcz6 qr points at $+35^{\circ}$ 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 51 cm long and points vsvafavsnr e z;6) *85at $30^{\circ}$ above the positive x axis. Vector B is 16 cm long
and points along the negative x axis. Vector C is 30 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 horizont j tuoo1* .nffze13u8wally with an initial speed of 10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of 8tnouuo 1wz3jf.ef *1the cliff to the bottom to be 4.9 s. What is the height of the cliff?

  A girl throws a rock horizontally, witsd2zgbp q6, d/r4/qsrario9 ( h a velocity of 18 m/s, from a bridge. It falls 26 m to the water below. How far does the rock travel ds qo iq9a,/zgspr 42rr/6(dbhorizontally before striking the water?

  A ball thrown horizontally from a pointq:5uv.vv60vus jd3b;ihh g i) 27 m above the ground, strikes the ground after traveling horizontally a distance of 19 m. With what speed vuv 3i) uq5;:hdv vsi60j.bhgwas it thrown?

  A jumper in the long-jump goes into the jump with a5erx r:h,o -z)r8; x fvllz5ml speed of 12 m/s at an angle ore 5h zrv5,lx8l xofm- :lrz);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 inte msv l+r1ay)av ,y)b4o the jump with a speed of 10 m/s at an angle o a1r,)e yb4mavsl+v) yf $26^{\circ}$ above the horizontal. How far does the jumper jump?

  A projectile is launched with7ob2(r fl0wjk an initial velocity of 36.2 m/s at an angle of $31.8^{\circ}$ above the horizontal. How far does it travel?

  A projectile is launched with an initial velocity of 31.3 m/s at an angle ot so2oj*8.pxn y g cxeag1dlsg):v 8w12m*+uu f $15.6^{\circ}$ above the horizontal. What is the maximum height reached by the projectile?

  A rifle bullet is fi;h rc:t bqm(c*red 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 horizontalvr+ a4imhq,v e0:aeq9 ly at 20.4 $m/s$ from the roof of a building 61.5 $m$ 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 5ynk6p6p yiv( zpsnx -j+x4)*p0.9 m/s at an angls )-*yz jpp6v+n ixxp 4pk6ny(e of $43.3^{\circ}$ 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 r n(,zrebk2q2 kun 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 speed by 2.0 m/s, the time it would take you to finish wouq2r, 2n(e bkzkld be

  A plane has an air speeq+mb; bc jfnfeb07 5xmf ,f4o/d of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground bf0f+fm c;e7n qx bf5jbom/,4 is

  A plane is flying duec vtmg8gp0 ;mo(igx79 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 ofg/ dtr8xg v:7z 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 movingn4p z5m).y m(mfoiky * 200 m/s horizontally fires a projectile with speed 50.0 m/s in a5myk zpni of.)y(m*m4 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 stil++o qy /d/k useqhw91ul 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 crosses t9wud1o/kqe uqyh/+s + he river?

  The driver of a motorboat that can move at 10 m/s in still water wishes to tix ahmtmpqi/ 3 x og9:0fhc99i.i+0kpravel directly across a river 1.5 km wide in which the current flows at 3.3 m/s. How long will it take to cross the r99 ipq pkht9ahx0m .:g3ic ix0+/ifo miver?

  The driver of a motorboat that can move at j f60g9cpu3crgnk./sh ns 9f -10 m/s in still water wishes to travel directly across a narrow strait in . ug06fpss n39cjr/hfn9 c g-kwhich 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 ,r z*5;d6k)sgjkzvyf reaches the opposite bank in 6 min 40 s. She is swept down5kr j zzfkd; sv,6y*g)stream 480 m. How fast can she swim in still water?

  A swimmer heading directly across a river 200 m wide reac-s7ldb nxu ;y/a;qa 0rhes the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the ; qbyxnsdul-a r; 70a/current?

  A boat, whose speed in still water is 1.52 m/s, z8ci(g6 izpij,3s c 5cmust aim upstream at an angle of ii(psz3c,z g8 65cci j$22.4^{\circ}$ (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)  $m/s$